Journal articles: 'Robust Counterpart Optimization'

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Shang, Ke, Zuren Feng, Liangjun Ke, and Felix T. S. Chan. "Comprehensive Pareto Efficiency in robust counterpart optimization." Computers & Chemical Engineering 94 (November 2016): 75–91. http://dx.doi.org/10.1016/j.compchemeng.2016.07.022.

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Li, Zukui, Ran Ding, and Christodoulos A. Floudas. "A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear Optimization and Robust Mixed Integer Linear Optimization." Industrial & Engineering Chemistry Research 50, no. 18 (September 21, 2011): 10567–603. http://dx.doi.org/10.1021/ie200150p.

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Cipta, Hendra, Saib Suwilo, Sutarman Sutarman, and Herman Mawengkang. "Improved Benders decomposition approach to complete robust optimization in box-interval." Bulletin of Electrical Engineering and Informatics 11, no. 5 (October 1, 2022): 2949–57. http://dx.doi.org/10.11591/eei.v11i5.4394.

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Robust optimization is based on the assumption that uncertain data has a convex set as well as a finite set termed uncertainty. The discussion starts with determining the robust counterpart, which is accomplished by assuming the indeterminate data set is in the form of boxes, intervals, box-intervals, ellipses, or polyhedra. In this study, the robust counterpart is characterized by a box-interval uncertainty set. Robust counterpart formulation is also associated with master and subproblems. Robust Benders decomposition is applied to address problems with convex goals and quasiconvex constraints in robust optimization. For all data parameters, this method is used to determine the best resilient solution in the feasible region. A manual example of this problem's calculation is provided, and the process is continued using production and operations management–quantitative methods (POM-QM) software.

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Chaerani, D., E. Rusyaman, Mahrudinda, A. Marcia, and A. Fridayana. "Adjustable robust counterpart optimization model for internet shopping online problem." Journal of Physics: Conference Series 1722 (January 2021): 012074. http://dx.doi.org/10.1088/1742-6596/1722/1/012074.

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Chaerani, D., E. Rusyaman, Mahrudinda, A. Marcia, and A. Fridayana. "Adjustable robust counterpart optimization model for internet shopping online problem." Journal of Physics: Conference Series 1722 (January 2021): 012074. http://dx.doi.org/10.1088/1742-6596/1722/1/012074.

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Sichau, Adrian, and Stefan Ulbrich. "A Second Order Approximation Technique for Robust Shape Optimization." Applied Mechanics and Materials 104 (September 2011): 13–22. http://dx.doi.org/10.4028/www.scientific.net/amm.104.13.

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We present a second order approximation for the robust counterpart of general uncertain nonlinear programs with state equation given by a partial di erential equation.We show how the approximated worst-case functions, which are the essential part of the approximated robust counterpart, can be formulated as trust-region problems that can be solved effciently using adjoint techniques. Further, we describe how the gradients of the worst-case functions can be computed analytically combining a sensitivity and an adjoint approach. This methodis applied to shape optimization in structural mechanics in order to obtain optimal solutions that are robust with respect to uncertainty in acting forces. Numerical results are presented.

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Mahrudinda, Mahrudinda, Diah Chaerani, and Endang Rusyaman. "Systematic literature review on adjustable robust counterpart for internet shopping optimization problem." International Journal of Data and Network Science 6, no. 2 (2022): 581–94. http://dx.doi.org/10.5267/j.ijdns.2021.11.006.

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Internet Shopping Optimization Problem (ISOP) is the application of optimization to online shopping activities of all complexity. The ISOP is useful for consumers in minimizing the cost of purchasing goods. This paper presents a bibliometric analysis of peer-reviewed papers based on ISOP topics by utilizing the R application program in the mapping. Overall, 101 papers (233 authors) in the Scopus database have used ISOP topics with research growth of 11.61% annually. The researcher presents a network of citations from productive authors, the impact of research, trends in terms that have been used, and shows a collaborative network of citations. Finally, the researcher presents the thematic analysis of the papers that apply the ISOP as a research topic and shows how the research forms clusters based on analytical solutions and numerical simulations that generate suggestions in finding the latest topics in the ISOP study. Another target for this paper is to produce review analysis results through Preferred Reporting Items for Systematic reviews and Meta Analyses (PRISMA). Through bibliometric and PRISMA analysis, it was found that the latest method in completing ISOP optimization is the ARC method. The ARC method in the ISOP is still little published among researchers in the world.

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Wang, Lei, and Hong Luo. "Robust Linear Programming with Norm Uncertainty." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/209239.

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We consider the linear programming problem with uncertainty set described byp,w-norm. We suggest that the robust counterpart of this problem is equivalent to a computationally convex optimization problem. We provide probabilistic guarantees on the feasibility of an optimal robust solution when the uncertain coefficients obey independent and identically distributed normal distributions.

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Kerdkaew, Jutamas, Rabian Wangkeeree, and Rattanaporn Wangkeeree. "Global optimality conditions and duality theorems for robust optimal solutions of optimization problems with data uncertainty, using underestimators." Numerical Algebra, Control & Optimization 12, no. 1 (2022): 93. http://dx.doi.org/10.3934/naco.2021053.

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In this paper, a robust optimization problem, which features a maximum function of continuously differentiable functions as its objective function, is investigated. Some new conditions for a robust KKT point, which is a robust feasible solution that satisfies the robust KKT condition, to be a global robust optimal solution of the uncertain optimization problem, which may have many local robust optimal solutions that are not global, are established. The obtained conditions make use of underestimators, which were first introduced by Jayakumar and Srisatkunarajah [<xref ref-type="bibr" rid="b1">1</xref>,<xref ref-type="bibr" rid="b2">2</xref>] of the Lagrangian associated with the problem at the robust KKT point. Furthermore, we also investigate the Wolfe type robust duality between the smooth uncertain optimization problem and its uncertain dual problem by proving the sufficient conditions for a weak duality and a strong duality between the deterministic robust counterpart of the primal model and the optimistic counterpart of its dual problem. The results on robust duality theorems are established in terms of underestimators. Additionally, to illustrate or support this study, some examples are presented.

