Journal articles: 'Chance Constraint Optimization'

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Doerr, Benjamin, Carola Doerr, Aneta Neumann, Frank Neumann, and Andrew Sutton. "Optimization of Chance-Constrained Submodular Functions." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 02 (April 3, 2020): 1460–67. http://dx.doi.org/10.1609/aaai.v34i02.5504.

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Submodular optimization plays a key role in many real-world problems. In many real-world scenarios, it is also necessary to handle uncertainty, and potentially disruptive events that violate constraints in stochastic settings need to be avoided. In this paper, we investigate submodular optimization problems with chance constraints. We provide a first analysis on the approximation behavior of popular greedy algorithms for submodular problems with chance constraints. Our results show that these algorithms are highly effective when using surrogate functions that estimate constraint violations based on Chernoff bounds. Furthermore, we investigate the behavior of the algorithms on popular social network problems and show that high quality solutions can still be obtained even if there are strong restrictions imposed by the chance constraint.

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Atta Mills, Yu, and Zeng. "Satisfying Bank Capital Requirements: A Robustness Approach in a Modified Roy Safety-First Framework." Mathematics 7, no. 7 (July 1, 2019): 593. http://dx.doi.org/10.3390/math7070593.

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This study considers an asset-liability optimization model based on constraint robustnesswith the chance constraint of capital to risk assets ratio in a safety-first framework under the conditionthat only moment information is known. This paper aims to extend the proposed single-objectivecapital to risk assets ratio chance constrained optimization model in the literature by considering themulti-objective constraint robustness approach in a modified safety-first framework. To solve theoptimization model, we develop a deterministic convex counterpart of the capital to risk assets ratiorobust probability constraint. In a consolidated risk measure of variance and safety-first framework,the proposed distributionally-robust capital to risk asset ratio chance-constrained optimization modelguarantees banks will meet the capital requirements of Basel III with a likelihood of 95% irrespectiveof changes in the future market value of assets. Even under the worst-case scenario, i.e., when loansdefault, our proposed capital to risk asset ratio chance-constrained optimization model meets theminimum total requirements of Basel III. The practical implications of the findings of this study arethat the model, when applied, will provide safety against extreme losses while maximizing returnsand minimizing risk, which is prudent in this post-financial crisis regime.

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Häussling Löwgren, Bartolomeus, Joris Weigert, Erik Esche, and Jens-Uwe Repke. "Uncertainty Analysis for Data-Driven Chance-Constrained Optimization." Sustainability 12, no. 6 (March 20, 2020): 2450. http://dx.doi.org/10.3390/su12062450.

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In this contribution our developed framework for data-driven chance-constrained optimization is extended with an uncertainty analysis module. The module quantifies uncertainty in output variables of rigorous simulations. It chooses the most accurate parametric continuous probability distribution model, minimizing deviation between model and data. A constraint is added to favour less complex models with a minimal required quality regarding the fit. The bases of the module are over 100 probability distribution models provided in the Scipy package in Python, a rigorous case-study is conducted selecting the four most relevant models for the application at hand. The applicability and precision of the uncertainty analyser module is investigated for an impact factor calculation in life cycle impact assessment to quantify the uncertainty in the results. Furthermore, the extended framework is verified with data from a first principle process model of a chloralkali plant, demonstrating the increased precision of the uncertainty description of the output variables, resulting in 25% increase in accuracy in the chance-constraint calculation.

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Li, Hang, Zhe Zhang, Xianggen Yin, and Buhan Zhang. "Preventive Security-Constrained Optimal Power Flow with Probabilistic Guarantees." Energies 13, no. 9 (May 8, 2020): 2344. http://dx.doi.org/10.3390/en13092344.

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The traditional security-constrained optimal power flow (SCOPF) model under the classical N-1 criterion is implemented in the power industry to ensure the secure operation of a power system. However, with increasing uncertainties from renewable energy sources (RES) and loads, the existing SCOPF model has difficulty meeting the practical requirements of the industry. This paper proposed a novel chance-constrained preventive SCOPF model that considers the uncertainty of power injections, including RES and load, and contingency probability. The chance constraint is used to constrain the overall line flow within the limits with high probabilistic guarantees and to significantly reduce the constraint scales. The cumulant and Johnson systems were combined to accurately approximate the cumulative distribution functions, which is important in solving chance-constrained optimization problems. The simulation results show that the model proposed in this paper can achieve better performance than traditional SCOPF.

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Wu, Xinyu, Xilong Cheng, Meng Zhao, Chuntian Cheng, and Qilin Ying. "Multi-Level Dependent-Chance Model for Hydropower Reservoir Operations." Energies 15, no. 13 (July 4, 2022): 4899. http://dx.doi.org/10.3390/en15134899.

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Some hydropower reservoirs are operated under different constraint levels. For these reservoirs, a multi-level (ML) dependent-chance (DC) model is established. In the model, only when the higher-level constraints are satisfied are the lower-level constraints or system benefits considered. The multi-level dependent-chance (MLDC) model is specified by two models. One is based on existing reliability-constrained (RC) dynamic programming (DP), in which the soft constraints are addressed using reliability constraints of 1, and the priorities are reflected using the order of magnitudes of Lagrange multipliers. The other is the explicit dependent-chance reasoning in the DP recursive function, in which each soft constraint is represented as an objective function of negative expected failure time and the optimum is the solution with a larger value for all higher-level objective functions. The proposed models are applied to derive long-term operation rules for the hydropower system on the middle-lower Lancang River. The results show the feasibility and performances of the explicit graded constraint control of the proposed model and the solution methods.

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Alshammari, G. A., F. A. Alshammari, T. Guesmi, B. M. Alshammari, A. S. Alshammari, and N. A. Alshammari. "A New Particle Swarm Optimization Based Strategy for the Economic Emission Dispatch Problem Including Wind Energy Sources." Engineering, Technology & Applied Science Research 11, no. 5 (October 12, 2021): 7585–90. http://dx.doi.org/10.48084/etasr.4279.

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Power dispatch has become an important issue due to the high integration of Wind Power (WP) in power grids. Within this context, this paper presents a new Particle Swarm Optimization (PSO) based strategy for solving the stochastic Economic Emission Dispatch Problem (EEDP). This problem was solved considering several constraints such as power balance, generation limits, and Valve Point Loading Effects (VPLEs). The power balance constraint is described by a chance constraint to consider the impact of WP intermittency on the EEDP solution. In this study, the chance constraint represents the tolerance that the power balance constraint cannot meet. The suggested framework was successfully evaluated on a ten-unit system. The problem was solved for various threshold tolerances to study further the impact of WP penetration.

