Inver-over Operator for the TSP
27 Sep 1998-pp 803-812
TL;DR: This paper investigates the usefulness of a new operator, inver-over, for an evolutionary algorithm for the TSP, and the proposed operator is unary, since the inversion is applied to a segment of a single individual, however, the selection of a segment to be inverted is population driven, thus the operator displays some characterictics of recombination.
Abstract: In this paper we investigate the usefulness of a new operator, inver-over, for an evolutionary algorithm for the TSP. Inver-over is based on simple inversion, however, knowledge taken from other individuals in the population influences its action. Thus, on one hand, the proposed operator is unary, since the inversion is applied to a segment of a single individual, however, the selection of a segment to be inverted is population driven, thus the operator displays some characterictics of recombination.
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TL;DR: This paper revision the terminology, which is unclear and confusing, thereby providing a classification of such control mechanisms, and surveys various forms of control which have been studied by the evolutionary computation community in recent years.
Abstract: The issue of controlling values of various parameters of an evolutionary algorithm is one of the most important and promising areas of research in evolutionary computation: it has a potential of adjusting the algorithm to the problem while solving the problem. In the paper we: 1) revise the terminology, which is unclear and confusing, thereby providing a classification of such control mechanisms, and 2) survey various forms of control which have been studied by the evolutionary computation community in recent years. Our classification covers the major forms of parameter control in evolutionary computation and suggests some directions for further research.
1,742 citations
Cites background from "Inver-over Operator for the TSP"
...In [128] a new adaptive operator (so-called inver-over) was proposed for permutation problems....
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TL;DR: A classification of different approaches based on a number of complementary features is provided, and special attention is paid to setting parameters on-the-fly, which has the potential of adjusting the algorithm to the problem while solving the problem.
Abstract: The issue of setting the values of various parameters of an evolutionary algorithm is crucial for good performance. In this paper we discuss how to do this, beginning with the issue of whether these values are best set in advance or are best changed during evolution. We provide a classification of different approaches based on a number of complementary features, and pay special attention to setting parameters on-the-fly. This has the potential of adjusting the algorithm to the problem while solving the problem. This paper is intended to present a survey rather than a set of prescriptive details for implementing an EA for a particular type of problem. For this reason we have chosen to interleave a number of examples throughout the text. Thus we hope to both clarify the points we wish to raise as we present them, and also to give the reader a feel for some of the many possibilities available for controlling different parameters. © Springer-Verlag Berlin Heidelberg 2007.
1,307 citations
Cites background from "Inver-over Operator for the TSP"
...In [128] a new adaptive operator (so-called inver-over) was proposed for permutation problems....
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TL;DR: A novel set-based PSO (S-PSO) method for the solutions of some combinatorial optimization problems (COPs) in discrete space is presented and tested on two famous COPs: the traveling salesman problem and the multidimensional knapsack problem.
Abstract: Particle swarm optimization (PSO) is predominately used to find solutions for continuous optimization problems. As the operators of PSO are originally designed in an n-dimensional continuous space, the advancement of using PSO to find solutions in a discrete space is at a slow pace. In this paper, a novel set-based PSO (S-PSO) method for the solutions of some combinatorial optimization problems (COPs) in discrete space is presented. The proposed S-PSO features the following characteristics. First, it is based on using a set-based representation scheme that enables S-PSO to characterize the discrete search space of COPs. Second, the candidate solution and velocity are defined as a crisp set, and a set with possibilities, respectively. All arithmetic operators in the velocity and position updating rules used in the original PSO are replaced by the operators and procedures defined on crisp sets, and sets with possibilities in S-PSO. The S-PSO method can thus follow a similar structure to the original PSO for searching in a discrete space. Based on the proposed S-PSO method, most of the existing PSO variants, such as the global version PSO, the local version PSO with different topologies, and the comprehensive learning PSO (CLPSO), can be extended to their corresponding discrete versions. These discrete PSO versions based on S-PSO are tested on two famous COPs: the traveling salesman problem and the multidimensional knapsack problem. Experimental results show that the discrete version of the CLPSO algorithm based on S-PSO is promising.
382 citations
Cites methods or result from "Inver-over Operator for the TSP"
...The data of MMAS, the Lin‐Kernighan algorithm, and the genetic algorithms with different crossover operators are extracted from [40], [ 44 ], and [45], respectively....
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...The results of Lin‐Kernighan are extracted from [ 44 ]....
