Relevant bibliographies by topics / Chance Constraint Optimization

Academic literature on the topic 'Chance Constraint Optimization'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "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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Dissertations / Theses on the topic "Chance Constraint Optimization"

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Koker, Ezgi. "Chance Constrained Optimization Of Booster Disinfection In Water Distribution Networks." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613640/index.pdf.

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Quality of municipal water is sustained by addition of disinfectant, generally chlorine, to the water distribution network. Because of health problems, chlorine concentration in the network is limited between maximum and minimum limits. Cancerogenic disinfectant by-products start to occur at high concentrations so it is desired to have minimum amount of chlorine without violating the limit. In addition to the health issues, minimum injection amount is favorable concerning cost. Hence, an optimization model is necessary which covers all of these considerations. However, there are uncertain factors as chlorine is reactive and decays both over time and space. Thus, probabilistic approach is necessary to obtain reliable and realistic results from the model. In this study, a linear programming model is developed for the chance constrained optimization of the water distribution network. The objective is to obtain minimum amount of injection mass subjected to maintaining more uniformly distributed chlorine concentrations within the limits while considering the randomness of chlorine concentration by probability distributions. Network hydraulics and chlorine concentration computations are done by the network simulation software, EPANET.
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Sassi, Achille. "Numerical methods for hybrid control and chance-constrained optimization problems." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLY005/document.

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Cette thèse est dediée à l'alanyse numérique de méthodes numériques dans le domaine du contrôle optimal, et est composée de deux parties. La première partie est consacrée à des nouveaux résultats concernant des méthodes numériques pour le contrôle optimal de systèmes hybrides, qui peuvent être contrôlés simultanément par des fonctions mesurables et des sauts discontinus dans la variable d'état. La deuxième partie est dédiée è l'étude d'une application spécifique surl'optimisation de trajectoires pour des lanceurs spatiaux avec contraintes en probabilité. Ici, on utilise des méthodes d'optimisation nonlineaires couplées avec des techniques de statistique non parametrique. Le problème traité dans cette partie appartient à la famille des problèmes d'optimisation stochastique et il comporte la minimisation d'une fonction de coût en présence d'une contrainte qui doit être satisfaite dans les limites d'un seuil de probabilité souhaité
This thesis is devoted to the analysis of numerical methods in the field of optimal control, and it is composed of two parts. The first part is dedicated to new results on the subject of numerical methods for the optimal control of hybrid systems, controlled by measurable functions and discontinuous jumps in the state variable simultaneously. The second part focuses on a particular application of trajectory optimization problems for space launchers. Here we use some nonlinear optimization methods combined with non-parametric statistics techniques. This kind of problems belongs to the family of stochastic optimization problems and it features the minimization of a cost function in the presence of a constraint which needs to be satisfied within a desired probability threshold
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Helmberg, Christoph, Sebastian Richter, and Dominic Schupke. "A Chance Constraint Model for Multi-Failure Resilience in Communication Networks." Universitätsbibliothek Chemnitz, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-175454.

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For ensuring network survivability in case of single component failures many routing protocols provide a primary and a back up routing path for each origin destination pair. We address the problem of selecting these paths such that in the event of multiple failures, occuring with given probabilities, the total loss in routable demand due to both paths being intersected is small with high probability. We present a chance constraint model and solution approaches based on an explicit integer programming formulation, a robust formulation and a cutting plane approach that yield reasonably good solutions assuming that the failures are caused by at most two elementary events, which may each affect several network components.
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Calfa, Bruno Abreu. "Data Analytics Methods for Enterprise-wide Optimization Under Uncertainty." Research Showcase @ CMU, 2015. http://repository.cmu.edu/dissertations/575.