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Ma, Litao, Jiqiang Chen, Sitian Qin, Lina Zhang, and Feng Zhang. "An Efficient Neurodynamic Approach to Fuzzy Chance-constrained Programming." International Journal on Artificial Intelligence Tools 30, no. 01 (January 29, 2021): 2140001. http://dx.doi.org/10.1142/s0218213021400017.

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In both practical applications and theoretical analysis, there are many fuzzy chance-constrained optimization problems. Currently, there is short of real-time algorithms for solving such problems. Therefore, in this paper, a continuous-time neurodynamic approach is proposed for solving a class of fuzzy chance-constrained optimization problems. Firstly, an equivalent deterministic problem with inequality constraint is discussed, and then a continuous-time neurodynamic approach is proposed. Secondly, a sufficient and necessary optimality condition of the considered optimization problem is obtained. Thirdly, the boundedness, global existence and Lyapunov stability of the state solution to the proposed approach are proved. Moreover, the convergence to the optimal solution of considered problem is studied. Finally, several experiments are provided to show the performance of proposed approach.

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Liu, Zhixin, Panpan Wang, Yuanqing Xia, Hongjiu Yang, and Xinping Guan. "Chance-constraint optimization of power control in cognitive radio networks." Peer-to-Peer Networking and Applications 9, no. 1 (December 18, 2014): 245–53. http://dx.doi.org/10.1007/s12083-014-0325-8.

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Wei, Dongyuan, Yue Wang, Xinchao Li, and Shan Lu. "A Closed-Loop Assembly Network Optimization Based on Chance Constraint with Robust Approximation." Journal of Physics: Conference Series 2203, no. 1 (February 1, 2022): 012060. http://dx.doi.org/10.1088/1742-6596/2203/1/012060.

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Abstract In this paper, an optimization algorithm of forward-reverse cyclic assembly network under uncertainty is studied. A chance constrained algorithm based on robust approximation is adopted, in which the size of uncertain set is used to describe the violation probability of constraint. Further, some parameters are set to describe the confidence probability of the model. By implementing the proposed algorithm, we can reduce the manufacturing cost of the final forward-reverse cycle assembly network by 3.17% while ensuring a certain confidence probability, and relax the lower bound of the probability of the model, which makes the model more adaptable. By calculating the scheduling data and comparing with flexible robust optimization, the effectiveness of the algorithm is proved.

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Kong, Xiangyu, Siqiong Zhang, Bowei Sun, Qun Yang, Shupeng Li, and Shijian Zhu. "Research on Home Energy Management Method for Demand Response Based on Chance-Constrained Programming." Energies 13, no. 11 (June 1, 2020): 2790. http://dx.doi.org/10.3390/en13112790.

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With the development of smart devices and information technology, it is possible for users to optimize their usage of electrical equipment through the home energy management system (HEMS). To solve the problems of daily optimal scheduling and emergency demand response (DR) in an uncertain environment, this paper provides an opportunity constraint programming model for the random variables contained in the constraint conditions. Considering the probability distribution of the random variables, a home energy management method for DR based on chance-constrained programming is proposed. Different confidence levels are set to reflect the influence mechanism of random variables on constraint conditions. An improved particle swarm optimization algorithm is used to solve the problem. Finally, the demand response characteristics in daily and emergency situations are analyzed by simulation examples, and the effectiveness of the method is verified.

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Li, Shu Rong, Feng Wang, and Xiao Yu He. "An Input-Output Optimal Control Model under Uncertain Influence and its Solution." Advanced Materials Research 433-440 (January 2012): 2974–79. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.2974.

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An input-output optimal control model is established under uncertain influence in environment. The objective function, terminal constraint of state variables and bound constraints of control variables are considered with fuzziness. The direct consumption coefficient matrix and investment coefficient matrix are regarded as stochastic variables. Membership function and chance constrained programming are applied to convert the uncertain model to a definite one. Penalty function and Particle Swarm Optimization are used to solve the model. The calculation results of an example demonstrate that the uncertain model has more practical value to decision makers compared to a definite one.

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Rodrigues Quemel e Assis Santana, Pedro, and Brian Williams. "Chance-Constrained Consistency for Probabilistic Temporal Plan Networks." Proceedings of the International Conference on Automated Planning and Scheduling 24 (May 11, 2014): 271–79. http://dx.doi.org/10.1609/icaps.v24i1.13651.

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Unmanned deep-sea and planetary vehicles operate in highly uncertain environments. Autonomous agents often are not adopted in these domains due to the risk of mission failure, and loss of vehicles. Prior work on contingent plan execution addresses this issue by placing bounds on uncertain variables and by providing consistency guarantees for a `worst-case' analysis, which tends to be too conservative for real-world applications. In this work, we unify features from trajectory optimization through risk-sensitive execution methods and high-level, contingent plan execution in order to extend existing guarantees of consistency for conditional plans to a chance-constrained setting. The result is a set of efficient algorithms for computing plan execution policies with explicit bounds on the risk of failure. To accomplish this, we introduce Probabilistic Temporal Plan Network (pTPN), which improve previous formulations, by incorporating probabilistic uncertainty and chance-constraints into the plan representation. We then introduce a novel method to the chance-constrained strong consistency problem, by leveraging a conflict-directed approach that searches for an execution policy that maximizes reward while meeting the risk constraint. Experimental results indicate that our approach for computing strongly consistent policies has an average scalability gain of about one order of magnitude, when compared to current methods based on chronological search.

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Rong, Xiao-Xia, Yi Lu, Rui-Rui Yin, and Jiang-Hua Zhang. "A Robust Optimization Approach to Emergency Vehicle Scheduling." Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/848312.

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The emergency vehicle scheduling problem is studied under the objective function to minimize the total transportation time with uncertain road travel time. Firstly, we build a stochastic programming model considering the constrained chance. Then, we analyze the model based on robust optimization method and get its equivalent set of uncertainty constraint, which has good mathematical properties with consideration of the robustness of solutions. Finally, we implement a numerical example to compare the results of robust optimization method and that of the particle swarm optimization algorithm. The case study shows that the proposed method achieves better performance on computational complexity and stability.

