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6th International Conference on Operations Research and Enterprise Systems (ICORES)

作者： Adasme, Pablo Leung, Janny Soto, Ismael Univ Santiago Chile Dept Ingn Elect Ave Ecuador 3519 Santiago Chile Chinese Univ Hong Kong Shaw Coll 2001 Longxiang Blvd Shenzhen Peoples R China

ISBN: (纸本)9789897582189

In this paper, we propose an adapted version of the progressive hedging algorithm (PHA) (Rockafellar and Wets, 1991;Lokketangen and Woodruff, 1996;Watson and Woodruff, 2011) for the two-stage stochastic traveling salesman problem (STSP) introduced in (Adasme et al., 2016). Thus, we compute feasible solutions for small, medium and large size instances of the problem. Additionally, we compare the PHA method with the sample average approximation (SAA) method for all the randomly generated instances and compute statistical lower and upper bounds. For this purpose, we use the compact polynomial formulation extended from (Miller et al., 1960) in (Adasme et al., 2016) as it is the one that allows us to solve large size instances of the problem in short CPU time with CPLEX. Our preliminary numerical results show that the results obtained with the PHA algorithm are tight when compared to the optimal solutions of small and medium size instances. Moreover, we obtain significantly better feasible solutions than CPLEX for large size instances with up to 100 nodes and 10 scenarios in significantly low CPU time. Finally, the bounds obtained with SAA method provide an average reference interval for the stochastic problem.

关键词： Two-stage Stochastic Programming Traveling Salesman Problem Progressive Hedging Algorithm sample average approximation method

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A green intermodal service network design problem with travel time uncertainty

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TRANSPORTATION RESEARCH PART B-methodOLOGICAL 2016年第PartB期93卷 789-807页

作者： Demir, Emrah Burgholzer, Wolfgang Hrusovsky, Martin Arikan, Emel Jammernegg, Werner Van Woensel, Tom Eindhoven Univ Technol Sch Ind Engn Operat Planning Accounting & Control NL-5600 MB Eindhoven Netherlands WU Vienna Univ Econ & Business Inst Prod Management Welthandelspl 1 A-1020 Vienna Austria

In a more and more competitive and global world, freight transports have to overcome increasingly long distances while at the same time becoming more reliable. In addition, a raising awareness of the need for environmentally friendly solutions increases the importance of transportation modes other than road. Intermodal transportation, in that regard, allows for the combination of different modes in order to exploit their individual advantages. Inter modal transportation networks offer flexible, robust and environmentally friendly alternatives to transport high volumes of goods over long distances. In order to reflect these advantages, it is the challenge to develop models which both represent multiple modes and their characteristics (e.g., fixed-time schedules and routes) as well as the transhipment between these transportation modes. In this paper, we introduce a Green Intermodal Service Network Design Problem with Travel Time Uncertainty (GISND-TTU) for combined offline intermodal routing decisions of multiple commodities. The proposed stochastic approach allows for the generation of robust transportation plans according to different objectives (i.e., cost, time and greenhouse gas (GHG) emissions) by considering uncertainties in travel times as well as demands with the help of the sample average approximation method. The proposed methodology is applied to a real-world network, which shows the advantages of stochasticity in achieving robust transportation plans. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Stochastic service network design problem Intermodal transportation CO2-equivalent emissions Travel time uncertainty Demand uncertainty sample average approximation method

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Minimum mean-squared deviation method for stochastic complementarity problems

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2016年第7期93卷 1173-1187页

作者： Yu, Haodong Shanghai Lixin Univ Commerce Sch Math & Informat Shanghai Peoples R China

In this paper, we propose a new reformulation for stochastic complementarity problems (SCPs). The new formulation is based on the minimum mean-squared deviation rule in statistics. Under mild conditions, we prove the existence of the solution of the new reformulation for SCP. Furthermore, we present a smoothing sample average approximation method for solving the problems. The convergence properties of the optimal solutions of the approximation problems are studied under mild conditions. Finally, some numerical results are listed as well.