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Yang, Feng. "Two-Stage Robust Counterpart Model for Humanitarian Logistics Management." Discrete Dynamics in Nature and Society 2021 (February 15, 2021): 1–15. http://dx.doi.org/10.1155/2021/6669691.

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In the early stages of a major public emergency, decision-makers were troubled by the timely distribution of a large number of donations. In order to distribute caring materials reasonably and efficiently, considering the transportation cost and time delay cost, this paper takes the humanitarian logistics management as an example to study the scheduling problem. Based on the actual situation of insufficient supply during the humanitarian logistics management, this paper using optimization theory establishes a two-stage stochastic chance constrained (TS-SCC) model. In addition, due to the randomness of emergency occurrence and uncertainty of demand, the TS-SCC model is further transformed into the two-stage robust counterpart (TS-RC) model. At the same time, the validity of the model and the efficiency of the algorithm are verified by simulations. The result shows that the model and algorithm constructed are capable to obtain the distribution scheme of caring materials even in worst case. In the TS-BRC (with box set) model, the logistics service level increased from 89.83% to 93.21%, while in the TS-BPRC (with mixed box and polyhedron set) model, it increases from 90.32% to 94.96%. Besides, the model built in this paper can provide a more reasonable dispatching plan according to the actual situation of caring material supply.

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Wu, Hsien-Chung. "Numerical Method for Solving the Robust Continuous-Time Linear Programming Problems." Mathematics 7, no. 5 (May 16, 2019): 435. http://dx.doi.org/10.3390/math7050435.

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A robust continuous-time linear programming problem is formulated and solved numerically in this paper. The data occurring in the continuous-time linear programming problem are assumed to be uncertain. In this paper, the uncertainty is treated by following the concept of robust optimization, which has been extensively studied recently. We introduce the robust counterpart of the continuous-time linear programming problem. In order to solve this robust counterpart, a discretization problem is formulated and solved to obtain the ϵ -optimal solution. The important contribution of this paper is to locate the error bound between the optimal solution and ϵ -optimal solution.

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Chaerani, Diah, Muttaqien Rodhiya Robbi, Elis Hertini, Endang Rusyaman, and Erick Paulus. "Determining Flood Protection Strategy with Uncertain Parameter Using Adjustable Robust Counterpart Methodology." Jurnal ILMU DASAR 21, no. 1 (January 21, 2020): 27. http://dx.doi.org/10.19184/jid.v21i1.10780.

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Flooding is a natural disaster that often occurs, it is not surprising that floods are one of the problems that must be resolved in various countries, one of which is Indonesia. Flood is very detrimental to the public because the impact could be the loss of material and non-material. A flood protection system is needed and must be managed properly. This aims in management of flood protection systems often requires efficient cost control strategies that are the lowest possible long-term costs, but still meets the flood protection standards imposed by regulators in all plans. In this paper a flood protection strategy is modeled using Adjustable Robust Optimization. In this approach, there are two kinds of variables that must be decided, i.e., adjustable and non-adjustable variables. A numerical simulation is presented using Scilab Software. Keywords: Flood Protection Strategy, Uncertainty, Adjustable Robust Optimization, Scilab Software.

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Chaerani, Diah, Siti Rabiatul Adawiyah, and Eman Lesmana. "Robust Optimization Model for Bi-objective Emergency Medical Service Design Problem with Demand Uncertainty." Jurnal Teknik Industri 20, no. 2 (January 12, 2019): 95. http://dx.doi.org/10.9744/jti.20.2.95-104.

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Bi-objective Emergency Medical Service Design Problem is a problem to determining the location of the station Emergency Medical Service among all candidate station location, the determination of the number of emergency vehicles allocated to stations being built so as to serve medical demand. This problem is a multi-objective problem that has two objective functions that minimize cost and maximize service. In real case there is often uncertainty in the model such as the number of demand. To deal the uncertainty on the bi-objective emergency medical service problem is using Robust Optimization which gave optimal solution even in the worst case. Model Bi-objective Emergency Medical Service Design Problem is formulated using Mixed Integer Programming. In this research, Robust Optimization is formulated for Bi-objective Emergency Medical Service Design Problem through Robust Counterpart formulation by assuming uncertainty in demand is box uncertainty and ellipsoidal uncertainty set. We show that in the case of bi-objective optimization problem, the robust counterpart remains computationally tractable. The example is performed using Lexicographic Method and Branch and Bound Method to obtain optimal solution.

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Ma, Changxi, Wei Hao, Ruichun He, and Bahman Moghimi. "A Multiobjective Route Robust Optimization Model and Algorithm for Hazmat Transportation." Discrete Dynamics in Nature and Society 2018 (October 9, 2018): 1–12. http://dx.doi.org/10.1155/2018/2916391.

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Aiming at route optimization problem of hazardous materials transportation in uncertain environment, this paper presents a multiobjective robust optimization model by taking robust control parameters into consideration. The objective of the model is to minimize not only transportation risk but also transportation time, and a robust counterpart of the model is introduced through applying the Bertsimas-Sim robust optimization theory. Moreover, a fuzzy C-means clustering-particle swarm optimization (FCMC-PSO) algorithm is designed, and the FCMC algorithm is used to cluster the demand points. In addition the PSO algorithm with the adaptive archives grid is used to calculate the robust optimization route of hazmat transportation. Finally, the computational results show the multiobjective route robust optimization model with 3 centers and 20 demand points’ sample studied and FCMC-PSO algorithm for hazmat transportation can obtain different robustness Pareto solution sets. As a result, this study will provide basic theory support for hazmat transportation safeguarding.