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OU, Mingyong, Zhenyu WU, Haifeng YU, Xing JIANG, Yinyi LI, and Wenlin LU. "The scheme of wind-storage combined system capacity configuration based on random fuzzy chance constrained bi-level programming." MATEC Web of Conferences 232 (2018): 04060. http://dx.doi.org/10.1051/matecconf/201823204060.

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A random fuzzy chance constrained bilevel programming scheme for distributed wind-storage combined system is proposed. The random fuzzy simulation is used to describe the uncertainty of distributed wind power output. The reliability of randomness and ambiguity is taken as the index to evaluate the capacity allocation scheme of the distributed wind-storage combined system. Considering system power balance, opportunity measurement constraint of static security index and active management (AM) measures, the random fuzzy expectation value of maximum annual profit is set as the upper optimization goal, and the minimum random fuzzy expectation value of the distributed wind power active reduction is set as the lower optimization target. The scheme is constructed by judging whether the static security index of the upper goal satisfies the confidence level of the random fuzzy chance constraint and the coordination of the upper and lower goals. Finally, the random fuzzy simulation, the forward pushback power flow calculation and the genetic algorithm (GA) are applied to solve the model. The simulation result of IEEE 14-bus example shows the effectiveness and superiority of the model and scheme.

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Bevers, Michael. "A chance constraint estimation approach to optimizing resource management under uncertainty." Canadian Journal of Forest Research 37, no. 11 (November 2007): 2270–80. http://dx.doi.org/10.1139/x07-076.

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Chance-constrained optimization is an important method for managing risk arising from random variations in natural resource systems, but the probabilistic formulations often pose mathematical programming problems that cannot be solved with exact methods. A heuristic estimation method for these problems is presented that combines a formulation for order statistic observations with the sample average approximation method as a substitute for chance constraints. The estimation method was tested on two problems, a small fire organization budgeting problem for which exact solutions are known and a much larger and more difficult habitat restoration problem for which exact solutions are unknown. The method performed well on both problems, quickly finding the correct solutions to the fire budgeting problem and repeatedly finding identical solutions to the habitat restoration problem.

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Yuan, Yu, Pengcheng Wang, and Minghui Wang. "Multi-Objective Stochastic Synchronous Timetable Optimization Model Based on a Chance-Constrained Programming Method Combined with Augmented Epsilon Constraint Algorithm." Mathematical Problems in Engineering 2022 (August 28, 2022): 1–18. http://dx.doi.org/10.1155/2022/9222636.

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The design of the timetable is essential to improve the service quality of the public transport system. A lot of random factors in the actual operation environment will affect the implementation of the synchronous timetable, and adjusting timetables to improve synchronization will break the order of normal service and increase the cost of operation. A multi-objective bus timetable optimization problem is characterized by considering the randomness of vehicle travel time and passenger transfer demand. A multi-objective optimization model is proposed, aiming at minimizing the total waiting time of passengers in the whole bus network and the inconsistency between the timetable after synchronous optimization and the original timetable. Through large sample analysis, it is found that the random variables in the model obey normal distribution, so the stochastic programming problem is transformed into the traditional deterministic programming problem by the chance-constrained programming method. A model solving method based on the augmented epsilon-constraint algorithm is designed. Examples show that when the random variables are considered, the proposed algorithm can obtain multiple high-quality Pareto optimal solutions in a short time, which can provide more practical benefits for decisionmakers. Ignoring the random influence will reduce the effectiveness of the schedule optimization scheme. Finally, sensitivity analysis of random variables and constraint confidence in the model is made.

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Dai, Qian, and Jiaqi Yang. "A Distributionally Robust Chance-Constrained Approach for Modeling Demand Uncertainty in Green Port-Hinterland Transportation Network Optimization." Symmetry 12, no. 9 (September 10, 2020): 1492. http://dx.doi.org/10.3390/sym12091492.

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This paper discusses a bi-objective programming of the port-hinterland freight transportation system based on intermodal transportation with the consideration of uncertain transportation demand for green concern. Economic and environmental aspects are integrated in order to obtain green flow distribution solutions for the proposed port-hinterland network. A distributionally robust chance constraint optimization model is then established for the uncertainty of transportation demand, in which the chance constraint is described such that transportation demand is satisfied under the worst-case distribution based on the partial information of the mean and variance. The trade-offs among different objectives and the uncertainty theory applied in the modeling both involve the notion of symmetry. Taking the actual port-hinterland transportation network of the Yangtze River Economic Belt as an example, the results reveal that the railway-road intermodal transport is promoted and the change in total network CO2 emissions is contrary to that in total network costs. Additionally, both network costs and network emissions increase significantly with the growth of the lower bound of probability for chance constraint. The higher the probability level grows, the greater the trade-offs between two objectives are influenced, which indicates that the operation capacity of inland intermodal terminals should be increased to meet the high probability level. These findings can help provide decision supports for the green development strategy of the port-hinterland container transportation network, which meanwhile faces a dynamic planning problem caused by stochastic demands in real life.

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Aggarwal, Remica. "A chance constraint based low carbon footprint supply chain configuration for an FMCG product." Management of Environmental Quality: An International Journal 29, no. 6 (September 10, 2018): 1002–25. http://dx.doi.org/10.1108/meq-11-2017-0130.

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Purpose Green supply chain management and new product innovation and diffusion have become quite popular and act as a rich source of providing competitive advantage for companies to trade without further deteriorating environmental quality. However, research on low-carbon footprint supply chain configuration for a new product represents a comparably new trend and needs to be explored further. Using relatively simple models, the purpose of this paper is to demonstrate how carbon emissions concerns, such as carbon emission caps and carbon tax scheme, could be integrated into an operational decision, such as product procurement, production, storage and transportation concerning new fast-moving consumer goods (FMCG) product introduction. Design/methodology/approach The situation titled “low-carbon footprint supply chain configuration problems” is mathematically formulated as a multi-objective optimization problem under the dynamic and stochastic phenomenon concerning receiver’s demand requirements and production plant capacity constraints. Further, the effects of demand and capacities’ uncertainties are modeled using the chance constraint approach proposed by Charnes and Cooper (1959, 1963). Findings Various cases have been validated using the case example of a new FMCG product manufacturer. To validate the proposed models, data are generated randomly and solved using optimization software LINGO 10.0. Originality/value The attempt is novel in the context of considering the dynamic and stochastic phenomenon with respect to demand center’s requirements and manufacturing plant’s capacity constraints with regard to the low-carbon footprints supply chain configuration of a new FMCG product.

