A Survey of Different Integer Programming Formulations of the Travelling Salesman Problem

Orman, A.J.; Williams, H. Paul

doi:10.1007/3-540-36626-1_5

Cited by 60 publications

(63 citation statements)

References 14 publications

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“…Diversas formulações do Problema do Caixeiro Viajante (PCV) podem ser encontradas em [11]. Somente duas destas formulações (a de [4] e a de [10]) podem ser adaptadas para o Problema do Caixeiro Viajante com Grupamento (PCVG) incorporando as restrições de [2].…”

Section: Formulação Matemática Propostaunclassified

Um Método Exato para o Problema do Caixeiro Viajante com Grupamentos Euclidiano e Simétrico

Mestria

2015

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Resumo: Nesse artigo,é proposto um método exato para resolver o Problema do Caixeiro Viajante com Grupamentos (PCVG). O PCVGé uma generalização do Problema do Caixeiro Viajante (PCV), onde os vértices são particionados em grupos disjuntos e o objetivoé encontrar um ciclo hamiltoniano de custo mínimo tal que os vértices de cada grupo são visitados de forma contígua. A formulação para o método inclui a restrição de Chisman (1975)

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Section: Formulação Matemática Propostaunclassified

Um Método Exato para o Problema do Caixeiro Viajante com Grupamentos Euclidiano e Simétrico

Mestria

2015

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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“…MTZ constraints are attractive due to their compactness, but they are well-known for producing weak LP bounds. Orman and Williams (1999) compare the strengths of several formulations of the well known Travelling Salesman Problem (TSP), including the ones with MTZ and flow constraints, on the basis of their LP bounds. The reader is referred to Nemhauser and Wolsey (1988), Gutin and punnen (2002), and Applegate et al (2007) for additional information on the TSP.…”

Section: Existing Mtz Based Formulations Of the Hmst Problemmentioning

confidence: 99%

“…The reader is referred to Nemhauser and Wolsey (1988), Gutin and punnen (2002), and Applegate et al (2007) for additional information on the TSP. Orman and Williams (1999) find out that the LP polytope of the TSP resulting from MTZ constraints contains some of the seven existing formulations of the TSP. This has led to various studies to augment the MTZ constraints and strengthen the LP bounds of the TSP formulation (Desrochers and Laporte, 1991;Gouveia and Pires, 1999;Sherali and Driscoll, 2002).…”

Section: Existing Mtz Based Formulations Of the Hmst Problemmentioning

confidence: 99%

New formulations of the Hop-Constrained Minimum Spanning Tree problem via Miller–Tucker–Zemlin constraints

Akgün

Tansel

2011

European Journal of Operational Research

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a b s t r a c tGiven an undirected network with positive edge costs and a natural number p, the Hop-Constrained Minimum Spanning Tree problem (HMST) is the problem of finding a spanning tree with minimum total cost such that each path starting from a specified root node has no more than p hops (edges). In this paper, we develop new formulations for HMST. The formulations are based on Miller-Tucker-Zemlin (MTZ) subtour elimination constraints, MTZ-based liftings in the literature offered for HMST, and a new set of topologyenforcing constraints. We also compare the proposed models with the MTZ-based models in the literature with respect to linear programming relaxation bounds and solution times. The results indicate that the new models give considerably better bounds and solution times than their counterparts in the literature and that the new set of constraints is competitive with liftings to MTZ constraints, some of which are based on well-known, strong liftings of Desrochers and Laporte (1991).

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“…Constraints 2 and 3 ensure that for active wells, and only for these wells, there must be one input and one output arc included in the route. Constraints 4, 5 and 6 are subtour-elimination constraints, where y ij represents the "flow" in arc (i, j) [22]. Constraint 7 prevents from exceeding the time limit, and constraint 8 ensures that OTS is included in the route.…”

Section: The Oil Collecting Vehicle Routing Problemmentioning

confidence: 99%

“…The best solution of all generations (with the highest value of fitness function f (x), where x is the evaluated solution) is kept and returned by the algorithm. Simpler versions of this algorithm (GA without Local Search and/or Data Mining) are just as the algorithm in Figure 4, except by the removal of modules of Data Mining (lines [13][14][15][16][17][18][19][20][21][22] and/or Local Search (calls to Insert and Swap).…”

Section: Genetic Algorithm With Data Mining and Local Searchmentioning

confidence: 99%

Combining an evolutionary algorithm with data mining to solve a single-vehicle routing problem

et al. 2006

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The aim of this work is to present some alternatives to improve the performance of an Evolutionary Algorithm applied to the problem known as the Oil Collecting Vehicle Routing Problem. Some proposals based on the insertion of Local Search and Data Mining modules in a Genetic Algorithm (GA) are presented. Four algorithms were developed: a Genetic Algorithm, a Genetic Algorithm with a Local Search procedure, a Genetic Algorithm including a Data Mining module and a Genetic Algorithm including Local Search and Data Mining. Experimental results demonstrate that the incorporation of Data Mining and Local Search modules in GA can improve the solution quality produced by this method.

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A Survey of Different Integer Programming Formulations of the Travelling Salesman Problem

Cited by 60 publications

References 14 publications

Um Método Exato para o Problema do Caixeiro Viajante com Grupamentos Euclidiano e Simétrico

Um Método Exato para o Problema do Caixeiro Viajante com Grupamentos Euclidiano e Simétrico

New formulations of the Hop-Constrained Minimum Spanning Tree problem via Miller–Tucker–Zemlin constraints

Combining an evolutionary algorithm with data mining to solve a single-vehicle routing problem

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