Ant Colony Systems for Large Sequential Ordering Problems
01 Apr 2007-pp 60-67
TL;DR: This paper proposes an extension of a well known ant colony system for the sequential ordering problem, aiming at making the approach more efficient on large problems.
Abstract: The sequential ordering problem is a version of the asymmetric traveling salesman problem where precedence constraints on vertices are imposed. A tour is feasible if these constraints are respected, and the objective is to find a feasible solution with minimum cost. The sequential ordering problem models a lot of real world applications, mainly in the fields of transportation and production planning. In this paper we propose an extension of a well known ant colony system for the problem, aiming at making the approach more efficient on large problems. The extension is based on a problem manipulation technique that heuristically reduces the search space. Computational results, where the extended ant colony system is compared to the original one, are presented
Citations
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TL;DR: In this paper some directions for improving the original framework when a strong local search routine is available, are identified and some modifications able to speed up the method and make it competitive on large problem instances are described.
80 citations
TL;DR: A particle swarm optimization approach hybridized with a local search procedure is discussed, shown to be very effective in guiding a sophisticated local search previously introduced in the literature towards high quality regions of the search space.
46 citations
TL;DR: A problem manipulation technique to be used in conjunction with heuristic algorithms is discussed, which aims to make the search space associated with each problem more attractive for the underlying heuristic algorithm.
41 citations
TL;DR: In this paper, the authors evaluate the contributions of the basic ingredients of the state-of-the-art algorithm for the sequential ordering problem: local search (LS), ant colony and heuristic manipulation.
Abstract: The Sequential Ordering Problem (SOP) is a version of the Asymmetric Travelling Salesman Problem (ATSP) where precedence constraints on vertices are imposed. A tour is feasible if these constraints are respected, and the objective is to find a feasible solution with minimum cost. The SOP models many real world applications, mainly in the fields of transportation and production planning. In particular, it can be used to optimise quay crane assignments. In this paper, we experimentally evaluate the contributions of the basic ingredients of the state-of-the-art algorithm for the SOPs: Local Searches (LSs), ant colony and heuristic manipulation.
30 citations
01 Mar 2020
TL;DR: A technique to tune the reinforcement learning parameters applied to the sequential ordering problem (SOP) using the Scott–Knott method is presented and indicates that SARSA overwhelms the performance of Q-learning.
Abstract: In this paper, we present a technique to tune the reinforcement learning (RL) parameters applied to the sequential ordering problem (SOP) using the Scott–Knott method. The RL has been widely recognized as a powerful tool for combinatorial optimization problems, such as travelling salesman and multidimensional knapsack problems. It seems, however, that less attention has been paid to solve the SOP. Here, we have developed a RL structure to solve the SOP that can partially fill that gap. Two traditional RL algorithms, Q-learning and SARSA, have been employed. Three learning specifications have been adopted to analyze the performance of the RL: algorithm type, reinforcement learning function, and $$\epsilon $$ parameter. A complete factorial experiment and the Scott–Knott method are used to find the best combination of factor levels, when the source of variation is statistically different in analysis of variance. The performance of the proposed RL has been tested using benchmarks from the TSPLIB library. In general, the selected parameters indicate that SARSA overwhelms the performance of Q-learning.
24 citations
References
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TL;DR: The results show that the ACS outperforms other nature-inspired algorithms such as simulated annealing and evolutionary computation, and it is concluded comparing ACS-3-opt, a version of the ACS augmented with a local search procedure, to some of the best performing algorithms for symmetric and asymmetric TSPs.
Abstract: This paper introduces the ant colony system (ACS), a distributed algorithm that is applied to the traveling salesman problem (TSP). In the ACS, a set of cooperating agents called ants cooperate to find good solutions to TSPs. Ants cooperate using an indirect form of communication mediated by a pheromone they deposit on the edges of the TSP graph while building solutions. We study the ACS by running experiments to understand its operation. The results show that the ACS outperforms other nature-inspired algorithms such as simulated annealing and evolutionary computation, and we conclude comparing ACS-3-opt, a version of the ACS augmented with a local search procedure, to some of the best performing algorithms for symmetric and asymmetric TSPs.
7,596 citations
"Ant Colony Systems for Large Sequen..." refers background or methods in this paper
...Local search is an optional component of ACO algorithms, although it has been shown since early implementations that it can greatly improve the overall performance of the ACO metaheuristic when static combinatorial optimization problems are considered (Dorigo and Gambardella [6])....
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...ACS-SOP is strongly based on the Ant Colony System algorithm (Dorigo and Gambardella [6])....
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TL;DR: An overview of recent work on ant algorithms, that is, algorithms for discrete optimization that took inspiration from the observation of ant colonies' foraging behavior, and the ant colony optimization (ACO) metaheuristic is presented.
