{"title":"Using QAP Bounds for the Circulant TSP to Design Reconfigurable","authors":"E. Medova","doi":"10.1090/dimacs/016/14","DOIUrl":"https://doi.org/10.1090/dimacs/016/14","url":null,"abstract":"","PeriodicalId":376860,"journal":{"name":"Quadratic Assignment and Related Problems","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134014138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Difficulties of Exact Methods for Solving the Quadratic Assignment Problem","authors":"T. Mautor, C. Roucairol","doi":"10.1090/dimacs/016/13","DOIUrl":"https://doi.org/10.1090/dimacs/016/13","url":null,"abstract":"","PeriodicalId":376860,"journal":{"name":"Quadratic Assignment and Related Problems","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115109607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Reformulation Scheme and New Lower Bounds for the QAP","authors":"P. Carraresi, F. Malucelli","doi":"10.1090/dimacs/016/06","DOIUrl":"https://doi.org/10.1090/dimacs/016/06","url":null,"abstract":"","PeriodicalId":376860,"journal":{"name":"Quadratic Assignment and Related Problems","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130077213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Partitioning Multiple Data Sets: Multidimensional Assignments and Lagrangian Relaxation","authors":"A. Poore, N. Rijavec","doi":"10.1090/dimacs/016/16","DOIUrl":"https://doi.org/10.1090/dimacs/016/16","url":null,"abstract":"","PeriodicalId":376860,"journal":{"name":"Quadratic Assignment and Related Problems","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117312343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A new hybrid procedure that combines genetic operators to existing heuristics is proposed to solve the Quadratic Assignment Problem (QAP). Genetic operators are found to improve the performance of both local search and tabu search. Some guidelines are also given to design good hybrid schemes. These hybrid algorithms are then used to improve on the best known solutions of many test problems in the literature.
{"title":"Genetic Hybrids for the Quadratic Assignment Problem","authors":"C. Fleurent, J. Ferland","doi":"10.1090/dimacs/016/08","DOIUrl":"https://doi.org/10.1090/dimacs/016/08","url":null,"abstract":"A new hybrid procedure that combines genetic operators to existing heuristics is proposed to solve the Quadratic Assignment Problem (QAP). Genetic operators are found to improve the performance of both local search and tabu search. Some guidelines are also given to design good hybrid schemes. These hybrid algorithms are then used to improve on the best known solutions of many test problems in the literature.","PeriodicalId":376860,"journal":{"name":"Quadratic Assignment and Related Problems","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133123822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Most real world problems especially circuit layout and VLSI design are too complex for any single processing technique to solve in isolation. Stochastic, adaptive and local search approaches have strengths and weaknesses and should be viewed not as competing models but as complimentary ones. This paper describes the application of a combined Tabu Search 1] and Genetic Algorithm heuristic to guide an eecient interchange algorithm to explore and exploit the solution space of a hypergraph partitioning problem. Results obtained indicate, that the generated solutions and running time of this hybrid are superior to results obtained from a combined eigenvector and node interchange method 11]. 1. Introduction In the combinatorial sense, the layout problem is a constrained optimization problem. We are given a description of a circuit (usually called a netlist) which is a description of switching elements and their connecting wires. We seek an assignment of geometric coordinates of the circuit components that satisses the requirements of the fabrication technology (suucient spacing between wires, restricted number of wiring layers, and so on), and that minimizes certain cost criteria. Practically all versions of the layout problem as a whole are intractable; that is, they are NP-hard. Thus, we have to resort to heuristic methods to attempt to solve such problems. One of these methods is to break up the problem into subproblems (circuit partitioning, component placement and wire routing).