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Shi, Shan Shan, Fang Liu, and Xiu Yang. "Micro-Grid Energy Optimization Base on Installing Heat Storage Tank to Decouple “Heat-Load-Based” Running Constraint of CHP." Applied Mechanics and Materials 672-674 (October 2014): 1274–80. http://dx.doi.org/10.4028/www.scientific.net/amm.672-674.1274.

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Installing heat storage tank (HST) to decouple CHP “heat-load-based” running mode, which will improve operation efficiency of CHP and enhance the ability of peak-adjusting in micro-grid (MG) system, and also be benefit for MG to consume high penetration renewable energy. For the randomness of wind turbines and photovoltaics output and the volatility of loads, a comprehensive optimization method for MG heat and electric energy based on chance-constrained programming is proposed. This method has considered thermal balance constraints and HST operation constraints, which made MG minimum operating cost as optimization goal, and optimize the output of each micro-source by genetic algorithm to form the best operation mode.

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Kepaptsoglou, Konstantinos, Grigorios Fountas, and Matthew G. Karlaftis. "Weather impact on containership routing in closed seas: A chance-constraint optimization approach." Transportation Research Part C: Emerging Technologies 55 (June 2015): 139–55. http://dx.doi.org/10.1016/j.trc.2015.01.027.

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Gu, Jinjin, Xiaorui Zhang, Xiaodong Xuan, and Yuan Cao. "Land use structure optimization based on uncertainty fractional joint probabilistic chance constraint programming." Stochastic Environmental Research and Risk Assessment 34, no. 11 (July 24, 2020): 1699–712. http://dx.doi.org/10.1007/s00477-020-01841-w.

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Chou, Glen, Hao Wang, and Dmitry Berenson. "Gaussian Process Constraint Learning for Scalable Chance-Constrained Motion Planning From Demonstrations." IEEE Robotics and Automation Letters 7, no. 2 (April 2022): 3827–34. http://dx.doi.org/10.1109/lra.2022.3148436.

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Seydali Seyf Abad, Mohammad, Jin Ma, Ahmad Ahmadyar, and Hesamoddin Marzooghi. "Distributionally Robust Distributed Generation Hosting Capacity Assessment in Distribution Systems." Energies 11, no. 11 (November 1, 2018): 2981. http://dx.doi.org/10.3390/en11112981.

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Uncertainties associated with the loads and the output power of distributed generations create challenges in quantifying the integration limits of distributed generations in distribution networks, i.e., hosting capacity. To address this, we propose a distributionally robust optimization-based method to determine the hosting capacity considering the voltage rise, thermal capacity of the feeders and short circuit level constraints. In the proposed method, the uncertain variables are modeled as stochastic variables following ambiguous distributions defined based on the historical data. The distributionally robust optimization model guarantees that the probability of the constraint violation does not exceed a given risk level, which can control robustness of the solution. To solve the distributionally robust optimization model of the hosting capacity, we reformulated it as a joint chance constrained problem, which is solved using the sample average approximation technique. To demonstrate the efficacy of the proposed method, a modified IEEE 33-bus distribution system is used as the test-bed. Simulation results demonstrate how the sample size of historical data affects the hosting capacity. Furthermore, using the proposed method, the impact of electric vehicles aggregated demand and charging stations are investigated on the hosting capacity of different distributed generation technologies.

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Pour, Fatemeh Karimi, Vicenç Puig, and Gabriela Cembrano. "Economic Reliability-Aware MPC-LPV for Operational Management of Flow-Based Water Networks Including Chance-Constraints Programming." Processes 8, no. 1 (January 2, 2020): 60. http://dx.doi.org/10.3390/pr8010060.

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This paper presents an economic reliability-aware model predictive control (MPC) for the management of drinking water transport networks (DWNs). The proposed controller includes a new goal to increase the system and components reliability based on a finite horizon stochastic optimization problem with joint probabilistic (chance) constraints. The proposed approach is based on a single-layer economic optimization problem with dynamic constraints. The inclusion of components and system reliability in the MPC model using an Linear Parameter Varying (LPV) modeling approach aims to maximize the availability of the system by estimating system reliability. On the other hand, the use of a LPV-MPC control approach allows the controller to consider nonlinearities in the model in a linear like way. Moreover, the resulting MPC optimization problem can be formulated as a Quadratic Programming (QP) problem at each sampling time reducing the computational burden/time compared to solving a nonlinear programming problem. The use of chance-constraint programming allows the computation of an optimal strategy with a pre-established risk acceptability levels to cope with the uncertainty of the demand forecast. Finally, the proposed approach is applied to a part of the water transport network of Barcelona for demonstrating its performance. The obtained results show that the system reliability of the DWN is maximized compared with the other approaches.

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Xu, Liyan, Bo Yu, and Wei Liu. "The Distributionally Robust Optimization Reformulation for Stochastic Complementarity Problems." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/469587.

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We investigate the stochastic linear complementarity problem affinely affected by the uncertain parameters. Assuming that we have only limited information about the uncertain parameters, such as the first two moments or the first two moments as well as the support of the distribution, we formulate the stochastic linear complementarity problem as a distributionally robust optimization reformation which minimizes the worst case of an expected complementarity measure with nonnegativity constraints and a distributionally robust joint chance constraint representing that the probability of the linear mapping being nonnegative is not less than a given probability level. Applying the cone dual theory and S-procedure, we show that the distributionally robust counterpart of the uncertain complementarity problem can be conservatively approximated by the optimization with bilinear matrix inequalities. Preliminary numerical results show that a solution of our method is desirable.

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Mou, Deyi, and Xiaoding Chang. "An Uncertain Programming for the Integrated Planning of Production and Transportation." Mathematical Problems in Engineering 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/419358.