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Li, Zukui, and Christodoulos A. Floudas. "A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: III. Improving the Quality of Robust Solutions." Industrial & Engineering Chemistry Research 53, no. 33 (August 5, 2014): 13112–24. http://dx.doi.org/10.1021/ie501898n.

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Kaoud, Essam, Mohammad A. M. Abdel-Aal, Tatsuhiko Sakaguchi, and Naoki Uchiyama. "Robust Optimization for a Bi-Objective Green Closed-Loop Supply Chain with Heterogeneous Transportation System and Presorting Consideration." Sustainability 14, no. 16 (August 18, 2022): 10281. http://dx.doi.org/10.3390/su141610281.

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In this study, we propose a robust bi-objective optimization model of the green closed-loop supply chain network considering presorting, a heterogeneous transportation system, and carbon emissions. The proposed model is an uncertain bi-objective mixed-integer linear optimization model that maximizes profit and minimizes carbon emissions by considering uncertain costs, selling price, and carbon emissions. The robust optimization approach is implemented using the combined interval and polyhedral, “Interval+ Polyhedral,” uncertainty set to develop the robust counterpart of the proposed model. Robust Pareto optimal solutions are obtained using a lexicographic weighted Tchebycheff optimization approach of the bi-objective model. Intensive computational experiments are conducted and a robust Pareto optimal front is obtained with a probability guarantee that the constraints containing uncertain parameters are not violated (constraint satisfaction).

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Wang, Lei, Xing Wang, and Nan-jing Huang. "Tractable Approximation to Robust Nonlinear Production Frontier Problem." Abstract and Applied Analysis 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/965835.

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Robust optimization is a rapidly developing methodology for handling optimization problems affected by the uncertain-but-bounded data perturbations. In this paper, we consider the nonlinear production frontier problem where the traditional expected linear cost minimization objective is replaced by one that explicitly addresses cost variability. We propose a robust counterpart for the nonlinear production frontier problem that preserves the computational tractability of the nominal problem. We also provide a guarantee on the probability that the robust solution is feasible when the uncertain coefficients obey independent and identically distributed normal distributions.

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Lin, Fengming, Xiaolei Fang, and Zheming Gao. "Distributionally Robust Optimization: A review on theory and applications." Numerical Algebra, Control & Optimization 12, no. 1 (2022): 159. http://dx.doi.org/10.3934/naco.2021057.

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In this paper, we survey the primary research on the theory and applications of distributionally robust optimization (DRO). We start with reviewing the modeling power and computational attractiveness of DRO approaches, induced by the ambiguity sets structure and tractable robust counterpart reformulations. Next, we summarize the efficient solution methods, out-of-sample performance guarantee, and convergence analysis. Then, we illustrate some applications of DRO in machine learning and operations research, and finally, we discuss the future research directions.

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Jiang, Dong Qing, and Qun Xiong Zhu. "Research on Emergency Supplies Scheduling Problem with Robust Optimization Approach." Advanced Materials Research 694-697 (May 2013): 3462–65. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.3462.

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This paper study multiple warehouses emergency supplies dispatch problem. Emergency dispatch vehicles route problem is different from traditional vehicle route problem, it does not take minimization freight, driving distance or driving total time as the goal, but take a minimization unmet needs and delay time as the goal. We use robust operator to transfer multiple warehouses emergency dispatch model into robust counterpart model, and verifying the correctness of the model with number experiment.

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Chaerani, Diah, Athaya Zahrani Irmansyah, Tomy Perdana, and Nurul Gusriani. "Contribution of robust optimization on handling agricultural processed products supply chain problem during Covid-19 pandemic." Uncertain Supply Chain Management 10, no. 1 (2022): 239–54. http://dx.doi.org/10.5267/j.uscm.2021.9.004.

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This research aims to show how decision sciences can make a significant contribution on handling the supply chain problem during Covid-19 Pandemic. The paper discusses how robust optimization handles uncertain demand in agricultural processed products supply chain problems within two scenarios during the pandemic situation, i.e., the large-scale social distancing and partial social distancing. The study assumes that demand and production capacity are uncertain during a pandemic situation. Robust counterpart methodology is employed to obtain the robust optimal solution. To this end, the uncertain data is assumed to lie within a polyhedral uncertainty set. The result shows that the robust counterpart model is a computationally tractable through linear programming problem. Numerical experiment is presented for the Bandung area with a case on sugar and cooking oil that is the most influential agricultural processed products besides the main staple food of the Indonesian people, rice.

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Du, Bo, and Hong Zhou. "A Robust Optimization Approach to the Multiple Allocation p-Center Facility Location Problem." Symmetry 10, no. 11 (November 2, 2018): 588. http://dx.doi.org/10.3390/sym10110588.

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In this study, we apply a robust optimization approach to a p-center facility location problem under uncertainty. Based on a symmetric interval and a multiple allocation strategy, we use three types of uncertainty sets to formulate the robust problem: box uncertainty, ellipsoidal uncertainty, and cardinality-constrained uncertainty. The equivalent robust counterpart models can be solved to optimality using Gurobi. Comprehensive numerical experiments have been conducted by comparing the performance of the different robust models, which illustrate the pattern of robust solutions, and allocating a demand node to multiple facilities can reduce the price of robustness, and reveal that alternative models of uncertainty can provide robust solutions with different conservativeness.

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Kocuk, Burak. "Conic reformulations for Kullback-Leibler divergence constrained distributionally robust optimization and applications." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 11, no. 2 (April 19, 2021): 139–51. http://dx.doi.org/10.11121/ijocta.01.2021.001001.