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This dissertation primarily proposes data-driven methods to handle uncertainty in problems related to Enterprise-wide Optimization (EWO). Datadriven methods are characterized by the direct use of data (historical and/or forecast) in the construction of models for the uncertain parameters that naturally arise from real-world applications. Such uncertainty models are then incorporated into the optimization model describing the operations of an enterprise. Before addressing uncertainty in EWO problems, Chapter 2 deals with the integration of deterministic planning and scheduling operations of a network of batch plants. The main contributions of this chapter include the modeling of sequence-dependent changeovers across time periods for a unitspecific general precedence scheduling formulation, the hybrid decomposition scheme using Bilevel and Temporal Lagrangean Decomposition approaches, and the solution of subproblems in parallel. Chapters 3 to 6 propose different data analytics techniques to account for stochasticity in EWO problems. Chapter 3 deals with scenario generation via statistical property matching in the context of stochastic programming. A distribution matching problem is proposed that addresses the under-specification shortcoming of the originally proposed moment matching method. Chapter 4 deals with data-driven individual and joint chance constraints with right-hand side uncertainty. The distributions are estimated with kernel smoothing and are considered to be in a confidence set, which is also considered to contain the true, unknown distributions. The chapter proposes the calculation of the size of the confidence set based on the standard errors estimated from the smoothing process. Chapter 5 proposes the use of quantile regression to model production variability in the context of Sales & Operations Planning. The approach relies on available historical data of actual vs. planned production rates from which the deviation from plan is defined and considered a random variable. Chapter 6 addresses the combined optimal procurement contract selection and pricing problems. Different price-response models, linear and nonlinear, are considered in the latter problem. Results show that setting selling prices in the presence of uncertainty leads to the use of different purchasing contracts.
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Liu, Jianzhe. "On Control and Optimization of DC Microgrids." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1512049527948171.

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Dai, Siyu S. M. Massachusetts Institute of Technology. "Probabilistic motion planning and optimization incorporating chance constraints." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/120230.

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Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 201-208).
For high-dimensional robots, motion planning is still a challenging problem, especially for manipulators mounted to underwater vehicles or human support robots where uncertainties and risks of plan failure can have severe impact. However, existing risk-aware planners mostly focus on low-dimensional planning tasks, meanwhile planners that can account for uncertainties and react fast in high degree-of-freedom (DOF) robot planning tasks are lacking. In this thesis, a risk-aware motion planning and execution system called Probabilistic Chekov (p-Chekov) is introduced, which includes a deterministic stage and a risk-aware stage. A systematic set of experiments on existing motion planners as well as p-Chekov is also presented. The deterministic stage of p-Chekov leverages the recent advances in obstacle-aware trajectory optimization to improve the original tube-based-roadmap Chekov planner. Through experiments in 4 common application scenarios with 5000 test cases each, we show that using sampling-based planners alone on high DOF robots can not achieve a high enough reaction speed, whereas the popular trajectory optimizer TrajOpt with naive straight-line seed trajectories has very high collision rate despite its high planning speed. To the best of our knowledge, this is the first work that presents such a systematic and comprehensive evaluation of state-of-the-art motion planners, which are based on a significant amount of experiments. We then combine different stand-alone planners with trajectory optimization. The results show that the deterministic planning part of p-Chekov, which combines a roadmap approach that caches the all pair shortest paths solutions and an online obstacle-aware trajectory optimizer, provides superior performance over other standard sampling-based planners' combinations. Simulation results show that, in typical real-life applications, this "roadmap + TrajOpt" approach takes about 1 s to plan and the failure rate of its solutions is under 1%. The risk-aware stage of p-Chekov accounts for chance constraints through state probability distribution and collision probability estimation. Based on the deterministic Chekov planner, p-Chekov incorporates a linear-quadratic Gaussian motion planning (LQG-MP) approach into robot state probability distribution estimation, applies quadrature-sampling theories to collision risk estimation, and adapts risk allocation approaches for chance constraint satisfaction. It overcomes existing risk-aware planners' limitation in real-time motion planning tasks with high-DOF robots in 3- dimensional non-convex environments. The experimental results in this thesis show that this new risk-aware motion planning and execution system can effectively reduce collision risk and satisfy chance constraints in typical real-world planning scenarios for high-DOF robots. This thesis makes the following three main contributions: (1) a systematic evaluation of several state-of-the-art motion planners in realistic planning scenarios, including popular sampling-based motion planners and trajectory optimization type motion planners, (2) the establishment of a "roadmap + TrajOpt" deterministic motion planning system that shows superior performance in many practical planning tasks in terms of solution feasibility, optimality and reaction time, and (3) the development of a risk-aware motion planning and execution system that can handle high-DOF robotic planning tasks in 3-dimensional non-convex environments.
by Siyu Dai.
S.M.
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Sun, Yufei. "Chance-constrained optimization & optimal control problems." Thesis, Curtin University, 2015. http://hdl.handle.net/20.500.11937/183.