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...Moreover, while the Lin‐Kernighan algorithm fails to obtain optimal results in all ten runs for all instances [ 44 ], S-CLPSO manages to find the optimal results of all instances in at least one out of ten runs except for kroD100 and pcb442....
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...Compared with the average results of ten runs of the Lin‐Kernighan algorithm reported in [ 44 ], S-CLPSO is able to achieve better averages in all instances....
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11 Oct 2009
TL;DR: A novel variation to biogeography-based optimization (BBO), which is an evolutionary algorithm (EA) developed for global optimization, employs opposition-based learning (OBL) alongside BBO's migration rates to create oppositional BBO (OB O), and a new opposition method named quasi-reflection is introduced.
Abstract: We propose a novel variation to biogeography-based optimization (BBO), which is an evolutionary algorithm (EA) developed for global optimization. The new algorithm employs opposition-based learning (OBL) alongside BBO's migration rates to create oppositional BBO (OB O). Additionally, a new opposition method named quasi-reflection is introduced. Quasi-reflection is based on opposite numbers theory and we mathematically prove that it has the highest expected probability of being closer to the problem solution among all OBL methods. The oppositional algorithm is further revised by the addition of dynamic domain scaling and weighted reflection. Simulations have been performed to validate the performance of quasi-opposition as well as a mathematical analysis for a single-dimensional problem. Empirical results demonstrate that with the assistance of quasi-reflection, OB O significantly outperforms BBO in terms of success rate and the number of fitness function evaluations required to find an optimal solution.
258 citations
Additional excerpts
...1 Vertex Coloring We selected vertex coloring [187] as our combinatorial benchmark because it is the most popular graph-coloring problem....
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TL;DR: A new hybrid algorithm is described that exploits a compact genetic algorithm in order to generate high-quality tours, which are then refined by means of the Lin-Kernighan (LK) local search.
Abstract: The combination of genetic and local search heuristics has been shown to be an effective approach to solving the traveling salesman problem (TSP). This paper describes a new hybrid algorithm that exploits a compact genetic algorithm in order to generate high-quality tours, which are then refined by means of the Lin-Kernighan (LK) local search. The local optima found by the LK local search are in turn exploited by the evolutionary part of the algorithm in order to improve the quality of its simulated population. The results of several experiments conducted on different TSP instances with up to 13,509 cities show the efficacy of the symbiosis between the two heuristics.
178 citations
Cites methods from "Inver-over Operator for the TSP"
...A good tradeoff between the two approaches is the Tao and Michalewicz’s [ 15 ] inver-over operator that tries to combine the computational efficiency of inversion with the power of crossover....
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References
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Book•
01 Jan 1992
TL;DR: GAs and Evolution Programs for Various Discrete Problems, a Hierarchy of Evolution Programs and Heuristics, and Conclusions.
Abstract: 1 GAs: What Are They?.- 2 GAs: How Do They Work?.- 3 GAs: Why Do They Work?.- 4 GAs: Selected Topics.- 5 Binary or Float?.- 6 Fine Local Tuning.- 7 Handling Constraints.- 8 Evolution Strategies and Other Methods.- 9 The Transportation Problem.- 10 The Traveling Salesman Problem.- 11 Evolution Programs for Various Discrete Problems.- 12 Machine Learning.- 13 Evolutionary Programming and Genetic Programming.- 14 A Hierarchy of Evolution Programs.- 15 Evolution Programs and Heuristics.- 16 Conclusions.- Appendix A.- Appendix B.- Appendix C.- Appendix D.- References.
12,212 citations
Book•
01 Jan 1991
TL;DR: This book sets out to explain what genetic algorithms are and how they can be used to solve real-world problems, and introduces the fundamental genetic algorithm (GA), and shows how the basic technique may be applied to a very simple numerical optimisation problem.