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In this paper, we consider a Kullback-Leibler divergence constrained distributionally robust optimization model. This model considers an ambiguity set that consists of all distributions whose Kullback-Leibler divergence to an empirical distribution is bounded. Utilizing the fact that this divergence measure has an exponential cone representation, we obtain the robust counterpart of the Kullback-Leibler divergence constrained distributionally robust optimization problem as a dual exponential cone constrained program under mild assumptions on the underlying optimization problem. The resulting conic reformulation of the original optimization problem can be directly solved by a commercial conic programming solver. We specialize our generic formulation to two classical optimization problems, namely, the Newsvendor Problem and the Uncapacitated Facility Location Problem. Our computational study in an out-of-sample analysis shows that the solutions obtained via the distributionally robust optimization approach yield significantly better performance in terms of the dispersion of the cost realizations while the central tendency deteriorates only slightly compared to the solutions obtained by stochastic programming.

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Muslihin, Khoirunnisa Rohadatul Aisy, Endang Rusyaman, and Diah Chaerani. "Conic Duality for Multi-Objective Robust Optimization Problem." Mathematics 10, no. 21 (October 24, 2022): 3940. http://dx.doi.org/10.3390/math10213940.

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Duality theory is important in finding solutions to optimization problems. For example, in linear programming problems, the primal and dual problem pairs are closely related, i.e., if the optimal solution of one problem is known, then the optimal solution for the other problem can be obtained easily. In order for an optimization problem to be solved through the dual, the first step is to formulate its dual problem and analyze its characteristics. In this paper, we construct the dual model of an uncertain linear multi-objective optimization problem as well as its weak and strong duality criteria via conic duality. The multi-objective form of the problem is solved using the utility function method. In addition, the uncertainty is handled using robust optimization with ellipsoidal and polyhedral uncertainty sets. The robust counterpart formulation for the two uncertainty sets belongs to the conic optimization problem class; therefore, the dual problem can be built through conic duality. The results of the analysis show that the dual model obtained meets the weak duality, while the criteria for strong duality are identified based on the strict feasibility, boundedness, and solvability of the primal and dual problems.

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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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Munari, Pedro, Alfredo Moreno, Jonathan De La Vega, Douglas Alem, Jacek Gondzio, and Reinaldo Morabito. "The Robust Vehicle Routing Problem with Time Windows: Compact Formulation and Branch-Price-and-Cut Method." Transportation Science 53, no. 4 (July 2019): 1043–66. http://dx.doi.org/10.1287/trsc.2018.0886.

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We address the robust vehicle routing problem with time windows (RVRPTW) under customer demand and travel time uncertainties. As presented thus far in the literature, robust counterparts of standard formulations have challenged general-purpose optimization solvers and specialized branch-and-cut methods. Hence, optimal solutions have been reported for small-scale instances only. Additionally, although the most successful methods for solving many variants of vehicle routing problems are based on the column generation technique, the RVRPTW has never been addressed by this type of method. In this paper, we introduce a novel robust counterpart model based on the well-known budgeted uncertainty set, which has advantageous features in comparison with other formulations and presents better overall performance when solved by commercial solvers. This model results from incorporating dynamic programming recursive equations into a standard deterministic formulation and does not require the classical dualization scheme typically used in robust optimization. In addition, we propose a branch-price-and-cut method based on a set partitioning formulation of the problem, which relies on a robust resource-constrained elementary shortest path problem to generate routes that are robust regarding both vehicle capacity and customer time windows. Computational experiments using Solomon’s instances show that the proposed approach is effective and able to obtain robust solutions within a reasonable running time. The results of an extensive Monte Carlo simulation indicate the relevance of obtaining robust routes for a more reliable decision-making process in real-life settings.

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Luo, Xiao, Chi-yung Chung, Hongming Yang, and Xiaojiao Tong. "Robust Optimization-Based Generation Self-Scheduling under Uncertain Price." Mathematical Problems in Engineering 2011 (2011): 1–17. http://dx.doi.org/10.1155/2011/497014.

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This paper considers generation self-scheduling in electricity markets under uncertain price. Based on the robust optimization (denoted as RO) methodology, a new self-scheduling model, which has a complicated max-min optimization structure, is set up. By using optimal dual theory, the proposed model is reformulated to an ordinary quadratic and quadratic cone programming problems in the cases of box and ellipsoidal uncertainty, respectively. IEEE 30-bus system is used to test the new model. Some comparisons with other methods are done, and the sensitivity with respect to the uncertain set is analyzed. Comparing with the existed uncertain self-scheduling approaches, the new method has twofold characteristics. First, it does not need a prediction of distribution of random variables and just requires an estimated value and the uncertain set of power price. Second, the counterpart of RO corresponding to the self-scheduling is a simple quadratic or quadratic cone programming. This indicates that the reformulated problem can be solved by many ordinary optimization algorithms.

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Wu, Hsien-Chung. "Extended Form of Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices." Axioms 11, no. 5 (May 1, 2022): 211. http://dx.doi.org/10.3390/axioms11050211.

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An extended form of robust continuous-time linear programming problem with time-dependent matrices is formulated in this paper. This complicated problem is studied theoretically in this paper. We also design a computational procedure to solve this problem numerically. The desired data that appeared in the problem are considered to be uncertain quantities, which are treated according to the concept of robust optimization. A discretization problem of the robust counterpart is formulated and solved to obtain the ϵ-optimal solutions.

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Yuliza, Evi, Fitri Maya, and Siti Suzlin Supadi. "Heuristic Approach For Robust Counterpart Open Capacitated Vehicle Routing Problem With Time Windows." Science and Technology Indonesia 6, no. 2 (April 21, 2021): 53–57. http://dx.doi.org/10.26554/sti.2021.6.2.53-57.

