Discrete Optimizing

Reiter, Stanley; Sherman, Gordon F.

doi:10.1137/0113056

Cited by 71 publications

(22 citation statements)

References 4 publications

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“…We therefore use the intra-route neighborhood to improve a solution within a route, which is a variant of Or-opt neighborhood used in TSP (Or 1976, Reiter andSherman 1965). …”

Section: Standard Neighborhoodsmentioning

confidence: 99%

“…In the literature, three types of neighborhoods, called the cross exchange, 2-opt * and Or-opt neighborhoods, have been widely used (Or 1976, Potvin et al 1996, Reiter and Sherman 1965, Taillard et al 1997. We refer to these neighborhoods as standard neighborhoods.…”

Section: Introductionmentioning

confidence: 99%

“…Among many possible metaheuristics based on local search, we use the multi-start local search (MLS) (Lin 1965, Lin and Kernighan 1973, Reiter and Sherman 1965, the iterated local search (ILS) (Johnson 1990, Martin, Otto and Felten 1991, Martin, Otto and Felten 1992 and the adaptive multi-start local search (AMLS) (Boese, Kahng andMuddu 1994, Taillard et al 1997). MLS repeatedly applies LS to a number of initial solutions which are generated randomly or by greedy methods, and the best solution obtained in the entire search is output.…”

Section: Introductionmentioning

confidence: 99%

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Effective Local Search Algorithms for Routing and Scheduling Problems with General Time-Window Constraints

Ibaraki

Imahori

Kubo

et al. 2005

Transportation Science

150

100

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Abstract:We propose local search algorithms for the vehicle routing problem with soft time window constraints. The time window constraint for each customer is treated as a penalty function, which is very general in the sense that it can be non-convex and discontinuous as long as it is piecewise linear. In our algorithm, we use local search to assign customers to vehicles and to find orders of customers for vehicles to visit. It employs an advanced neighborhood, called the cyclic exchange neighborhood, in addition to standard neighborhoods for the vehicle routing problem. After fixing the order of customers for a vehicle to visit, we must determine the optimal start times of processing at customers so that the total penalty is minimized. We show that this problem can be efficiently solved by using dynamic programming, which is then incorporated in our algorithm. We then report computational results for various benchmark instances of the vehicle routing problem. The generality of time window constraints allows us to handle a wide variety of scheduling problems. As such an example, we mention in this paper an application to a production scheduling problem with inventory cost, and report computational results for real world instances.

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“…We therefore use the intra-route neighborhood to improve a solution within a route, which is a variant of Or-opt neighborhood used in TSP (Or 1976, Reiter andSherman 1965). …”

Section: Standard Neighborhoodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Effective Local Search Algorithms for Routing and Scheduling Problems with General Time-Window Constraints

Ibaraki

Imahori

Kubo

et al. 2005

Transportation Science

150

100

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“…[9]. Thus, If our initial schedule Is represented by an ordering (l, 2 ..... n), the next generation will consist of [_] possible schedules.…”

Section: Representation Of the Scheduling Problem As A Decision Treementioning

confidence: 99%

“…Strategies for reducing the solution space of possible sequences and schedules, or improving efflciency of search algorlthms vla the exploitation of precedence constraints and/or dominance concepts appear In Ill, [2], [5], [9] …”

Section: Introductionmentioning

confidence: 99%

Application of a hybrid generation/utility assessment heuristic to a class of scheduling problems

Heyward¹

Conference Proceedings., IEEE International Conference on Systems, Man and Cybernetics

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On metaheuristic algorithms for combinatorial optimization problems

Yagiura

Ibaraki

2001

Syst. Comp. Jpn.

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PrefaceThere are numerous combinatorial optimization problems, for which computing exact optimal solutions is computationally intractable, e.g., those problems known as NP-hard. However, in practice, we are often asked to deal with large scale instances of such difficult problems. One possibility to overcome this difficulty is that, in most practical cases, we do not need exact optimal solutions and are satisfied with sufficiently good solutions. In this sense, approximate (or heuristic) algorithms, which provide reasonably good solutions in practically meaningful time, are very important and have been well studied recently.There are several useful tools used to design approximate algorithms, such as greedy method and local search. The so-called metaheuristics combine these tools into more sophisticated algorithms. Among the well-known metaheuristics are multi-start local search, simulated annealing, tabu search, genetic algorithm and so on. Many variants of these, such as GRASP, threshold accepting, iterated local search and others, have also been proposed and extensively studied.One of the attractive features of these metaheuristics is in its flexibility. They can be hybridized with other heuristic or exact algorithms to create more powerful tools. As an example of such hybrid algorithms, we propose to use dynamic programming (DP) to improve candidate solutions within the framework of genetic algorithm, which is called the genetic DP algorithm. Good prospects of the proposed algorithm are observed by the computational experiments to three representative NP-hard problems: single machine scheduling problem, optimal linear arrangement problem and traveling salesman problem.During the experience of developing the genetic DP, we realized that crossover is one of the most important operators in genetic algorithms, on which the overall performance of the algorithms critically depends. To pursue this direction, we review a variety of crossover operators proposed for sequencing problems, and analyze the relationship between characteristics of the operator and performance of the algorithm. Based on this analysis, we propose simple criteria for measuring the quality of crossover operators. Some computational analysis on single machine scheduling problem is then added to validate the effectiveness of the proposed criteria.Another attractive feature of metaheuristics is in its robustness and simplicity. They i can be developed even if deep mathematical properties of the problem domain are not at hand, and still can provide reasonably good solutions, much better than those obtainable by simple heuristics. To investigate this direction, we compare representative metaheuristic algorithms using rather simple inner operators to observe general tendency of their performance. From these results, we propose a recommendation about the use of metaheuristics as simple optimization tools.We then consider a problem arising from the implementation issue of a crossover operator.

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Discrete Optimizing

Cited by 71 publications

References 4 publications

Effective Local Search Algorithms for Routing and Scheduling Problems with General Time-Window Constraints

Effective Local Search Algorithms for Routing and Scheduling Problems with General Time-Window Constraints

Application of a hybrid generation/utility assessment heuristic to a class of scheduling problems

On metaheuristic algorithms for combinatorial optimization problems

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