Feasibility-preserving crossover for maximum k-coverage problem
12 Jul 2008-pp 593-598
TL;DR: A new crossover tailored to the maximum k-coverage problem is proposed, which has an additional advantage of always producing feasible solutions.
Abstract: The maximum k-coverage problem is a generalized version of covering problems. We introduce the problem formally and analyze its property in relation to the operators of genetic algorithm. Based on the analysis, we propose a new crossover tailored to the maximum k-coverage problem. While traditional n-point crossovers have a problem of requiring repair steps, the proposed crossover has an additional advantage of always producing feasible solutions. We give a comparative analysis of the proposed crossover through experiments.
Citations
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TL;DR: This work extends a geometric framework for the interpretation of search operators to encompass the genotype-phenotype mapping derived from an equivalence relation defined by an isometry group, and shows that this mapping can be naturally interpreted using the concept of quotient space.
16 citations
Cites background or methods from "Feasibility-preserving crossover fo..."
...The basic evolutionary model we used is the genetic algorithm of [44], which is quite similar to the CHC [11] that uses a restart technique without mutation....
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...Some evolutionary studies have been made on such problems over sets [44] or real vector space [39]....
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Posted Content•
TL;DR: The genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics and the quotient geometric crossover has the effect of reducing the search space actually searched by geometric crossover, and it introduces problem knowledge in the search by using a distance better tailored to the specific solution interpretation.
Abstract: In this paper, we present that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics Quotient space can be considered as mathematically-defined phenotype space in the evolutionary computation theory The quotient geometric crossover has the effect of reducing the search space actually searched by geometric crossover, and it introduces problem knowledge in the search by using a distance better tailored to the specific solution interpretation Quotient geometric crossovers are directly applied to the genotype space but they have the effect of the crossovers performed on phenotype space We give many example applications of the quotient geometric crossover
3 citations
Cites background from "Feasibility-preserving crossover fo..."
...Some evolutionary studies have been made on such problems [28, 32]....
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24 Mar 2014
TL;DR: This paper investigates mating schemes using the Hungarian method, applies the schemes to well-known combinatorial optimization problems, the traveling salesman problem and the graph bisection problem, and analyzes how the quality of the best individual changes over generations.
Abstract: Mating scheme is the way of selecting two parents to make offspring. It takes effect on the performance of genetic algorithms. In this paper, we investigate mating schemes using the Hungarian method. The schemes include i) minimizing the sum of matching distances, ii) maximizing the sum, and iii) random matching for comparison. We apply the schemes to well-known combinatorial optimization problems, the traveling salesman problem and the graph bisection problem, and analyze how the quality of the best individual changes over generations. Based on the analysis, we finally suggest a new hybrid mating scheme. The suggested scheme showed better performance than the non-hybrid schemes.
2 citations
Cites methods from "Feasibility-preserving crossover fo..."
...The Hungarian method has been used in various studies [11][21][27][28]....
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TL;DR: This paper proposes an adaptive mating scheme using previously suggested Hungarian mating schemes, and shows better results than not only pure and previous hybrid schemes but also existing distance-based mating schemes.
Abstract: In genetic algorithms, selection or mating scheme is one of the important operations. In this paper, we suggest an adaptive mating scheme using previously suggested Hungarian mating schemes. Hungarian mating schemes consist of maximizing the sum of mating distances, minimizing the sum, and random matching. We propose an algorithm to elect one of these Hungarian mating schemes. Every mated pair of solutions has to vote for the next generation mating scheme. The distance between parents and the distance between parent and offspring are considered when they vote. Well-known combinatorial optimization problems, the traveling salesperson problem, and the graph bisection problem are used for the test bed of our method. Our adaptive strategy showed better results than not only pure and previous hybrid schemes but also existing distance-based mating schemes.
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01 Jan 1979
42,654 citations
Book•
01 Jan 1979
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Abstract: This is the second edition of a quarterly column the purpose of which is to provide a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NP-Completeness,’’ W. H. Freeman & Co., San Francisco, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed. Readers having results they would like mentioned (NP-hardness, PSPACE-hardness, polynomial-time-solvability, etc.), or open problems they would like publicized, should send them to David S. Johnson, Room 2C355, Bell Laboratories, Murray Hill, NJ 07974, including details, or at least sketches, of any new proofs (full papers are preferred). In the case of unpublished results, please state explicitly that you would like the results mentioned in the column. Comments and corrections are also welcome. For more details on the nature of the column and the form of desired submissions, see the December 1981 issue of this journal.
40,020 citations
TL;DR: This paper has always been one of my favorite children, combining as it does elements of the duality of linear programming and combinatorial tools from graph theory, and it may be of some interest to tell the story of its origin this article.
Abstract: This paper has always been one of my favorite “children,” combining as it does elements of the duality of linear programming and combinatorial tools from graph theory. It may be of some interest to tell the story of its origin.
11,096 citations
TL;DR: This clearly written, mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NPcomplete problems, more.
Abstract: This clearly written , mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NPcomplete problems, more All chapters are supplemented by thoughtprovoking problems A useful work for graduate-level students with backgrounds in computer science, operations research, and electrical engineering Mathematicians wishing a self-contained introduction need look no further—American Mathematical Monthly 1982 ed
7,221 citations
"Feasibility-preserving crossover fo..." refers methods in this paper
...The Hungarian method gives an optimum assignment and it can be implemented in O(k(3)) time [13]....
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01 Jan 2010
TL;DR: This paper has always been one of my favorite “children,” combining as it does elements of the duality of linear programming and combinatorial tools from graph theory.
Abstract: This paper has always been one of my favorite “children,” combining as it does elements of the duality of linear programming and combinatorial tools from graph theory. It may be of some interest to tell the story of its origin.
3,108 citations
"Feasibility-preserving crossover fo..." refers background in this paper
...Fortunately, Kuhn [10] proposed an efficient way to solve the problem....
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...[10] H. W. Kuhn....
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...Fortunately, Kuhn [10] proposed an e.cient way to solve the problem....
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