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Garbage is one of the environmental problems. The process of transporting garbage sometimes occurs delays such as congestion and engine failure. Robust optimization model called a robust counterpart open capacitated vehicle routing problem (RCOCVRP) with time windows was formulated to get over this delays. This model has formulated with the limitation of vehicle capacity and time windows with an uncertainty of waste volume and travel time. The RCOCVRP model with time windows is solved by a heuristic approach. The heuristic approach used to solve the RCOCVRP model with time windows uses the nearest neighbor and the cheapest insertion heuristic algorithm. The RCOCVRP with time windows model is implemented on the problem of transporting waste in Sako sub-district. The solutions of these two heuristic approaches are compared and analyzed. The RCOCVRP model with time windows to optimize the route problems of waste transport vehicles that is solved using the cheapest insertion heuristics algorithm is more effective than the nearest neighbor method.

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Jia, Ru-Ru, and Xue-Jie Bai. "Robust Optimization Approximation for Ambiguous P-Model and Its Application." Mathematical Problems in Engineering 2018 (July 18, 2018): 1–14. http://dx.doi.org/10.1155/2018/5203127.

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Robust optimization is a powerful and relatively novel methodology to cope with optimization problems in the presence of uncertainty. The positive aspect of robust optimization approach is its computational tractability that attracts more and more attention. In this paper, we focus on an ambiguous P-model where probability distributions are partially known. We discuss robust counterpart (RC) of uncertain linear constraints under two refined uncertain sets by robust approach and further find the safe tractable approximations of chance constraints in the ambiguous P-model. Because of the probability constraints embedded in the ambiguous P-model, it is computationally intractable. The advantage of our approach lies in choosing an implicit way to treat stochastic uncertainty models instead of solving them directly. The process above can enable the transformation of proposed P-model to a tractable deterministic one under the refined uncertainty sets. A numerical example about portfolio selection demonstrates that the ambiguous P-model can help the decision maker to determine the optimal investment proportions of various stocks. Sensitivity analyses explore the trade-off between optimization and robustness by adjusting parameter values. Comparison study is conducted to validate the benefit of our ambiguous P-model.

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Sengupta, Raghu Nandan, and Rakesh Kumar. "Robust and Reliable Portfolio Optimization Formulation of a Chance Constrained Problem." Foundations of Computing and Decision Sciences 42, no. 1 (February 1, 2017): 83–117. http://dx.doi.org/10.1515/fcds-2017-0004.

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AbstractWe solve a linear chance constrained portfolio optimization problem using Robust Optimization (RO) method wherein financial script/asset loss return distributions are considered as extreme valued. The objective function is a convex combination of portfolio’s CVaR and expected value of loss return, subject to a set of randomly perturbed chance constraints with specified probability values. The robust deterministic counterpart of the model takes the form of Second Order Cone Programming (SOCP) problem. Results from extensive simulation runs show the efficacy of our proposed models, as it helps the investor to (i) utilize extensive simulation studies to draw insights into the effect of randomness in portfolio decision making process, (ii) incorporate different risk appetite scenarios to find the optimal solutions for the financial portfolio allocation problem and (iii) compare the risk and return profiles of the investments made in both deterministic as well as in uncertain and highly volatile financial markets.

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Li, Zukui, Qiuhua Tang, and Christodoulos A. Floudas. "A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: II. Probabilistic Guarantees on Constraint Satisfaction." Industrial & Engineering Chemistry Research 51, no. 19 (May 4, 2012): 6769–88. http://dx.doi.org/10.1021/ie201651s.

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Guzman, Yannis A., Logan R. Matthews, and Christodoulos A. Floudas. "New a priori and a posteriori probabilistic bounds for robust counterpart optimization: I. Unknown probability distributions." Computers & Chemical Engineering 84 (January 2016): 568–98. http://dx.doi.org/10.1016/j.compchemeng.2015.09.014.

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Yang, Feng, Zhong Wu, Xiaoyan Teng, and Shaojian Qu. "Robust Counterpart Models for Fresh Agricultural Product Routing Planning Considering Carbon Emissions and Uncertainty." Sustainability 14, no. 22 (November 13, 2022): 14992. http://dx.doi.org/10.3390/su142214992.

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Cold chain transportation guarantees the quality of fresh agricultural products in people’s lives, but it comes with huge environmental costs. In order to improve transportation efficiency and reduce environmental impact, it is crucial to quantify the routing planning problem under the impact of carbon emissions. Considering fixed costs, transportation costs, and carbon emission costs, we propose a mixed integer linear programming model with the aim of minimizing costs. However, in real conditions, uncertainty poses a great challenge to the rationality of routing planning. The uncertainty is described through robust optimization theory and several robust counterpart models are proposed. We take the actual transportation enterprises as the research object and verify the validity of the model by constructing a Benders decomposition algorithm. The results reveal that the increase in uncertainty parameter volatility forces enterprises to increase uncontrollable transportation costs and reduce logistics service levels. An increase in the level of security parameters could undermine the downward trend and reduce 1.4% of service level losses.

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Yuliza, Evi, Fitri Maya Puspita, and Siti Suzlin Supadi. "The robust counterpart open capacitated vehicle routing problem with time windows on waste transport problems." Bulletin of Electrical Engineering and Informatics 9, no. 5 (October 1, 2020): 2074–81. http://dx.doi.org/10.11591/eei.v9i5.2439.

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The optimum route for garbage transport vehicles is restricted by vehicle capacity and time windows that the garbage transport vehicle starts at the origin and does not return to the origin. The problem of transporting waste routes is a robust optimization problem where the amount of waste in an area and travel time is uncertain. In the real world, traffic jams and vehicle engine damage can cause delays. This paper proposes the robust counterpart open capacitated vehicle routing problem (denoted by RCOCVRP) with soft time windows model. The aim of RCOCVRP with soft time windows model is to find schedule and optimum route of transporting waste. This model calculation uses LINGO software and GAMS software. Finally for the evaluation of the RCOCVRP model with soft time windows on the proposed waste transportation problem is conducted so that it hasa feasible solution.

