Efficient Genetic Algorithms Using Simple Genes Exchange Local Search Policy for the Quadratic Assignment Problem

In this paper, we describe an approach for solving the quadratic assignment problem (QAP) that is based on genetic algorithms (GA). It will be shown that a standard canonical GA (SGA), which involves genetic operators of selection, reproduction, crossover, and mutation, tends to fall short of the desired performance expected of a search algorithm. The performance deteriorates significantly as the size of the problem increases. To address this syndrome, it is common for GA-based techniques to be embedded with deterministic local search procedures. It is proposed that the local search should involve simple procedure of genome reordering that should not be too complex. More importantly, from a computational point of view, the local search should not carry with it the full cost of evaluating a chromosome after each move in the localized landscape. Results of simulation on several difficult QAP benchmarks showed the effectiveness of our approaches.     

On the Hardness of the Quadratic Assignment Problem with Metaheuristics

Meta-heuristics are a powerful way to approximately solve hard combinatorial optimization problems. However, for a problem, the quality of results can vary considerably from one instance to another. Understanding such a behaviour is important from a theoretical point of view, but also has practical applications such as for the generation of instances during the evaluation stage of a heuristic.In this paper we propose a new complexity measure for the Quadratic Assignment Problem in the context of metaheuristics based on local search, e.g. simulated annealing. We show how the ruggedness coefficient previously introduced by the authors, in conjunction with the well known concept of dominance, provides important features of the search space explored during a local search algorithm, and gives a rather precise idea of the complexity of an instance for these heuristics. We comment previous experimental studies concerning tabu search methods and genetic algorithms with local search in the light of our complexity measure. New computational results with simulated annealing and taboo search are presented.     

Applying an Extended Guided Local Search to the Quadratic Assignment Problem

In this paper, we show how an extended Guided Local Search (GLS) can be applied to the Quadratic Assignment Problem (QAP). GLS is a general, penalty-based meta-heuristic, which sits on top of local search algorithms, to help guide them out of local minima. We present empirical results of applying several extended versions of GLS to the QAP, and show that these extensions can improve the range of parameter settings within which Guided Local Search performs well. Finally, we compare the results of running our extended GLS with some state of the art algorithms for the QAP.     

A Tabu Search Algorithm for the Quadratic Assignment Problem

Tabu search approach based algorithms are among the widest applied to various combinatorial optimization problems. In this paper, we propose a new version of the tabu search algorithm for the well-known problem, the quadratic assignment problem (QAP). One of the most important features of our tabu search implementation is an efficient use of mutations applied to the best solutions found so far. We tested this approach on a number of instances from the library of the QAP instances—QAPLIB. The results obtained from the experiments show that the proposed algorithm belongs to the most efficient heuristics for the QAP. The high efficiency of this algorithm is also demonstrated by the fact that the new best known solutions were found for several QAP instances.     

二次分配问题的大洪水算法求解

大洪水算法是一种求解组合优化问题的独特方法,该方法通过模拟洪水上涨的过程来达到求解一些组合优化难题的目的.本文运用该方法求解二次分配问题(QAP),设计了相应的算法程序,并对QAPLIB(二次分配基准问题库)中的算例进行了实验测试,结果表明,大洪水算法可以快速有效地求得二次分配问题的优化解,是求解二次分配问题的一个新的较好方案.     

一种求解物流设施二次分配问题的混合分布估计算法

为了求解物流设施二次分配问题,提出了一种混合分布估计算法(HEDA)。首先,根据QAP的距离和物流量矩阵信息,提出了一种基于假设物流中心启发式规则的种群初始化方法,用于提高初始种群的质量和算法的搜索效率;其次,针对HEDA的概率模型,提出了一种概率矩阵初始构型生成机制和扰动操作,用于提高算法的全局探索能力;最后,在分析QAP的结构性质的基础上,设计了一种基于快速评价的局部搜索策略,用于提高算法的局部开发能力。仿真计算实验和算法比较验证了HEDA的优化性能。     

一种基于匈牙利算法的二次分配问题求解方法

二次分配问题(Quadratic assignment problem,QAP)属于NP-hard组合优化难题.二次分配问题的线性化及下界计算方法,是求解二次分配问题的重要途径.以Frieze-Yadegar线性化模型和Gilmore-Lawler下界为基础,详细论述了二次分配问题线性化模型的结构特征,并分析了Gilmore-Lawler下界值往往远离目标函数最优值的原因.在此基础上,提出一种基于匈牙利算法的二次分配问题对偶上升下界求解法.通过求解QAPLIB中的部分实例,说明了方法的有效和可行性.     