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The goal of this paper is to tackle joint decisions in assigning production and organizing transportation for single product in a production-transportation network system with multiple manufacturers and multiple demands. In order to meet practical situation, assume that the variant costs and the amounts of the consumption of raw materials that every manufacturer produces per unit product are all uncertain variables in manufacturing processes; meanwhile, the demands that each destination needs are random variables in the transportation problem. Then, a joint optimization model of production and transportation is developed, in which the uncertain chance constraint and the stochastic chance constraint are applied in the manufacturing processes and the transporting processes, respectively, and transformed into a deterministic form by taking expected value on objective function and confidence level on the constraint functions. Finally, a practical example points out the effectiveness of our model.

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Srizongkhram, Shayarath, Pisacha Suthamanondh, Kittitath Manitayakul, Kunio Shirahada, and Navee Chiadamrong. "Fuzzy Multi-Objective Portfolio Optimization Considering Investment Return and Investment Risk." International Journal of Fuzzy System Applications 11, no. 1 (January 2022): 1–35. http://dx.doi.org/10.4018/ijfsa.285552.

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Portfolio selection and optimization deal with the selection of the most suitable projects in a portfolio. The expected goals can be achieved while considering the balance among selected projects, to ensure that all selected projects consume resources effectively. This study proposes and compares multi-objective portfolio investment optimization algorithms under uncertain conditions. The investment return (in terms of the fuzzy net present value of the portfolio) and investment risk (in terms of the credibilistic risk index) have simultaneously been considered. In addition, fuzzy chance-constrained programming is introduced as an optimization constraint to handle such uncertainty by specifying a desired confidence level of the decision makers. The outcome of this study can then help decision makers to decide what projects and when to invest. Decision makers can deal with a limited budget with logical relationships, and within their desired financial and risk requirements.

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Sahoo, Anuradha, and J. K. Dash. "A Novel Method for Optimal Solution of Fuzzy Chance Constraint Single-Period Inventory Model." Advances in Fuzzy Systems 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/6132768.

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A method is proposed for solving single-period inventory fuzzy probabilistic model (SPIFPM) with fuzzy demand and fuzzy storage space under a chance constraint. Our objective is to maximize the total profit for both overstock and understock situations, where the demandD~jfor each productjin the objective function is considered as a fuzzy random variable (FRV) and with the available storage space areaW~, which is also a FRV under normal distribution and exponential distribution. Initially we used the weighted sum method to consider both overstock and understock situations. Then the fuzziness of the model is removed by ranking function method and the randomness of the model is removed by chance constrained programming problem, which is a deterministic nonlinear programming problem (NLPP) model. Finally this NLPP is solved by using LINGO software. To validate and to demonstrate the results of the proposed model, numerical examples are given.

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Zhao, Yan Wei, F. L. Huang, Z. F. Li, and Guo Xian Zhang. "Research in Method of Reliability Optimization Based-On Multi-Objective Fuzzy Matter-Element with Fuzzy Chance Constraint." Key Engineering Materials 315-316 (July 2006): 430–35. http://dx.doi.org/10.4028/www.scientific.net/kem.315-316.430.

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This paper study on the problem of fuzzy multi-objective optimization, provides the method uses multi-objective fuzzy matter-element optimization to solve the problem of multi-objective programming which the parameter of the model is fuzzy, and provides the process of a fuzzy simulated based genetic algorithm to solve this problem. And a instance of multi-objective optimization of fuzzy reliability is given, verified the genetic algorithm based on fuzzy simulation of multi-objective matter-element is validity, and the virtue of the algorithm not only can solve the problem that the objective function is generalized function, but also can solve the problem that the objective function is normal function.

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Pınarbaşı, Mehmet, and Hacı Mehmet Alakaş. "Balancing stochastic type-II assembly lines: chance-constrained mixed integer and constraint programming models." Engineering Optimization 52, no. 12 (February 26, 2020): 2146–63. http://dx.doi.org/10.1080/0305215x.2020.1716746.

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Alqunun, K. "Optimal Unit Commitment Problem Considering Stochastic Wind Energy Penetration." Engineering, Technology & Applied Science Research 10, no. 5 (October 26, 2020): 6316–22. http://dx.doi.org/10.48084/etasr.3795.

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Wind energy has attracted much attention as a clean energy resource with low running cost over the last decade,. However, due to the unpredictable nature of wind speed, the Unit Commitment (UC) problem including wind power becomes more difficult. Therefore, engineers and researchers are required to seek reliable models and techniques to plan the operation of thermal units in presence of wind farms. This paper presents a new attempt to solve the stochastic UC including wind energy sources. In order to achieve this, the problem is modeled as a chance-constrained optimization problem. Then, a method based on the here-and-now strategy is used to convert the uncertain power balance constraint into a deterministic constraint. The obtained deterministic problem is modeled using Mixed Integer Programming (MIP) on GAMS interface whereas the CEPLEX MIP solver is employed for its solution.

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Barutcu, I. C. "Examination of the Chance Constrained Optimal WT Penetration Level in Distorted Distribution Network with Wind Speed and Load Uncertainties." Engineering, Technology & Applied Science Research 11, no. 4 (August 21, 2021): 7311–20. http://dx.doi.org/10.48084/etasr.4226.

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Harmonic penetration can be problematic by the growing interconnection of Wind Turbines (WTs) in distribution networks. Since the active power outputs of WTs and loads in the distribution system have uncertainties, the optimal WT penetration level problem can be considered to have a stochastic nature. In this study, this problem is taken into account in the stochastic optimization method with the consideration of uncertainties in wind speed and distribution network load profile. Chance constraint programming is taken into account in the determination of optimal WT penetration levels by applying the Genetic Algorithm (GA) along with Monte Carlo Simulation (MCS). The harmonic power flow analysis based on the decoupled harmonic load flow approach is employed in the distorted distribution network. Chance constraints are considered for the harmonic issues such as the Total Harmonic Distortion of Voltage (VTHD), Individual Harmonic Distortion of Voltage (VIHDh), and Root Mean Square of Voltage (VRMS).

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Cohen, Maxime C., Philipp W. Keller, Vahab Mirrokni, and Morteza Zadimoghaddam. "Overcommitment in Cloud Services: Bin Packing with Chance Constraints." Management Science 65, no. 7 (July 2019): 3255–71. http://dx.doi.org/10.1287/mnsc.2018.3091.