{"title":"Advanced Search Techniques for Circuit Partitioning","authors":"S. Areibi, A. Vannelli","doi":"10.1090/dimacs/016/03","DOIUrl":"https://doi.org/10.1090/dimacs/016/03","url":null,"abstract":"Most real world problems especially circuit layout and VLSI design are too complex for any single processing technique to solve in isolation. Stochastic, adaptive and local search approaches have strengths and weaknesses and should be viewed not as competing models but as complimentary ones. This paper describes the application of a combined Tabu Search 1] and Genetic Algorithm heuristic to guide an eecient interchange algorithm to explore and exploit the solution space of a hypergraph partitioning problem. Results obtained indicate, that the generated solutions and running time of this hybrid are superior to results obtained from a combined eigenvector and node interchange method 11]. 1. Introduction In the combinatorial sense, the layout problem is a constrained optimization problem. We are given a description of a circuit (usually called a netlist) which is a description of switching elements and their connecting wires. We seek an assignment of geometric coordinates of the circuit components that satisses the requirements of the fabrication technology (suucient spacing between wires, restricted number of wiring layers, and so on), and that minimizes certain cost criteria. Practically all versions of the layout problem as a whole are intractable; that is, they are NP-hard. Thus, we have to resort to heuristic methods to attempt to solve such problems. One of these methods is to break up the problem into subproblems (circuit partitioning, component placement and wire routing).","PeriodicalId":376860,"journal":{"name":"Quadratic Assignment and Related Problems","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114631544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Improved Linear Programming-based Lower Bounds for the Quadratic Assignment Proglem","authors":"Warren P. Adams, T. Johnson","doi":"10.1090/dimacs/016/02","DOIUrl":"https://doi.org/10.1090/dimacs/016/02","url":null,"abstract":"","PeriodicalId":376860,"journal":{"name":"Quadratic Assignment and Related Problems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132063619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Constructive Method to Improve Lower Bounds for the Quadratic Assignment Problem","authors":"Jaishankar Chakrapani, J. Skorin-Kapov","doi":"10.1090/dimacs/016/07","DOIUrl":"https://doi.org/10.1090/dimacs/016/07","url":null,"abstract":"","PeriodicalId":376860,"journal":{"name":"Quadratic Assignment and Related Problems","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114332935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A special class of the quadratic assignment problem (QAP) is considered. This class of QAP describes the multiway partitioning problem which is the problem of partitioning a graph into disjoint subgraphs of prescribed sizes by removing the fewest number of edges. A genetic algorithm (GA) for solving this problem is described. A novel feature of this algorithm is the schema preprocessing phase that helps create important building blocks, which in turn improves the performance of the GA. Experimental tests on graphs with published solutions showed that the algorithm performed comparable to or better than the simulated annealing algorithm. Consider the quadratic assignment problem (QAP) where the n x n flow matrix F is a 0-1 symmetric matrix with O'son the main diagonal and the n x n distance matrix D is a block matrix of the form whereObi is a bi x bi matrix of all zeros, for integers b1, ... , bk such that L:~=lbi = n. All other entries of Dare 1. This QAP can be easily seen to describe the followinggraph problem. Let G = (V,E) be an undirected graph on n vertices and k integers b1, ... ,bk be given. The multiway partitioning problem is the 1993 Mathematics Subject Classification. Primary 65KlO; Secondary 68T05, 68RlO. This paper is in preliminary form. problem of finding the smallest set of edges in G whose removal separates G into k disjoint subgraphs Gi = (Vi, Ei), i = 1, ... ,k