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Yu, Wuyang. "Robust Model of Discrete Competitive Facility Location Problem with Partially Proportional Rule." Mathematical Problems in Engineering 2020 (January 21, 2020): 1–12. http://dx.doi.org/10.1155/2020/3107431.

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When consumers faced with the choice of competitive chain facilities that offer exclusive services, current rules cannot describe these customers’ behaviors very well. So we propose a partially proportional rule to represent this kind of customer behavior. In addition, the exact demands of customers in many real-world environments are often difficult to determine. This is contradicting to the assumption in most studies of the competitive facility location problem. For the competitive facility location problem with the partially proportional rule, we establish a robust optimization model to handle the uncertainty of customers’ demands. We propose two methods to solve the robust model by studying the properties of the counterpart problem. The first method MIP is presented by solving a mixed-integer optimization model of the counterpart problem directly. The second method SAS is given by embedding a sorting subalgorithm into the simulated annealing framework, in which the sorting subalgorithm can easily solve the subproblem. The effects of the budget and the robust control parameter to the location scheme are analyzed in a quasi-real example. The result shows that changes in the robust control parameter can affect the customer demands that were captured by the new entrants, thereby changing the optimal solution for facility location. In addition, there is a threshold of the robust control parameter for any given budget. Only when the robust control parameter is larger than this threshold, the market share captured by the new entering firm increases with the increases of this parameter. Finally, numerical experiments show the superiority of the algorithm SAS in large-scare competitive facility location problems.

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Perelman, Lina, Mashor Housh, and Avi Ostfeld. "Least-cost design of water distribution systems under demand uncertainty: the robust counterpart approach." Journal of Hydroinformatics 15, no. 3 (January 31, 2013): 737–50. http://dx.doi.org/10.2166/hydro.2013.138.

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In this study, a non-probabilistic robust counterpart (RC) approach is demonstrated and applied to the least-cost design/rehabilitation problem of water distribution systems (WDSs). The uncertainty of the information is described by a deterministic user-defined ellipsoidal uncertainty set that implies the level of risk. The advantages of the RC approach on previous modelling attempts to include uncertainty are in making no assumptions about the probability density functions of the uncertain parameters and their interdependencies, having no requirements on the construction of a representative sample of scenarios, and the deterministic equivalent problem preserves the same size (i.e. computational complexity) as the original problem. The RC is coupled with the cross-entropy heuristic optimization technique for seeking robust solutions. The methodology is demonstrated on an illustrative example and on the Hanoi network. The results show considerable promise of the proposed approach to incorporate uncertainty in the least-cost design problem of WDSs. Further research is warranted to extend the model for more complex WDSs, incorporate extended period simulations, and develop RC schemes for other WDSs related management problems.

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Hayelom, Assefa, and Avi Ostfeld. "Network Subsystems for Robust Design Optimization of Water Distribution Systems." Water 14, no. 15 (August 7, 2022): 2443. http://dx.doi.org/10.3390/w14152443.

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The optimal design of WDS has been extensively researched for centuries, but most of these studies have employed deterministic optimization models, which are premised on the assumption that the parameters of the design are perfectly known. Given the inherently uncertain nature of many of the WDS design parameters, the results derived from such models may be infeasible or suboptimal when they are implemented in reality due to parameter values that differ from those assumed in the model. Consequently, it is necessary to introduce some uncertainty in the design parameters and find more robust solutions. Robust counterpart optimization is one of the methods used to deal with optimization under uncertainty. In this method, a deterministic data set is derived from an uncertain problem, and a solution is computed such that it remains viable for any data realization within the uncertainty bound. This study adopts the newly emerging robust optimization technique to account for the uncertainty associated with nodal demand in designing water distribution systems using the subsystem-based two-stage approach. Two uncertainty data models with ellipsoidal uncertainty set in consumer demand are examined. The first case, referred to as the uncorrelated problem, considers the assumption that demand uncertainty only affects the mass balance constraint, while the second case, referred to as the correlated case, assumes uncertainty in demand and also propagates to the energy balance constraint.

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Kolvenbach, Philip, Stefan Ulbrich, Martin Krech, and Peter Groche. "Robust Design of a Smart Structure under Manufacturing Uncertainty via Nonsmooth PDE-Constrained Optimization." Applied Mechanics and Materials 885 (November 2018): 131–44. http://dx.doi.org/10.4028/www.scientific.net/amm.885.131.

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We consider the problem of finding the optimal shape of a force-sensing element which is integrated into a tubular structure. The goal is to make the sensor element sensitive to specific forces and insensitive to other forces. The problem is stated as a PDE-constrained minimization program with both nonconvex objective and nonconvex constraints. The optimization problem depends on uncertain parameters, because the manufacturing process of the structures underlies uncertainty, which causes unwanted deviations in the sensory properties. In order to maintain the desired properties of the sensor element even in the presence of uncertainty, we apply a robust optimization method to solve the uncertain program.The objective and constraint functions are continuous but not differentiable with respect to the uncertain parameters, so that existing methods for robust optimization cannot be applied. Therefore, we consider the nonsmooth robust counterpart formulated in terms of the worst-case functions, and show that subgradients can be computed efficiently. We solve the problem with a BFGS--SQP method for nonsmooth problems recently proposed by Curtis, Mitchell and Overton.

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Soltani, Roya, Jalal Safari, and Seyed Jafar Sadjadi. "Robust counterpart optimization for the redundancy allocation problem in series-parallel systems with component mixing under uncertainty." Applied Mathematics and Computation 271 (November 2015): 80–88. http://dx.doi.org/10.1016/j.amc.2015.08.069.