Recent Advances for the Quadratic Assignment Problem with Special Emphasis on Instances that are Difficult for Meta-Heuristic Methods

This paper reports heuristic and exact solution advances for the Quadratic Assignment Problem (QAP).QAPinstances most often discussed in the literature are relatively well solved by heuristic approaches. Indeed, solutions at a fraction of one percent from the best known solution values are rapidly found by most heuristic methods. Exact methods are not able to prove optimality for these instances as soon as the problem size approaches 30 to 40. This article presents new QAP instances that are ill conditioned for many metaheuristic-based methods. However, these new instances are shown to be solved relatively well by some exact methods, since problem instances up to a size of 75 have been exactly solved.     

On A Special Case of the Quadratic Assignment Problem with an Application to Storage-and-Retrieval Devices

In a storage-and-retrieval device, items are retrieved on demand from a storage bank by a picking mechanism. Many varieties of these robotic devices are in use in manufacturing, logistics and computer peripherals. In printed circuit board manufacturing, storage-and-retrieval is intertwined with component placement and product clustering. Under certain circumstances, the problem of assigning items by type to storage slots to minimize the expected retrieval time is a quadratic assignment problem. Although such models are very difficult to solve to optimality, an important special case considered here admits an easy solution, namely, the well known “organ pipe” arrangement of items.     

Extensive Testing of a Hybrid Genetic Algorithm for Solving Quadratic Assignment Problems

A robust search algorithm should ideally exhibit reasonable performance on a diverse and varied set of problems. In an earlier paper Lim et al. (Computational Optimization and Applications, vol. 15, no. 3, 2000), we outlined a class of hybrid genetic algorithms based on the k-gene exchange local search for solving the quadratic assignment problem (QAP). We follow up on our development of the algorithms by reporting in this paper the results of comprehensive testing of the hybrid genetic algorithms (GA) in solving QAP. Over a hundred instances of QAP benchmarks were tested using a standard set of parameters setting and the results are presented along with the results obtained using simple GA for comparisons. Results of our testing on all the benchmarks show that the hybrid GA can obtain good quality solutions of within 2.5% above the best-known solution for 98% of the instances of QAP benchmarks tested. The computation time is also reasonable. For all the instances tested, all except for one require computation time not exceeding one hour. The results will serve as a useful baseline for performance comparison against other algorithms using the QAP benchmarks as a basis for testing.     

求解二次分配问题的新的流量模型

二次分配问题是具有广泛应用背景的经典组合优化难题之一。本文在二次分配问题已有线性化模型的基础上,提出了一种新的基于流量的线性化模型。数值试验结果表明,新模型无论从时间上还是计算节点数都更具有优势。     

几种基于匈牙利算法求解二次分配问题的方法及其分析比较

二次分配问题(Quadratic assignment problem,QAP)属于NP-hard组合优化难题。二次分配问题的线性化模型和下界计算方法,是求解二次分配问题的重要途径。本文以二次分配问题的线性化模型为基础,根据现有QAP对偶上升下界计算方法中的具体操作,提出几种可行的QAP对偶上升计算新方法。最后,通过求解QA-PLIB中的部分实例,深入分析其运行结果,详细讨论了基于匈牙利算法求解二次分配问题的对偶方法中哪些操作可较大程度地提高目标函数最优解的下界增长速度,这为基于匈牙利算法求解二次分配问题的方法的改进奠定了基础。     

求解二次分配问题的拉格朗日松弛新方法

以改进的拉格朗日松弛(Lagrangian relaxation,LR)方法和二次分配问题(quadratic assignment problem,QAP)的线性化模型为基础,给出了求解QAP的拉格朗日松弛新方法,这为有效求解QAP提供了一种新的解决方案.通过求解二次分配基准问题库(QAPLIB)中的实际算例,从实验的角度说明了拉格朗日松弛新方法求解QAP的可行性及存在的不足之处,并对今后进一步的研究工作指明了方向.     