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This paper considers a traditional problem of resource allocation: scheduling jobs on machines. One such recent application is cloud computing; jobs arrive in an online fashion with capacity requirements and need to be immediately scheduled on physical machines in data centers. It is often observed that the requested capacities are not fully utilized, hence offering an opportunity to employ an overcommitment policy, that is, selling resources beyond capacity. Setting the right overcommitment level can yield a significant cost reduction for the cloud provider while only inducing a very low risk of violating capacity constraints. We introduce and study a model that quantifies the value of overcommitment by modeling the problem as bin packing with chance constraints. We then propose an alternative formulation that transforms each chance constraint to a submodular function. We show that our model captures the risk pooling effect and can guide scheduling and overcommitment decisions. We also develop a family of online algorithms that are intuitive, easy to implement, and provide a constant factor guarantee from optimal. Finally, we calibrate our model using realistic workload data and test our approach in a practical setting. Our analysis and experiments illustrate the benefit of overcommitment in cloud services and suggest a cost reduction of 1.5% to 17%, depending on the provider’s risk tolerance. The online appendices are available at https://doi.org/10.1287/mnsc.2018.3091 . This paper was accepted by Yinyu Ye, optimization.

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Fazli-Khalaf, Mohamadreza, Soheyl Khalilpourazari, and Mohammad Mohammadi. "Mixed robust possibilistic flexible chance constraint optimization model for emergency blood supply chain network design." Annals of Operations Research 283, no. 1-2 (December 11, 2017): 1079–109. http://dx.doi.org/10.1007/s10479-017-2729-3.

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Zaeimi, Mehdi Bavaghar, and Amir Abbas Rassafi. "Optimization Model for Integrated Municipal Solid Waste System Using Stochastic Chance-Constraint Programming under Uncertainty: A Case Study in Qazvin, Iran." Journal of Advanced Transportation 2021 (July 30, 2021): 1–16. http://dx.doi.org/10.1155/2021/9994853.

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Municipal solid waste management (MSW) is a factor that affects environmental pollution and the spread of diseases in cities. Therefore, an efficient MSW management system results in reducing the cost of environmental impact by tackling the processes of waste collection, recycling, and disposal. In this study, a biobjective optimization model is developed which aims to minimize the costs of facility location and transportation planning and the emission of environmental pollutants. Furthermore, to consider the uncertain nature of the problem, demand or the volume of the generated waste is considered as a random parameter. As a result, a stochastic mathematical programming model with probable constraints is developed. To solve and validate the model, the ε-constraint approach has been employed. Moreover, for a real-world application of the proposed model, a case study is implemented in Qazvin, Iran. Finally, various problems are solved for different levels of reliability and an efficient MSW system is designed for each of them. Results show that the proposed method was able to achieve Pareto solutions where managers can decide to choose one of them based on their priorities in comparison with the current status. Moreover, results revealed cost and emission would be reduced by increasing confidence level. Finally, a comparison is made between our proposed ε-constraint method and one of the recently used solution approaches.

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Yan, Zehao, and Mo Li. "A Stochastic Optimization Model for Agricultural Irrigation Water Allocation Based on the Field Water Cycle." Water 10, no. 8 (August 3, 2018): 1031. http://dx.doi.org/10.3390/w10081031.

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Agricultural water scarcity is a global problem and this reinforces the need for optimal allocation of irrigation water resources. However, decision makers are challenged by the complexity of fluctuating stream condition and irrigation quota as well as the dynamic changes of the field water cycle process, which make optimal allocation more complex. A two-stage chance-constrained programming model with random parameters in the left- and right-hand sides of constraints considering field water cycle process has been developed for agricultural irrigation water allocation. The model is capable of generating reasonable irrigation allocation strategies considering water transformation among crop evapotranspiration, precipitation, irrigation, soil water content, and deep percolation. Moreover, it can deal with randomness in both the right-hand side and the left-hand side of constraints to generate schemes under different flow levels and constraint-violation risk levels, which are informative for decision makers. The Yingke irrigation district in the middle reaches of the Heihe River basin, northwest China, was used to test the developed model. Tradeoffs among different crops in different time periods under different flow levels, and dynamic changes of soil moisture and deep percolation were analyzed. Scenarios with different violating probabilities were conducted to gain insight into the sensitivity of irrigation water allocation strategies on water supply and irrigation quota. The performed analysis indicated that the proposed model can efficiently optimize agricultural irrigation water for an irrigation district with water scarcity in a stochastic environment.

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Alshammari, Motaeb Eid, Makbul A. M. Ramli, and Ibrahim M. Mehedi. "An Elitist Multi-Objective Particle Swarm Optimization Algorithm for Sustainable Dynamic Economic Emission Dispatch Integrating Wind Farms." Sustainability 12, no. 18 (September 4, 2020): 7253. http://dx.doi.org/10.3390/su12187253.

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In recent years, wind energy has been widely used as an alternative energy source as it is a clean energy with a low running cost. However, the high penetration of wind power (WP) in power networks has created major challenges due to their intermittency. In this study, an elitist multi-objective evolutionary algorithm called non-dominated sorting particle swarm optimization (NSPSO) is proposed to solve the dynamic economic emission dispatch (DEED) problem with WP. The proposed optimization technique referred to as NSPSO uses the non-dominated sorting principle to rank the non-dominated solutions. A crowding distance calculation is added at the end of all iterations of the algorithm. In this study, WP is represented by a chance-constraint which describes the probability that the power balance cannot be met. The uncertainty of WP is described by the Weibull distribution function. In this study, the chance constraint DEED problem is converted into a deterministic problem. Then, the NSPSO is applied to simultaneously minimize the total generation cost and emission of harmful gases. To proof the performance of the proposed method, the ten-unit and forty-unit systems—including wind farms—are used. Simulation results obtained by the NSPSO method are compared with other optimization techniques that were presented recently in the literature. Moreover, the impact of the penetration ratio of WP is investigated.

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Kalantari Khalil Abad, Amin Reza, and Seyed Hamid Reza Pasandideh. "Green closed-loop supply chain network design: a novel bi-objective chance-constraint approach." RAIRO - Operations Research 55, no. 2 (March 2021): 811–40. http://dx.doi.org/10.1051/ro/2021035.