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Four optimization or optimal control problems subject to probabilistic constraints are studied. The first identifies the optimal portfolio using a new probabilistic risk measure while maximizing return. The second explores a preventive-based maintenance scheduling problem while minimizing the total cost of operation. The third investigates how asset allocation of a pension fund should change in the face of default risk. The fourth suggests the optimal manpower scheduling which minimizes the salary costs of the employees.
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Yang, Yi. "Sequential convex approximations of chance constrained programming /." View abstract or full-text, 2008. http://library.ust.hk/cgi/db/thesis.pl?IELM%202008%20YANG.

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Arellano-Garcia, Harvey. "Chance constrained optimization of process systems under uncertainty." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=982225652.

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Luedtke, James. "Integer Programming Approaches for Some Non-convex and Stochastic Optimization Problems." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19711.

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In this dissertation we study several non-convex and stochastic optimization problems. The common theme is the use of mixed-integer programming (MIP) techniques including valid inequalities and reformulation to solve these problems. We first study a strategic capacity planning model which captures the trade-off between the incentive to delay capacity installation to wait for improved technology and the need for some capacity to be installed to meet current demands. This problem is naturally formulated as a MIP with a bilinear objective. We develop several linear MIP formulations, along with classes of strong valid inequalities. We also present a specialized branch-and-cut algorithm to solve a compact concave formulation. Computational results indicate that these formulations can be used to solve large-scale instances. We next study methods for optimization with joint probabilistic constraints. These problems are challenging because evaluating solution feasibility requires multidimensional integration and the feasible region is not convex. We propose and analyze a Monte Carlo sampling scheme to simplify the probabilistic structure of such problems. Computational tests of the approach indicate that it can yield good feasible solutions and reasonable bounds on their quality. Next, we study a MIP formulation of the non-convex sample approximation problem. We obtain two strengthened formulations. As a byproduct of this analysis, we obtain new results for the previously studied mixing set, subject to an additional knapsack inequality. Computational results indicate that large-scale instances can be solved using the strengthened formulations. Finally, we study optimization problems with stochastic dominance constraints. A stochastic dominance constraint states that a random outcome which depends on the decision variables should stochastically dominate a given random variable. We present new formulations for both first and second order stochastic dominance which are significantly more compact than existing formulations. Computational tests illustrate the benefits of the new formulations.
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Book chapters on the topic "Chance Constraint Optimization"

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Loucks, Daniel P. "Lagrangian Models." In International Series in Operations Research & Management Science, 135–41. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-93986-1_11.

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AbstractLagrangian models use calculus to solve multi-variable non-linear constrained optimization models of problems and for identifying the marginal changes (‘shadow prices’) of optimal solutions to changes in constraint bounds. This is especially useful when the constraints represent resource limitations.
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Zhao, Y. W., 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." In Advances in Machining & Manufacturing Technology VIII, 430–35. Stafa: Trans Tech Publications Ltd., 2006. http://dx.doi.org/10.4028/0-87849-999-7.430.

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Alanazi, Eisa. "Preference Constrained Optimization under Change." In Advances in Artificial Intelligence, 323–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38457-8_33.