关键词： stochastic complementarity problems minimum mean-squared deviation sample average approximation method complementarity function smoothing technique

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Optimization over the Pareto outcome set associated with a convex bi-objective optimization problem: theoretical results, deterministic algorithm and application to the stochastic case

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JOURNAL OF GLOBAL OPTIMIZATION 2015年第3期62卷 481-505页

作者： Bonnel, Henri Collonge, Julien Univ New Caledonia ERIM Noumea 98851 New Caledonia

Our paper consists of two main parts. In the first one, we deal with the deterministic problem of minimizing a real valued function over the Pareto outcome set associated with a deterministic convex bi-objective optimization problem (BOP), in the particular case where depends on the objectives of (BOP), i.e. we optimize over the Pareto set in the outcome space. In general, the optimal value of such a kind of problem cannot be computed directly, so we propose a deterministic outcome space algorithm whose principle is to give at every step a range (lower bound, upper bound) that contains . Then we show that for any given error bound, the algorithm terminates in a finite number of steps. In the second part of our paper, in order to handle also the stochastic case, we consider the situation where the two objectives of (BOP) are given by expectations of random functions, and we deal with the stochastic problem of minimizing a real valued function over the Pareto outcome set associated with this Stochastic bi-objective Optimization Problem (SBOP). Because of the presence of random functions, the Pareto set associated with this type of problem cannot be explicitly given, and thus it is not possible to compute the optimal value of problem . That is why we consider a sequence of sample average approximation problems (SAA-, where is the sample size) whose optimal values converge almost surely to as the sample size goes to infinity. Assuming nondecreasing, we show that the convergence rate is exponential, and we propose a confidence interval for . Finally, some computational results are given to illustrate the paper.

关键词： Optimization over the Pareto image set Multi-objective deterministic optimization Multi-objective stochastic optimization Multi-objective convex optimization sample average approximation method

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Chance-Constrained Programming method of IT Risk Countermeasures for Social Consensus Making

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2015年第5期45卷 725-733页

作者： Samejima, Masaki Sasaki, Ryoichi Osaka Univ Grad Sch Informat Sci & Technol Dept Multimedia Engn Suita Osaka 5650871 Japan Tokyo Denki Univ Sch Sci & Technol Future Life Tokyo 1208551 Japan

The authors address a social consensus making support in discussing countermeasures for information technology risks (IT risks). For supporting stakeholders' discussion on which IT risk countermeasures the stakeholders should implement, experts of the risk management estimate parameter values of the countermeasure, define a goal and constraints, and formulate the decision problem of the countermeasures to be implemented as one of 0-1 integer programming problems. Because parameter values and constraint values are uncertain, the decision problem is reformulated as a chance-constrained programming problem. The sample average approximation method is a well-known method for solving the chance-constrained programming problem. However, the computational time is still so long that the opinion leaders cannot use a solution of the chance-constrained programming problem in their discussion. The authors propose a high-speed chance-constrained programming method by aggregating the constraints that are generated by approximation of the problem in the sample average method. By applying the proposed method to real decision problems, the authors confirmed that computational time is decreased to 1 min while obtaining the same error rate and the same rate of the feasible solutions as a conventional method.

关键词： Chance-constrained programming constraint aggregation information technology risk (IT risk) sample average approximation method social consensus making

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Stochastic methods Based on VU-Decomposition methods for Stochastic Convex Minimax Problems

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MATHEMATICAL PROBLEMS IN ENGINEERING 2014年第1期2014卷 1-5页

作者： Lu, Yuan Wang, Wei Chen, Shuang Huang, Ming Shenyang Univ Normal Coll Shenyang 110044 Peoples R China Liaoning Normal Univ Sch Math Dalian 116029 Peoples R China Dalian Univ Technol Sch Math Sci Dalian 116024 Peoples R China

This paper applies sample average approximation (SAA) method based on VU-space decomposition theory to solve stochastic convex minimax problems. Under some moderate conditions, the SAA solution converges to its true counterpart with probability approaching one and convergence is exponentially fast with the increase of sample size. Based on the VU-theory, a superlinear convergent VU-algorithm frame is designed to solve the SAA problem.