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In this paper, a novel chance-constrained programming model has been proposed for handling uncertainties in green closed loop supply chain network design. In addition to locating the facilities and establishing a flow between them, the model also determines the transportation mode between facilities. The objective functions are applied to minimize the expected value and variance of the total cost CO2 released is also controlled by providing a novel chance-constraint including a stochastic upper bound of emission capacity. To solve the mathematical model using the General Algebraic Modeling System (GAMS) software, four multi-objective decision-making (MODM) methods were applied. The proposed methodology was subjected to various numerical experiments. The solutions provided by different methods were compared in terms of the expected value of cost, variance of cost, and CPU time using Pareto-based analysis and optimality-based analysis. In Pareto-based analysis, a set of preferable solutions were presented using the Pareto front; then optimality-based optimization was chosen as the best method by using a Simple Additive Weighting (SAW) method. Experimental experiments and sensitivity analysis demonstrated that the performance of the goal attainment method was 13% and 24% better that of global criteria and goal programming methods, respectively.

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MEHLAWAT, MUKESH KUMAR, and PANKAJ GUPTA. "CREDIBILITY-BASED FUZZY MATHEMATICAL PROGRAMMING MODEL FOR PORTFOLIO SELECTION UNDER UNCERTAINTY." International Journal of Information Technology & Decision Making 13, no. 01 (January 2014): 101–35. http://dx.doi.org/10.1142/s0219622014500059.

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In this paper, we develop a hybrid bi-objective credibility-based fuzzy mathematical programming model for portfolio selection under fuzzy environment. To deal with imprecise parameters, we use a hybrid credibility-based approach that combines the expected value and chance constrained programming techniques. The model simultaneously maximizes the portfolio return and minimizes the portfolio risk. We also consider an additional important criterion, namely, portfolio liquidity as a constraint in the model to make it better suited for practical applications. The proposed fuzzy optimization model is solved using a two-phase approach. An empirical study is included to demonstrate applicability of the proposed model and the solution approach in real-world applications of portfolio selection.

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Sun, Yan, Martin Hrušovský, Chen Zhang, and Maoxiang Lang. "A Time-Dependent Fuzzy Programming Approach for the Green Multimodal Routing Problem with Rail Service Capacity Uncertainty and Road Traffic Congestion." Complexity 2018 (June 24, 2018): 1–22. http://dx.doi.org/10.1155/2018/8645793.

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This study explores an operational-level container routing problem in the road-rail multimodal service network. In response to the demand for an environmentally friendly transportation, we extend the problem into a green version by using both emission charging method and bi-objective optimization to optimize the CO2 emissions in the routing. Two uncertain factors, including capacity uncertainty of rail services and travel time uncertainty of road services, are formulated in order to improve the reliability of the routes. By using the triangular fuzzy numbers and time-dependent travel time to separately model the capacity uncertainty and travel time uncertainty, we establish a fuzzy chance-constrained mixed integer nonlinear programming model. A linearization-based exact solution strategy is designed, so that the problem can be effectively solved by any exact solution algorithm on any mathematical programming software. An empirical case is presented to demonstrate the feasibility of the proposed methods. In the case discussion, sensitivity analysis and bi-objective optimization analysis are used to find that the bi-objective optimization method is more effective than the emission charging method in lowering the CO2 emissions for the given case. Then, we combine sensitivity analysis and fuzzy simulation to identify the best confidence value in the fuzzy chance constraint. All the discussion will help decision makers to better organize the green multimodal transportation.

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Aupy, Guillaume, and Anne Benoit. "Approximation Algorithms for Energy, Reliability, and Makespan Optimization Problems." Parallel Processing Letters 26, no. 01 (March 2016): 1650001. http://dx.doi.org/10.1142/s0129626416500018.

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We consider the problem of scheduling an application on a parallel computational platform. The application is a particular task graph, either a linear chain of tasks, or a set of independent tasks. The platform is made of identical processors, whose speed can be dynamically modified. It is also subject to failures: if a processor is slowed down to decrease the energy consumption, it has a higher chance to fail. Therefore, the scheduling problem requires us to re-execute or replicate tasks (i.e., execute twice the same task, either on the same processor, or on two distinct processors), in order to increase the reliability. It is a tri-criteria problem: the goal is to minimize the energy consumption, while enforcing a bound on the total execution time (the makespan), and a constraint on the reliability of each task. Our main contribution is to propose approximation algorithms for linear chains of tasks and independent tasks. For linear chains, we design a fully polynomial-time approximation scheme. However, we show that there exists no constant factor approximation algorithm for independent tasks, unless P=NP, and we propose in this case an approximation algorithm with a relaxation on the makespan constraint.

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Rao, Yingxue, Min Zhou, Chunxia Cao, Shukui Tan, Yan Song, Zuo Zhang, Deyi Dai, et al. "Exploring the quantitive relationship between economic benefit and environmental constraint using an inexact chance-constrained fuzzy programming based industrial structure optimization model." Quality & Quantity 53, no. 4 (March 28, 2019): 2199–220. http://dx.doi.org/10.1007/s11135-019-00865-x.

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Zhou, Yi, Lianshui Li, Ruiling Sun, Zaiwu Gong, Mingguo Bai, and Guo Wei. "Haze Influencing Factors: A Data Envelopment Analysis Approach." International Journal of Environmental Research and Public Health 16, no. 6 (March 14, 2019): 914. http://dx.doi.org/10.3390/ijerph16060914.

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This paper investigates the meteorological factors and human activities that influence PM2.5 pollution by employing the data envelopment analysis (DEA) approach to a chance constrained stochastic optimization problem. This approach has the two advantages of admitting random input and output, and allowing the evaluation unit to exceed the front edge under the given probability constraint. Furthermore, by utilizing the meteorological observation data incorporated with the economic and social data for Jiangsu Province, the chance constrained stochastic DEA model was solved to explore the relationship between the meteorological elements and human activities and PM2.5 pollution. The results are summarized by the following: (1) Among all five primary indexes, social progress, energy use and transportation are the most significant for PM2.5 pollution. (2) Among our selected 14 secondary indexes, coal consumption, population density and civil car ownership account for a major portion of PM2.5 pollution. (3) Human activities are the main factor producing PM2.5 pollution. While some meteorological elements generate PM2.5 pollution, some act as influencing factors on the migration of PM2.5 pollution. These findings can provide a reference for the government to formulate appropriate policies to reduce PM2.5 emissions and for the communities to develop effective strategies to eliminate PM2.5 pollution.