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Loucks, Daniel P. "Chance Constrained and Monte Carlo Modeling." In International Series in Operations Research & Management Science, 177–85. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-93986-1_14.

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AbstractConstraints of models that contain random variables may be applicable only some of the time. Constraints that apply only a specified fraction of the time are called chance constraints. This chapter illustrates how chance constraints can be included in optimization models. In addition, the chapter demonstrates how to generate values of random variables fitting user defined probability distributions. These random variable values often serve as inputs to stochastic simulation models.
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Chai, Runqi, Al Savvaris, Antonios Tsourdos, and Senchun Chai. "Stochastic Trajectory Optimization Problems with Chance Constraints." In Design of Trajectory Optimization Approach for Space Maneuver Vehicle Skip Entry Problems, 163–91. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-9845-2_8.

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Wets, Roger J.-B. "Stochastic Programs with Chance Constraints: Generalized Convexity and Approximation Issues." In Nonconvex Optimization and Its Applications, 61–74. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4613-3341-8_2.

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Mayer, János. "On the Numerical Solution of Jointly Chance Constrained Problems." In Nonconvex Optimization and Its Applications, 220–35. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4757-3150-7_12.

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Xie, Weijun, and Shabbir Ahmed. "On the Quantile Cut Closure of Chance-Constrained Problems." In Integer Programming and Combinatorial Optimization, 398–409. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-33461-5_33.

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Dinh, Thai, Ricardo Fukasawa, and James Luedtke. "Exact Algorithms for the Chance-Constrained Vehicle Routing Problem." In Integer Programming and Combinatorial Optimization, 89–101. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-33461-5_8.

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Medova, E. A., and J. E. Scott. "Management of Quality of Service through Chance-constraints in Multimedia Networks." In Nonconvex Optimization and Its Applications, 236–51. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4757-3150-7_13.

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Conference papers on the topic "Chance Constraint Optimization"

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Li, Yingxiong, and Xiangyang Li. "Chance Constraint Model for Unconventional Emergency Response." In 2011 Fourth International Joint Conference on Computational Sciences and Optimization (CSO). IEEE, 2011. http://dx.doi.org/10.1109/cso.2011.100.

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Neumann, Frank, and Carsten Witt. "Runtime Analysis of Single- and Multi-Objective Evolutionary Algorithms for Chance Constrained Optimization Problems with Normally Distributed Random Variables." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/665.

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Chance constrained optimization problems allow to model problems where constraints involving stochastic components should only be violated with a small probability. Evolutionary algorithms have been applied to this scenario and shown to achieve high quality results. With this paper, we contribute to the theoretical understanding of evolutionary algorithms for chance constrained optimization. We study the scenario of stochastic components that are independent and Normally distributed. Considering the simple single-objective (1+1)~EA, we show that imposing an additional uniform constraint already leads to local optima for very restricted scenarios and an exponential optimization time. We therefore introduce a multi-objective formulation of the problem which trades off the expected cost and its variance. We show that multi-objective evolutionary algorithms are highly effective when using this formulation and obtain a set of solutions that contains an optimal solution for any possible confidence level imposed on the constraint. Furthermore, we prove that this approach can also be used to compute a set of optimal solutions for the chance constrained minimum spanning tree problem. Experimental investigations on instances of the NP-hard stochastic minimum weight dominating set problem confirm the benefit of the multi-objective approach in practice.
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Najafi, Soroush, Mohammad Mansour Lakouraj, Seyed Amin Sedgh, Hanif Livani, Mohammed Benidris, and M. S. Fadali. "Chance-Constraint Volt-VAR Optimization in PV-Penetrated Distribution Networks." In 2022 IEEE Kansas Power and Energy Conference (KPEC). IEEE, 2022. http://dx.doi.org/10.1109/kpec54747.2022.9814811.

