Decomposition-based exact algorithms for risk-constrained traveling salesman problems with discrete random arc costs

Huang, Zhouchun; Zheng, Qipeng P.

doi:10.1007/s11590-014-0798-7

Cited by 6 publications

(5 citation statements)

References 21 publications

(27 reference statements)

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“…Sherali and Lunday [24] proposed generating a set of initial cuts for the master problem. Huang and Zheng [36] proposed a type of feasibility cut to iteratively remove infeasible solutions with certain characteristics. Another strategy is to propose and introduce valid inequalities in the master problem before starting the method in order to eliminate infeasible solutions ( [27,37,38]).…”

Section: Combinatorial Benders Decompositionmentioning

confidence: 99%

Improved Combinatorial Benders Decomposition for a Scheduling Problem with Unrelated Parallel Machines

Gomes¹,

Mateus²

2017

Journal of Applied Mathematics

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This paper addresses the unrelated parallel machines scheduling problem with sequence and machine dependent setup times. Its goal is to minimize the makespan. The problem is solved by a combinatorial Benders decomposition. This method can be slow to converge. Therefore, three procedures are introduced to accelerate its convergence. The first procedure is a new method that consists of terminating the execution of the master problem when a repeated optimal solution is found. The second procedure is based on the multicut technique. The third procedure is based on the warm-start. The improved Benders decomposition scheme is compared to a mathematical formulation and a standard implementation of Benders decomposition algorithm. In the experiments, two test sets from the literature are used, with 240 and 600 instances with up to 60 jobs and 5 machines. For the first set the proposed method performs 21.85% on average faster than the standard implementation of the Benders algorithm. For the second set the proposed method failed to find an optimal solution in only 31 in 600 instances, obtained an average gap of 0.07%, and took an average computational time of 377.86 s, while the best results of the other methods were 57, 0.17%, and 573.89 s, respectively.

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Section: Combinatorial Benders Decompositionmentioning

confidence: 99%

Improved Combinatorial Benders Decomposition for a Scheduling Problem with Unrelated Parallel Machines

Gomes¹,

Mateus²

2017

Journal of Applied Mathematics

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“…Different risk measurement metrics are adopted in the literature for risk-averse twostage stochastic programming, such as variance, variability index, probabilistic financial risk, downside risk, value-at-risk (VaR), etc [25]. In this paper, the conditional value-atrisk, CVaR, first proposed by Rockafellar and Uryasev [10] is used to measure risks because of its ability to account for the worse case scenario and computational tractability, and its close relationship to VaR [10] [26] [27] [28].…”

Section: Introductionmentioning

confidence: 99%

“…The other way is to bound CVaR in constraints. Some applications with CVaR in constraints include portfolio optimization [10], oil and energy optimization [20], oil supply chain [32], large-scale industrial batch plants [33] [34], traveling saleman's problem [28]. Modeling CVaR as objective and as constraints have been shown by Krokhmal et al to provide the same efficient frontier [26].…”

Section: Introductionmentioning

confidence: 99%

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Extended cross decomposition for mixed-integer linear programs with strong and weak linking constraints

Ogbe

2018

Computers & Chemical Engineering

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Large-scale mixed-integer linear programming (MILP) problems, such as those from twostage stochastic programming, usually have a decomposable structure that can be exploited to design efficient optimization methods. Classical Benders decomposition can solve MILPs with weak linking constraints (which are decomposable when linking variables are fixed) but not strong linking constraints (which are not decomposable even when linking variables are fixed). In this paper, we first propose a new rigorous bilevel decomposition strategy for solving MILPs with strong and weak linking constraints, then extend a recently developed cross decomposition method based on this strategy. We also show how to apply the extended cross decomposition method to two-stage stochastic programming problems with conditional-value-at-risk (CVaR) constraints. In the case studies, we demonstrate the significant computational advantage of the proposed extended cross decomposition method as well as the benefit of including CVaR constraints in stochastic programming.

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“…A Benders-like decomposition approach was proposed in (CARAMIA; MARI, 2016) for solving a capacitated facility location problem with two decision makers. Exact solution algorithms based on Benders decomposition are presented in (HUANG; ZHENG, 2015) for the traveling salesman problem with risk constraints. This Chapter develops a Benders Decomposition approach for the Berth Allocation Problem (BAP).…”

Section: A Benders Decomposition Algorithm For the Berth Allocation P...mentioning

confidence: 99%

Recent advances on the berth allocation problem

Barbosa¹

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The intermodal transportation of goods by vessels has increased over the years. In this context, the Berth Allocation Problem (BAP) arises and becomes fundamental to guarantee the efficiency of the maritime terminals, deciding where and when to allocate the vessel over a planning horizon taking into account constraints of time and space. Because the problem is proved NP-hard, this study proposes an exact method and analyzes metaheuristics for tackling the problem. First, considering the BAP as a parallel-machine scheduling problem, an approach for this problem is proposed based on an Evolutionary Metaheuristic, aiming to Ąnd several good quality solutions in a single round of the algorithm, considering explicitly the BAP with multiple objectives. A lower bound based on a maximal flow problem was derived in order to evaluate the quality of the solutions. Next, based on a heterogeneous vehicle routing problem with time windows a basic Benders Decomposition algorithm and its variants are reviewed and applied to the BAP. Then, a hybrid optimization procedure based on Genetic Algorithm (GA) and Scatter Search (SS)is developed, and data envelopment analysis (DEA) is adopted to choose the efficient combination of the operators for the algorithm proposed. Because most papers in literature use in their experiments data generated randomly, making comparisons between researches difficult, this thesis proposes a problem generator for the BAP, allowing the generation of appropriate test problems to be commonly used with speciĄc desired properties and under controlled conditions. The data are generated using different parameters and the difficulty of solving the BAP with such data is analyzed through the resolution using the CPLEX. Finally, the instances classiĄed as more difficult are solved through two metaheuristics implemented.

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Decomposition-based exact algorithms for risk-constrained traveling salesman problems with discrete random arc costs

Cited by 6 publications

References 21 publications

Improved Combinatorial Benders Decomposition for a Scheduling Problem with Unrelated Parallel Machines

Improved Combinatorial Benders Decomposition for a Scheduling Problem with Unrelated Parallel Machines

Extended cross decomposition for mixed-integer linear programs with strong and weak linking constraints

Recent advances on the berth allocation problem

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