Solving the Routing Problems with Time Windows

Čičková, Zuzana; Brezina, Ivan; Pekár, Juraj

doi:10.1007/978-3-319-28161-2_10

Cited by 2 publications

(1 citation statement)

References 31 publications

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“…Another possibility of solving the TSP problem is to use specialized software products for solving sets of optimization problems. We, in particular, used the GAMS package (Čičková, Brezina, Pekár, 2016).…”

Section: то -Minimization Criterion (Min)mentioning

confidence: 99%

Computer tools for solving the traveling salesman problem

Pekár

Brezina

Kultan

et al. 2020

Development Management

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The task of the traveling salesman, which is to find the shortest or least costly circular route, is one of the most common optimization problems that need to be solved in various fields of practice. The article analyzes and demonstrates various methods for solving this problem using a specific example: heuristic (the nearest neighbor method, the most profitable neighbor method), metaheuristic (evolutionary algorithm), methods of mathematical programming. In addition to classic exact methods (which are difficult to use for large-scale tasks based on existing software) and heuristic methods, the article suggests using the innovative features of the commercially available MS Excel software using a meta-heuristic base. To find the optimal solution using exact methods, the Excel (Solver) software package was used, as well as the specialized GAMS software package. Comparison of different approaches to solving the traveling salesman problem using a practical example showed that the use of traditional heuristic approaches (the nearest neighbor method or the most profitable neighbor method) is not difficult from a computational point of view, but does not provide solutions that would be acceptable in modern conditions. The use of MS Excel for solving the problem using the methods of mathematical programming and metaheuristics enabled us to obtain an optimal solution, which led to the conclusion that modern tools are an appropriate addition to solving the traveling salesman problem while maintaining the quality of the solution.

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Section: то -Minimization Criterion (Min)mentioning

confidence: 99%

Computer tools for solving the traveling salesman problem

Pekár

Brezina

Kultan

et al. 2020

Development Management

Self Cite

View full text Add to dashboard Cite

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Discrete self-organizing migration algorithm and p-location problems

Janáček

Kvet

2020

Cro. Oper. Res. Rev.

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Mathematical modelling, and integer programming generally, has many practical applications in different areas of human life. Effective and fast solving approaches for various optimization problems play an important role in the decision-making process and therefore, big attention is paid to the development of many exact and approximate algorithms. This paper deals only with a special class of location problems in which given number of facilities are to be chosen to minimize the objective function value. Since the exact methods are not suitable for their unpredictable computational time or memory demands, we focus here on possible usage of a special type of a particle swarm optimization algorithm transformed by discretization and meme usage into so-called discrete self-organizing migrating algorithm. In the paper, there is confirmed that it is possible to suggest a sophisticated heuristic for zero-one programming problem, which can produce near-to-optimal solution in much smaller time than the time demanded by exact methods. We introduce a special adaptation of the discrete self-organizing migration algorithm to the $p$-location problem making use of the path-relinking method. In the theoretical part of this paper, we introduce several strategies of the migration process. To verify their features and effectiveness, a computational study with real-sized benchmarks was performed. The main goal of the experiments was to find the most efficient version of the suggested solving tool.

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Solving the Routing Problems with Time Windows

Cited by 2 publications

References 31 publications

Computer tools for solving the traveling salesman problem

Computer tools for solving the traveling salesman problem

Discrete self-organizing migration algorithm and p-location problems

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