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Albey, Erinc, Reha Uzsoy, and Karl G. Kempf. "A chance constraint based multi-item production planning model using simulation optimization." In 2016 Winter Simulation Conference (WSC). IEEE, 2016. http://dx.doi.org/10.1109/wsc.2016.7822309.

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Zhang, Peiyao, Ji Woong Kim, and Marin Kobilarov. "Towards Safer Retinal Surgery through Chance Constraint Optimization and Real-Time Geometry Estimation." In 2021 60th IEEE Conference on Decision and Control (CDC). IEEE, 2021. http://dx.doi.org/10.1109/cdc45484.2021.9683329.

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Gong, Yanxue, Dao Huang, Enbo Wang, and Yigong Peng. "A Fuzzy Chance Constraint Programming Approach for Location-Allocation Problem under Uncertainty in a Closed-Loop Supply Chain." In 2009 International Joint Conference on Computational Sciences and Optimization, CSO. IEEE, 2009. http://dx.doi.org/10.1109/cso.2009.151.

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Halim, Nurfadhlina Abdul, Saiful Hafizah Jaaman, Noriszura Ismail, and Rokiah Ahmad. "Profit sharing ratio modeling for islamic hire-purchase contract: Robust optimization and chance constraint approach." In THE 5TH INTERNATIONAL CONFERENCE ON RESEARCH AND EDUCATION IN MATHEMATICS: ICREM5. AIP, 2012. http://dx.doi.org/10.1063/1.4724117.

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8

Sirouspour, Shahin. "Optimal scheduling of a storage device in a grid-connected microgrid using stochastic chance-constraint optimization." In IECON 2016 - 42nd Annual Conference of the IEEE Industrial Electronics Society. IEEE, 2016. http://dx.doi.org/10.1109/iecon.2016.7793476.

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Cousin, A., J. Garnier, M. Guiton, and M. Zuniga. "Chance Constraint Optimization of a Complex System: Application to the Fatigue Design of a Floating Offshore Wind Turbine Mooring System." In 14th WCCM-ECCOMAS Congress. CIMNE, 2021. http://dx.doi.org/10.23967/wccm-eccomas.2020.082.

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10

Du, Xiaoping. "Reliability-Based Design Using Saddlepoint Approximation." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99077.

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Abstract:
Reliability-based design optimization is much more computationally expensive than deterministic design optimization. To alleviate the computational demand, the First Order Reliability Method (FORM) is usually used in reliability-based design. Since FORM requires a nonlinear transformation from non-normal random variables to normal random variables, the nonlinearity of a constraint function may increase. As a result, the transformation may lead to a large error in reliability calculation. In order to improve accuracy, a new reliability-based design method with Saddlepoint Approximation is proposed in this work. The strategy of sequential optimization and reliability assessment is employed where the reliability analysis is decoupled from deterministic optimization. The accurate First Order Saddlepoint method is used for reliability analysis in the original random space without any transformation, and the chance of increasing nonlinearity of a constraint function is therefore eliminated. The overall reliability-based design is conducted in a sequence of cycles of deterministic optimization and reliability analysis. In each cycle, the percentile value of the constraint function corresponding to the required reliability is calculated with the Saddlepoint Approximation at the optimal point of the deterministic optimization. Then the reliability analysis results are used to formulate a new deterministic optimization model for the next cycle. The solution process converges within a few cycles. The demonstrative examples show that the proposed method is more accurate and efficient than the reliability-based design with FORM.
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Reports on the topic "Chance Constraint Optimization"

1

Singh, Bismark, and Jean-Paul Watson. Chance-Constrained Optimization for Critical Infrastructure Protection. Office of Scientific and Technical Information (OSTI), September 2018. http://dx.doi.org/10.2172/1474266.

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2

Vincent, Charles, Saiful I. Ansari, and Mohammad Khodabakhshi. Joint chance-constrained reliability optimization with general form of distributions. CENTRUM Catolica Graduate Business School, January 2014. http://dx.doi.org/10.7835/ccwp-2014-01-0005.

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