Abstract: This book sets out to explain what genetic algorithms are and how they can be used to solve real-world problems. The first objective is tackled by the editor, Lawrence Davis. The remainder of the book is turned over to a series of short review articles by a collection of authors, each explaining how genetic algorithms have been applied to problems in their own specific area of interest. The first part of the book introduces the fundamental genetic algorithm (GA), explains how it has traditionally been designed and implemented and shows how the basic technique may be applied to a very simple numerical optimisation problem. The basic technique is then altered and refined in a number of ways, with the effects of each change being measured by comparison against the performance of the original. In this way, the reader is provided with an uncluttered introduction to the technique and learns to appreciate why certain variants of GA have become more popular than others in the scientific community. Davis stresses that the choice of a suitable representation for the problem in hand is a key step in applying the GA, as is the selection of suitable techniques for generating new solutions from old. He is refreshingly open in admitting that much of the business of adapting the GA to specific problems owes more to art than to science. It is nice to see the terminology associated with this subject explained, with the author stressing that much of the field is still an active area of research. Few assumptions are made about the reader's mathematical background. The second part of the book contains thirteen cameo descriptions of how genetic algorithmic techniques have been, or are being, applied to a diverse range of problems. Thus, one group of authors explains how the technique has been used for modelling arms races between neighbouring countries (a non- linear, dynamical system), while another group describes its use in deciding design trade-offs for military aircraft. My own favourite is a rather charming account of how the GA was applied to a series of scheduling problems. Having attempted something of this sort with Simulated Annealing, I found it refreshing to see the authors highlighting some of the problems that they had encountered, rather than sweeping them under the carpet as is so often done in the scientific literature. The editor points out that there are standard GA tools available for either play or serious development work. Two of these (GENESIS and OOGA) are described in a short, third part of the book. As is so often the case nowadays, it is possible to obtain a diskette containing both systems by sending your Visa card details (or $60) to an address in the USA.
6,758 citations
"Inver-over Operator for the TSP" refers background or methods in this paper
..., it would be interesting to experiment with ( ; )-selection and compare it with the current one, which allows competition between parent and o spring only), (2) adaptive (or self-adaptive) change of the parameter p (if successful, the system will have only one parameter: population size, apart from termination condition), (3) the signi cance of the population size and the termination condition (the current version of the system has xed population size of 100 and terminates if there is no improvement in 10 iterations of the while loop), (4) full comparison of the proposed technique with other algorithms (including other evolutionary systems, tabu search, simulated annealing, and other heuristic methods), (5) experiments with larger instances of TSP (up to 1,000,000 cities)....
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...For example, assume that after a few inversions, the current individual S0 is S0 = (9; 3; 6; 8; 5;1;4; 2; 7),...
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..., rand() > p), another individual is (randomly) selected from the population; assume, it is (1; 6; 4; 3; 5; 7;9;2; 8)....
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TL;DR: This paper discusses a highly effective heuristic procedure for generating optimum and near-optimum solutions for the symmetric traveling-salesman problem based on a general approach to heuristics that is believed to have wide applicability in combinatorial optimization problems.
Abstract: This paper discusses a highly effective heuristic procedure for generating optimum and near-optimum solutions for the symmetric traveling-salesman problem. The procedure is based on a general approach to heuristics that is believed to have wide applicability in combinatorial optimization problems. The procedure produces optimum solutions for all problems tested, "classical" problems appearing in the literature, as well as randomly generated test problems, up to 110 cities. Run times grow approximately as n2; in absolute terms, a typical 100-city problem requires less than 25 seconds for one case GE635, and about three minutes to obtain the optimum with above 95 per cent confidence.
3,761 citations
TL;DR: This paper contains the description of a traveling salesman problem library (TSPLIB) which is meant to provide researchers with a broad set of test problems from various sources and with various properties.
Abstract: This paper contains the description of a traveling salesman problem library (TSPLIB) which is meant to provide researchers with a broad set of test problems from various sources and with various properties. For every problem a short description is given along with known lower and upper bounds. Several references to computational tests on some of the problems are given. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
2,397 citations
Book•
01 Jan 1987
TL;DR: A detergent composition mainly for automatic laundering machines which comprises, on the basis of 100 parts by weight of total composition, at least 60 parts of soap and no more than 10 parts of a mixture of surfactants which impart an excellent detergent ability and foam control even in very soft waters and non-polluting properties.
Abstract: A detergent composition mainly for automatic laundering machines which comprises, on the basis of 100 parts by weight of total composition, at least 60 parts of soap and no more than 10 parts of a mixture of surfactants comprising 10 to 30% of at least one non-ionic polyoxyalkylated surfactant and 90 to 70% of an anionic surfactant selected essentially from alpha -sulfonated fatty acids derivatives, the remainder of the composition comprising at least one ingredient selected from alkaline detergent additives, bleaching agents, optical brighteners, fragrances, antiredeposition agents and enzymes. The non-ionic surfactants are preferably fatty acid amides derived from tallow, copra or palm-oil condensed with polyoxyethylene residues. The anionic surfactants are preferably alpha -sulfonated fatty esters or amides derived from tallow, copra or palm-oil. The proper combination of said non-ionic and anionic surfactants with soaps impart to the laundering compositions an excellent detergent ability and foam control even in very soft waters and non-polluting properties.
1,406 citations