QAPLIB – A Quadratic Assignment Problem Library

A collection of electronically available data instances for the QuadraticAssignment Problem is described. For each instance, we provide detailedinformation, indicating whether or not the problem is solved to optimality. Ifnot, we supply the best known bounds for the problem. Moreover we surveyavailable software and describe recent dissertations related to the QuadraticAssignment Problem.     

On the Applicability of Lower Bounds for Solving Rectilinear Quadratic Assignment Problems in Parallel

The quadratic assignment problem (QAP) belongs to the hard core of NP-hard optimization problems. After almost forty years of research only relatively small instances can be solved to optimality. The reason is that the quality of the lower bounds available for exact methods is not sufficient. Recently, lower bounds based on decomposition were proposed for the so called rectilinear QAP that proved to be the strongest for a large class of problem instances. We investigate the strength of these bounds when applied not only at the root node of a search tree but as the bound function used in a Branch-and-Bound code solving large scale QAPs.     

蚁群算法在战损装备抢修任务指派中的应用研究

结合战时装备保障实际情况和战损装备抢修任务特点,分析了现有战损装备抢修任务指派模型的特点及不足.依据紧急程度对战损装备抢修任务进行分类,建立了不同紧急度对应的装备抢修任务指派模型,重点是利用蚁群算法对模型进行求解.最后通过某装备保障想定的实例进行了验证,结果表明该算法操作简单、切实有效,能有效实施战损装备应急抢修任务的指派,在装备保障智能决策系统中有较好的应用前景.     

COSEARCH: A Parallel Cooperative Metaheuristic

In order to design a well-balanced metaheuristic for robustness, we propose the COSEARCH approach which manages the cooperation of complementary heuristic methods via an adaptive memory which contains a history of the search already done. In this paper, we present the idiosyncrasies of the COSEARCH approach and its application for solving large scale instances of the quadratic assignment problem (QAP). We propose an original design of the adaptive memory in order to focus on high quality regions of the search and avoid attractive but deceptive areas. For the QAP, we have hybridized three heuristic agents of complementary behaviours: a Tabu Search is used as the main search algorithm, a Genetic Algorithm is in charge of the diversification and a Kick Operator is applied to intensify the search. The evaluations have been executed on large scale network of workstations via a parallel environment which supports fault tolerance and adaptive dynamic scheduling of tasks.     

Well Solvable Cases of the Quadratic Assignment Problem with Monotone and Bimonotone Matrices

Conditions imposed on the matrices of the Quadratic Assignment Problem (QAP) are derived such that an optimum of the QAP is attained on a given permutation. These conditions describe four new sets of matrices, which, in the general case, are not anti-Monge and Toeplitz matrices that were used for most of the known well solvable special cases of the QAP.     

A study of exponential neighborhoods for the Travelling Salesman Problem and for the Quadratic Assignment Problem

This paper deals with exponential neighborhoods for combinatorial optimization problems. Exponential neighborhoods are large sets of feasible solutions whose size grows exponentially with the input length. We are especially interested in exponential neighborhoods over which the TSP (respectively, the QAP) can be solved in polynomial time, and we investigate combinatorial and algorithmical questions related to such neighborhoods.?First, we perform a careful study of exponential neighborhoods for the TSP. We investigate neighborhoods that can be defined in a simple way via assignments, matchings in bipartite graphs, partial orders, trees and other combinatorial structures. We identify several properties of these combinatorial structures that lead to polynomial time optimization algorithms, and we also provide variants that slightly violate these properties and lead to NP-complete optimization problems. Whereas it is relatively easy to find exponential neighborhoods over which the TSP can be solved in polynomial time, the corresponding situation for the QAP looks pretty hopeless: Every exponential neighborhood that is considered in this paper provably leads to an NP-complete optimization problem for the QAP. Received: September 5, 1997 / Accepted: November 15, 1999?Published online February 23, 2000