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Wang, Xiuyun, Junyu Tian, Rutian Wang, Jiakai Xu, Shaoxin Chen, Jian Wang, and Yang Cui. "Multi-Objective Economic Dispatch of Cogeneration Unit with Heat Storage Based on Fuzzy Chance Constraint." Energies 12, no. 1 (December 29, 2018): 103. http://dx.doi.org/10.3390/en12010103.

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With the increasing expansion of wind power, its impact on economic dispatch of power systems cannot be ignored. Adding a heat storage device to a traditional cogeneration unit can break the thermoelectric coupling constraint of the cogeneration unit and meet the economic and stable operation of a power system. In this paper, an economy-environment coordinated scheduling model with the lowest economic cost and the lowest pollutant emissions is constructed. Economic costs include the cost of conventional thermal power generating units, the operating cost of cogeneration units, and the operating cost of wind power. At the same time, green certificate costs are introduced into the economic costs to improve the absorption of wind power. Pollutant emissions include SO2 and NOx emissions from conventional thermal power units and cogeneration units. The randomness and uncertainty of wind power output are fully considered, and the prediction error of wind power is fuzzy treated according to the fuzzy random theory, and the electric power balance and spinning reserve fuzzy opportunity conditions are established, which are converted into the explicit equivalent. The improved multi-objective particle swarm optimization (MOPSO) was used to solve the model. With this method, the validity of the model is verified by taking a system with 10 machines as an example.

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Charles, Vincent, and Pankaj Gupta. "Optimization of chance constraint programming with sum-of-fractional objectives – An application to assembled printed circuit board problem." Applied Mathematical Modelling 37, no. 5 (March 2013): 3564–74. http://dx.doi.org/10.1016/j.apm.2012.07.043.

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Sun and Li. "Fuzzy Programming Approaches for Modeling a Customer-Centred Freight Routing Problem in the Road-Rail Intermodal Hub-and-Spoke Network with Fuzzy Soft Time Windows and Multiple Sources of Time Uncertainty." Mathematics 7, no. 8 (August 12, 2019): 739. http://dx.doi.org/10.3390/math7080739.

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In this study, we systematically investigate a road-rail intermodal routing problem the optimization of which is oriented on the customer demands on transportation economy, timeliness and reliability. The road-rail intermodal transportation system is modelled as a hub-and-spoke network that contains time-flexible container truck services and scheduled container train services. The transportation timeliness is optimized by using fuzzy soft time windows associated with the service level of the transportation. Reliability is enhanced by considering multiple sources of time uncertainty, including road travel time and loading/unloading time. Such uncertainty is modelled by using fuzzy set theory. Triangular fuzzy numbers are adopted to represent the uncertain time. Under the above consideration, we first establish a fuzzy mixed integer nonlinear programming model with a weighted objective that includes minimizing the costs and maximizing the service level for accomplishing transportation orders. Then we use the fuzzy expected value model and fuzzy chance-constrained programming separately to realize the defuzzification of the fuzzy objective and use fuzzy chance-constrained programming to deal with the fuzzy constraint. After defuzzification and linearization, an equivalent mixed integer linear programming (MILP) model is generated to enable the problem to be solved by mathematical programming software. Finally, a numerical case modified from our previous study is presented to demonstrate the feasibility of the proposed fuzzy programming approaches. Sensitivity analysis and fuzzy simulation are comprehensively utilized to discuss the effects of the fuzzy soft time windows and time uncertainty on the routing optimization and help decision makers to better design a crisp transportation plan that can effectively make tradeoffs among economy, timeliness and reliability.

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Chen, Ying Guo, Shuai Lu, Xiao Lu Liu, and Ying Wu Chen. "Derivative-Free Hybrid Optimization Method for Top Design of Satellite System." Advanced Materials Research 308-310 (August 2011): 2413–17. http://dx.doi.org/10.4028/www.scientific.net/amr.308-310.2413.

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This paper combines a derivative-free hybrid optimization algorithm, generalize pattern search (GPS), with Treed Gaussian Processes (TGP) to create a new hybrid optimization algorithm. The goal is to use the method for top design of satellite system, in which the objective or constraint functions usually are computationally expensive black-box functions. TGP model partitions the design space into disjoint regions, and employs independent Gaussian Processes (GP) in each partition to represent the time consumption of true problem responses. Utilizing the TGP, we generate the new “promising” points, which are the combination of model-predicted values and estimated model errors. Then, these points are used to guide GPS search in the design space efficiently. The hybrid optimization method is applied to top design of multi-satellites cooperated observation. The results demonstrate that the proposed method can not only increase the chance of obtaining optimal solution but also cut down the cost of function evaluations.

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Khojasteh, Meysam, and Shahram Jadid. "Optimal risk-based strategy of distributed generation-owning retailer in the day-ahead electricity market: Chance constraint optimization approach." Journal of Renewable and Sustainable Energy 6, no. 5 (September 2014): 053111. http://dx.doi.org/10.1063/1.4896786.

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Gorji-Bandpy, M., and A. Mozaffari. "Multiobjective Optimization of Irreversible Thermal Engine Using Mutable Smart Bee Algorithm." Applied Computational Intelligence and Soft Computing 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/652391.

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A new method called mutable smart bee (MSB) algorithm proposed for cooperative optimizing of the maximum power output (MPO) and minimum entropy generation (MEG) of an Atkinson cycle as a multiobjective, multi-modal mechanical problem. This method utilizes mutable smart bee instead of classical bees. The results have been checked with some of the most common optimizing algorithms like Karaboga’s original artificial bee colony, bees algorithm (BA), improved particle swarm optimization (IPSO), Lukasik firefly algorithm (LFFA), and self-adaptive penalty function genetic algorithm (SAPF-GA). According to obtained results, it can be concluded that Mutable Smart Bee (MSB) is capable to maintain its historical memory for the location and quality of food sources and also a little chance of mutation is considered for this bee. These features were found as strong elements for mining data in constraint areas and the results will prove this claim.

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Huang, Kai, Gordon Huang, Liming Dai, and Yurui Fan. "Inexact fuzzy integer chance constraint programming approach for noise control within an urban environment." Engineering Optimization 48, no. 8 (November 9, 2015): 1350–64. http://dx.doi.org/10.1080/0305215x.2015.1107336.

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Journal articles on the topic 'Chance Constraint Optimization'

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