Abstract: This article presents an overview of recent work on ant algorithms, that is, algorithms for discrete optimization that took inspiration from the observation of ant colonies' foraging behavior, and introduces the ant colony optimization (ACO) metaheuristic. In the first part of the article the basic biological findings on real ants are reviewed and their artificial counterparts as well as the ACO metaheuristic are defined. In the second part of the article a number of applications of ACO algorithms to combinatorial optimization and routing in communications networks are described. We conclude with a discussion of related work and of some of the most important aspects of the ACO metaheuristic.
2,862 citations
TL;DR: A new local optimizer called SOP-3-exchange is presented for the sequential ordering problem that extends a local search for the traveling salesman problem to handle multiple constraints directly without increasing computational complexity.
Abstract: We present a new local optimizer called SOP-3-exchange for the sequential ordering problem that extends a local search for the traveling salesman problem to handle multiple constraints directly without increasing computational complexity. An algorithm that combines the SOP-3-exchange with an Ant Colony Optimization algorithm is described, and we present experimental evidence that the resulting algorithm is more effective than existing methods for the problem. The best-known results for many of a standard test set of 22 problems are improved using the SOP-3-exchange with our Ant Colony Optimization algorithm or in combination with the MPO/AI algorithm (Chen and Smith 1996).
386 citations
"Ant Colony Systems for Large Sequen..." refers methods in this paper
...Since the description of such a local search method is out of the scope of this paper (although the local search routine is used by the algorithm we propose) we refer the interested reader to Gambardella and Dorigo [9] for its detailed description....
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...The resulting algorithm is a Hybrid Ant System for the SOP called HAS-SOP, which is described in detail in Gambardella and Dorigo [9]....
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...Gambardella and Dorigo [9] presented an approach based on Ant Colony Optimization enriched with sophisticated local search procedures....
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...The contribution of the present article will be an extension of the method described in [9], aiming at improving the performance of the method on large problems....
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...All the methods have been coded in C++ (starting from the original implementation of HAS-SOP, see [9]) and all the experiments have been run on a Intel Pentium 4 1....
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12 Feb 1996
TL;DR: This thesis computationally compare several on-line heuristics and derive lower bounds on the value obtained by an optimal on--line strategy by analyzing two off--line Combinatorial Optimization problems: the asymmetric Hamiltonian path problem with precedence constraints and the asymmetry of time windows.
Abstract: In this thesis we describe a practical problem that we encountered in the on--line optimization of a complex Flexible Manufacturing System. In the considered system a stacker crane has to fulfill all transportation tasks (jobs) in a single aisled automatic storage system. The jobs have to be sequenced in such a way, that the time needed for the unloaded moves is minimized. The modelling of this question leads to the so--called on--line Hamiltonian path problem. We computationally compare several on--line heuristics and derive lower bounds on the value obtained by an optimal on--line strategy by analyzing two off--line Combinatorial Optimization problems: the asymmetric Hamiltonian path problem with precedence constraints, also called sequential ordering problem (SOP), and the asymmetric Hamiltonian path problem with time windows (AHPPTW). We study the SOP and AHPPTW from a polyhedral point of view and derive several new classes of valid inequalities. Based on the polyhedral investigations we develop branch&cut algorithms for both problems and can achieve encouraging results on solving problem instances from real--world examples of the practical application.
174 citations
"Ant Colony Systems for Large Sequen..." refers background in this paper
...The SOP models real-world problems such as production planning (Escudero [7]), single vehicle routing problems with pick-up and delivery constraints (Pulleyblank and Timlin [13], Savelsbergh [14]) and transportation problems in flexible manufacturing systems (Ascheuer [1])....
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...Ascheuer [1] has proposed a new class of valid inequalities and has described a new...
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...The approach in [1] also investigates the possibility to compute and improve sub-optimal feasible solutions starting from the upper bound provided by the polyhedral investigation....
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TL;DR: This paper studies the Precedence-Constrained Asymmetric Traveling Salesman (PCATS) polytope, i.e. the convex hull of incidence vectors of tours in a precedence-constrained directed graph, and derives several families of valid inequalities.
Abstract: Many applications of the traveling salesman problem require the introduction of additional constraints. One of the most frequently occurring classes of such constraints are those requiring that certain cities be visited before others (precedence constraints). In this paper we study the Precedence-Constrained Asymmetric Traveling Salesman (PCATS) polytope, i.e. the convex hull of incidence vectors of tours in a precedence-constrained directed graph. We derive several families of valid inequalities, and give polynomial time separation algorithms for important subfamilies. We then establish the dimension of the PCATS polytope and show that, under reasonable assumptions, the two main classes of inequalities derived are facet inducing.
147 citations