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Wang, Congke, Yankui Liu, Peiyu Zhang, and Guoqing Yang. "Two-Stage Distributionally Robust Optimization for a Two-Allocation p-Hub Median Problem." Journal of Uncertain Systems 14, no. 01 (March 2021): 2150004. http://dx.doi.org/10.1142/s1752890921500045.

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This paper presents a novel two-stage distributionally robust optimization model of the two-allocation p-hub median problem with different hub link scales. With the objective of minimizing overall costs of building and operating the hub network, the choices of hub locations and hub link scales are decided in the first stage, while the optimal flows are determined in the second stage once the uncertain demands have been realized. Before establishing the hub network, we just have partial distribution information about the uncertain flow demands, which can be described by a given perturbation set based on the historical information. Due to the ambiguous distributions leading to a computationally intractable model, we reformulate the proposed model into the tractable robust counterpart forms under two types of uncertainty sets (Box[Formula: see text]ellipsoidal perturbation set and Generalized ellipsoidal perturbation set). Finally, to demonstrate the effectiveness and applicability for our model, we conduct a case study for the express network system in the Beijing–Tianjin–Hebei region.

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Subramanyam, Anirudh, Panagiotis P. Repoussis, and Chrysanthos E. Gounaris. "Robust Optimization of a Broad Class of Heterogeneous Vehicle Routing Problems Under Demand Uncertainty." INFORMS Journal on Computing 32, no. 3 (July 2020): 661–81. http://dx.doi.org/10.1287/ijoc.2019.0923.

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This paper studies robust variants of an extended model of the classical heterogeneous vehicle routing problem (HVRP), where a mixed fleet of vehicles with different capacities, availabilities, fixed costs, and routing costs is used to serve customers with uncertain demand. This model includes, as special cases, all variants of the HVRP studied in the literature with fixed and unlimited fleet sizes, accessibility restrictions at customer locations, and multiple depots. Contrary to its deterministic counterpart, the goal of the robust HVRP is to determine a minimum cost set of routes and fleet composition that remains feasible for all demand realizations from a prespecified uncertainty set. To solve this problem, we develop robust versions of classical node and edge exchange neighborhoods that are commonly used in local search and establish that efficient evaluation of the local moves can be achieved for five popular classes of uncertainty sets. The proposed local search is then incorporated in a modular fashion within two metaheuristic algorithms to determine robust HVRP solutions. The quality of the metaheuristic solutions is quantified using an integer programming model that provides lower bounds on the optimal solution. An extensive computational study on literature benchmarks shows that the proposed methods allow us to obtain high-quality robust solutions for different uncertainty sets and with minor additional effort compared with deterministic solutions.

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Li, Hongbo, Zhe Xu, Li Xiong, and Yinbin Liu. "Robust Proactive Project Scheduling Model for the Stochastic Discrete Time/Cost Trade-Off Problem." Discrete Dynamics in Nature and Society 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/586087.

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We study the project budget version of the stochastic discrete time/cost trade-off problem (SDTCTP-B) from the viewpoint of the robustness in the scheduling. Given the project budget and a set of activity execution modes, each with uncertain activity time and cost, the objective of the SDTCTP-B is to minimize the expected project makespan by determining each activity’s mode and starting time. By modeling the activity time and cost using interval numbers, we propose a proactive project scheduling model for the SDTCTP-B based on robust optimization theory. Our model can generate robust baseline schedules that enable a freely adjustable level of robustness. We convert our model into its robust counterpart using a form of the mixed-integer programming model. Extensive experiments are performed on a large number of randomly generated networks to validate our model. Moreover, simulation is used to investigate the trade-off between the advantages and the disadvantages of our robust proactive project scheduling model.

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Yılmaz, Ömer Faruk. "Robust optimization for U-shaped assembly line worker assignment and balancing problem with uncertain task times." Croatian Operational Research Review 11, no. 2 (2020): 229–39. http://dx.doi.org/10.17535/crorr.2020.0018.

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Awareness of the importance of U-shaped assembly line balancing problems is all on the rise. In the U-shaped assembly line, balancing is affected by the uncertainty associated with the assembly task times. Therefore, it is crucial to develop an approach to respond to the uncertainty caused by the task times. When the great majority of existing literature related to uncertainty in the assembly line is considered, it is observed that the U-shaped assembly line balancing problem under uncertainty is scarcely investigated. That being the case, we aim to fill this research gap by proposing a robust counterpart formulation for the addressed problem. In this study, a robust optimization model is developed for the U-shaped assembly line worker assignment and balancing problem (UALWABP) to cope with the task time uncertainty characterized by a combined interval and polyhedral uncertainty set. A real case study is conducted through data from a company producing water meters.

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Puspita, Fitri Maya, Yusuf Hartono, Nadia Zuliaty Syaputri, Evi Yuliza, and Weni Dwi Pratiwi. "Robust Counterpart Open Capacitated Vehicle Routing (RC-OCVRP) Model in Optimization of Garbage Transportation in District Sako and Sukarami, Palembang City." International Journal of Electrical and Computer Engineering (IJECE) 8, no. 6 (December 1, 2018): 4382. http://dx.doi.org/10.11591/ijece.v8i6.pp4382-4390.