such that (i) IViI = bi, for all i, (ii) U~=lVi = V, and (iii) Vj n Vi = 0 for j f. t. In other words, it is the problem of finding a partition of the vertex set V into k disjoint subsets of specified sizes and minimizing the number of edges with endpoints in different subsets of the partition. The number of edges having endpoints in different parts of the partition is called the size or cut size of the partition. The flowmatrix F in the QAP is simply the adjacency matrix of the graph G and the number of edges connecting different parts of the partition, Le., the quantity to be minimized, is n L D[i,j)F[1r(i),1r(j)],
研究一类特殊的二次分配问题(QAP)。这类QAP描述了多路分区问题，即通过去除最少边数将图划分为规定大小的不相交子图的问题。提出了一种求解该问题的遗传算法。该算法的一个新特性是模式预处理阶段，它有助于创建重要的构建块，从而提高遗传算法的性能。用已发表的解对图进行的实验测试表明，该算法的性能与模拟退火算法相当或优于模拟退火算法。考虑二次分配问题(QAP)，其中n x n流矩阵F是一个0-1对称矩阵，O'son为主对角线，n x n距离矩阵D是一个块矩阵，其形式为obi是一个全零的bi x bi矩阵，对于整数b1，…， bk使得L:~=lbi = n。这个QAP可以很容易地描述下面的图问题。设G = (V,E)是有n个顶点k个整数的无向图b1，…我不知道。多路划分问题是1993年《数学学科分类》中的问题。主65 klo;二级68T05, 68RlO。这篇论文是初步的。求G中最小边集的问题，其移除将G分成k个不相交子图Gi = (Vi, Ei)， i = 1，…，k使得(i) iv = bi，对于所有i， (ii) U~=lVi = V， (iii) Vj n Vi = 0，对于j f. t。换句话说，它是找到顶点集V划分为k个指定大小的不相交子集的问题，并最小化在该划分的不同子集中端点的边的数量。在分区的不同部分具有端点的边的数量称为分区的大小或切割大小。QAP中的流矩阵F就是图G的邻接矩阵和连接分区不同部分Le的边的数目。，最小量为n L D[i,j] F[1r(i)，1r(j)]，
{"title":"A Genetic Algorithm for a Special Class of the Quadratic Assignment Problem","authors":"T. N. Bui, B. Moon","doi":"10.1090/dimacs/016/04","DOIUrl":"https://doi.org/10.1090/dimacs/016/04","url":null,"abstract":"A special class of the quadratic assignment problem (QAP) is considered. This class of QAP describes the multiway partitioning problem which is the problem of partitioning a graph into disjoint subgraphs of prescribed sizes by removing the fewest number of edges. A genetic algorithm (GA) for solving this problem is described. A novel feature of this algorithm is the schema preprocessing phase that helps create important building blocks, which in turn improves the performance of the GA. Experimental tests on graphs with published solutions showed that the algorithm performed comparable to or better than the simulated annealing algorithm. Consider the quadratic assignment problem (QAP) where the n x n flow matrix F is a 0-1 symmetric matrix with O'son the main diagonal and the n x n distance matrix D is a block matrix of the form whereObi is a bi x bi matrix of all zeros, for integers b1, ... , bk such that L:~=lbi = n. All other entries of Dare 1. This QAP can be easily seen to describe the followinggraph problem. Let G = (V,E) be an undirected graph on n vertices and k integers b1, ... ,bk be given. The multiway partitioning problem is the 1993 Mathematics Subject Classification. Primary 65KlO; Secondary 68T05, 68RlO. This paper is in preliminary form. problem of finding the smallest set of edges in G whose removal separates G into k disjoint subgraphs Gi = (Vi, Ei), i = 1, ... ,k such that (i) IViI = bi, for all i, (ii) U~=lVi = V, and (iii) Vj n Vi = 0 for j f. t. In other words, it is the problem of finding a partition of the vertex set V into k disjoint subsets of specified sizes and minimizing the number of edges with endpoints in different subsets of the partition. The number of edges having endpoints in different parts of the partition is called the size or cut size of the partition. The flowmatrix F in the QAP is simply the adjacency matrix of the graph G and the number of edges connecting different parts of the partition, Le., the quantity to be minimized, is n L D[i,j)F[1r(i),1r(j)],","PeriodicalId":376860,"journal":{"name":"Quadratic Assignment and Related Problems","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133572856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Approximation of Association Data by Structures and Clusters","authors":"B. Mirkin","doi":"10.1090/dimacs/016/15","DOIUrl":"https://doi.org/10.1090/dimacs/016/15","url":null,"abstract":"","PeriodicalId":376860,"journal":{"name":"Quadratic Assignment and Related Problems","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126431340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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