关键词： DECOMPOSITION method (Mathematics) STOCHASTIC analysis sample average approximation method STOCHASTIC convergence PROBABILITY theory sample size (Statistics)

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Stochastic Optimization over a Pareto Set Associated with a Stochastic Multi-Objective Optimization Problem

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2014年第2期162卷 405-427页

作者： Bonnel, Henri Collonge, Julien Univ New Caledonia ERIM Noumea 98851 New Caledonia

We deal with the problem of minimizing the expectation of a real valued random function over the weakly Pareto or Pareto set associated with a Stochastic Multi-objective Optimization Problem, whose objectives are expectations of random functions. Assuming that the closed form of these expectations is difficult to obtain, we apply the sample average approximation method in order to approach this problem. We prove that the Hausdorff-Pompeiu distance between the weakly Pareto sets associated with the sample average approximation problem and the true weakly Pareto set converges to zero almost surely as the sample size goes to infinity, assuming that our Stochastic Multi-objective Optimization Problem is strictly convex. Then we show that every cluster point of any sequence of optimal solutions of the sample average approximation problems is almost surely a true optimal solution. To handle also the non-convex case, we assume that the real objective to be minimized over the Pareto set depends on the expectations of the objectives of the Stochastic Optimization Problem, i.e. we optimize over the image space of the Stochastic Optimization Problem. Then, without any convexity hypothesis, we obtain the same type of results for the Pareto sets in the image spaces. Thus we show that the sequence of optimal values of the sample average approximation problems converges almost surely to the true optimal value as the sample size goes to infinity.

关键词： Optimization over a Pareto set Optimization over the Pareto image set Multi-objective stochastic optimization Multi-objective convex optimization sample average approximation method

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Sampling average approximation method for a class of stochastic Nash equilibrium problems

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OPTIMIZATION methodS & SOFTWARE 2013年第4期28卷 785-795页

作者： Li, Pei-Yu He, Zhi-Feng Lin, Gui-Hua Dalian Univ Technol Sch Math Sci Dalian 116024 Peoples R China Shanghai Univ Sch Management Shanghai 200444 Peoples R China

We consider a class of stochastic Nash equilibrium problems (SNEP). Under some mild conditions, we reformulate the SNEP as a stochastic mixed complementarity problem (SMCP). We apply the well-known sample average approximation (SAA) method to solve the SMCP. We further introduce a semismooth Newton method to solve the SAA problems. The comprehensive convergence analysis is given as well. In addition, we demonstrate the proposed approach on a stochastic Nash equilibrium model in the wholesale gas-oil markets.

关键词： stochastic Nash equilibrium problem sample average approximation method semismooth Newton method

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A Regularization SAA Scheme for a Stochastic Mathematical Program with Complementarity Constraints

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JOURNAL OF APPLIED MATHEMATICS 2014年第unknown期2014卷 1-12页

作者： Li, Yu-xin Zhang, Jie Xia, Zun-quan Dalian Univ Technol Sch Math Sci Inst ORCT Dalian 116024 Peoples R China Liaoning Normal Univ Sch Math Dalian 116029 Peoples R China

To reflect uncertain data in practical problems, stochastic versions of the mathematical program with complementarity constraints (MPCC) have drawn much attention in the recent literature. Our concern is the detailed analysis of convergence properties of a regularization sample average approximation (SAA) method for solving a stochastic mathematical program with complementarity constraints (SMPCC). The analysis of this regularization method is carried out in three steps: First, the almost sure convergence of optimal solutions of the regularized SAA problem to that of the true problem is established by the notion of epiconvergence in variational analysis. Second, under MPCC-MFCQ, which is weaker than MPCC-LICQ, we show that any accumulation point of Karash-Kuhn-Tucker points of the regularized SAA problem is almost surely a kind of stationary point of SMPCC as the sample size tends to infinity. Finally, some numerical results are reported to show the efficiency of the method proposed.

关键词： REGULARIZATION (Mathematics) sample average approximation method STOCHASTIC analysis MATHEMATICAL programming COMPLEMENTARITY constraints (Mathematics)

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Validation analysis of mirror descent stochastic approximation method

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MATHEMATICAL PROGRAMMING 2012年第2期134卷 425-458页

作者： Lan, Guanghui Nemirovski, Arkadi Shapiro, Alexander Univ Florida Gainesville FL 32611 USA Georgia Inst Technol Atlanta GA 30332 USA

The main goal of this paper is to develop accuracy estimates for stochastic programming problems by employing stochastic approximation (SA) type algorithms. To this end we show that while running a Mirror Descent Stochastic approximation procedure one can compute, with a small additional effort, lower and upper statistical bounds for the optimal objective value. We demonstrate that for a certain class of convex stochastic programs these bounds are comparable in quality with similar bounds computed by the sample average approximation method, while their computational cost is considerably smaller.

关键词： Stochastic approximation sample average approximation method Stochastic programming Monte Carlo sampling Mirror descent algorithm Prox-mapping Optimality bounds Large deviations estimates Asset allocation problem Conditional value-at-risk

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