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In this paper, the Robust Counterpart Open Capacitation Vehicle Rounting Problem (RC-OCVRP) Model has been established to optimize waste transport in districts Sako and districts Sukarami, Palembang City. This model is completed with the aid of LINGO 13.0 by using Branch and Bound solver to get the optimum route. For Sako districs, the routes are as follows: working area 1 is TPS 1-TPS 2-TPS 3-TPA with distance 53.39 km, working area 2 is TPS 1-TPS 2-TPS 3-TPA with distance 48.14 km, working area 3 is TPS 1-TPA with a distance of 22.98 km, and working area 4 is TPS 1-TPS 2-TPS 3-TPS 4-TPA with 45.45 km distance, and obtained the optimum route in Sukarami districts is as follows: working area 1 is TPS 1-TPS 2-TPA 44.39 km, working area 2 is TPS 1-TPS 2-TPS 3-TPA with distance 49.32 km, working area 3 is TPS 1-TPS 3-TPA-TPS 2-TPA with distance 58.57 km, and working area 4 is TPS 1-TPA with a distance of 24.07 km, working area 5 is TPS 1-TPS 3-TPA-TPS 2-TPS 4-TPA with a distance of 77.66 km, and working area 6 is a TPS 1-TPS 2-TPS 3-TPA with a distante 44.94 km.

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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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Asgharizadeh, Ezzatollah, Mahsa Kadivar, Mohammad Noroozi, Vahid Mottaghi, Hamed Mohammadi, and Adel Pourghader Chobar. "The intelligent Traffic Management System for Emergency Medical Service Station Location and Allocation of Ambulances." Computational Intelligence and Neuroscience 2022 (July 7, 2022): 1–9. http://dx.doi.org/10.1155/2022/2340856.

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In the present study, the optimization of medical services considering the role of intelligent traffic management is of concern. In this regard, a two-objective mathematical model of a medical emergency system is assessed in order to determine the location of emergency stations and determine the required number of ambulances to be allocated to the station. The objective functions are the maximization of covering the emergency demands and minimization of total costs. Moreover, the use of an intelligent traffic management system to speed up the ambulance is addressed. In this regard, the proposed two-objective mathematical model has been formulated, and a robust counterpart formulation under uncertainty is applied. In the proposed method, the values of the objective function increase as the problem becomes wider and, with a slight difference in large dimensions, converge in terms of the solution. The numerical results indicate that, as the problem's complexity increases, the robust optimization method is still effective because, with the increasing complexity of the problem, it can still solve large-scale problems in a reasonable time. Moreover, the difference between the value of the objective function in the proposed method and the presence of uncertainty parameters is very small and, in large dimensions, is quite logical and negligible. The sensitivity analysis shows that, with increasing demand, both the number of ambulances required and the amount of objective function have increased significantly.

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Guzman, Yannis A., Logan R. Matthews, and Christodoulos A. Floudas. "New a priori and a posteriori probabilistic bounds for robust counterpart optimization: II. A priori bounds for known symmetric and asymmetric probability distributions." Computers & Chemical Engineering 101 (June 2017): 279–311. http://dx.doi.org/10.1016/j.compchemeng.2016.07.002.

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Altaf, Faisal, Ching-Lung Chang, Naveed Ishtiaq Chaudhary, Khalid Mehmood Cheema, Muhammad Asif Zahoor Raja, Chi-Min Shu, and Ahmad H. Milyani. "Novel Fractional Swarming with Key Term Separation for Input Nonlinear Control Autoregressive Systems." Fractal and Fractional 6, no. 7 (June 22, 2022): 348. http://dx.doi.org/10.3390/fractalfract6070348.

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In recent decades, fractional order calculus has become an important mathematical tool for effectively solving complex problems through better modeling with the introduction of fractional differential/integral operators; fractional order swarming heuristics are also introduced and applied for better performance in different optimization tasks. This study investigates the nonlinear system identification problem of the input nonlinear control autoregressive (IN-CAR) model through the novel implementation of fractional order particle swarm optimization (FO-PSO) heuristics; further, the key term separation technique (KTST) is introduced in the FO-PSO to solve the over-parameterization issue involved in the parameter estimation of the IN-CAR model. The proposed KTST-based FO-PSO, i.e., KTST-FOPSO accurately estimates the parameters of an unknown IN-CAR system with robust performance in cases of different noise scenarios. The performance of the KTST-FOPSO is investigated exhaustively for different fractional orders as well as in comparison with the standard counterpart. The results of statistical indices through Monte Carlo simulations endorse the reliability and stability of the KTST-FOPSO for IN-CAR identification.

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Kamarudin, Muhammad Nizam, Sahazati Md Rozali, T. Sutikno, and Abdul Rashid Husain. "New robust bounded control for uncertain nonlinear system using mixed backstepping and lyapunov redesign." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 2 (April 1, 2019): 1090. http://dx.doi.org/10.11591/ijece.v9i2.pp1090-1099.

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This paper presents a new robust bounded control law to stabilize uncertain nonlinear system with time varying disturbance. The design idea comes from the advantages of backstepping with Lyapunov redesign, which avoid the needs of fast switching of discontinuous control law offered by its counterpart - a variable structure control. We reduce the conservatism in the design process where the control law can be flexibly chosen from Lyapunov function, hence avoiding the use of convex optimization via linear matrix inequality (LMI) in which the feasibility is rather hard to be obtained. For this work, we design two type control algorithms namely normal control and bounded control. As such, our contribution is the introduction of a new bounded control law that can avoid excessive control energy, high magnitude chattering in control signal and small oscillation in stabilized states. Computation of total energy for both control laws confirmed that the bounded control law can stabilize with less enegry consumption. We also use Euler's approximation to compute average power for both control laws. The robustness of the proposed controller is achieved via saturation-like function in Lyapunov redesign, and hence guaranting asymptotic stability of the closed-loop system.

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Guzman, Yannis A., Logan R. Matthews, and Christodoulos A. Floudas. "New a priori and a posteriori probabilistic bounds for robust counterpart optimization: III. Exact and near-exact a posteriori expressions for known probability distributions." Computers & Chemical Engineering 103 (August 2017): 116–43. http://dx.doi.org/10.1016/j.compchemeng.2017.03.001.

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Journal articles on the topic 'Robust Counterpart Optimization'

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