A two-stage intelligent search algorithm for the two-dimensional strip packing problem

This paper presents a two-stage intelligent search algorithm for a two-dimensional strip packing problem without guillotine constraint. In the first stage, a heuristic algorithm is proposed, which is based on a simple scoring rule that selects one rectangle from all rectangles to be packed, for a given space. In the second stage, a local search and a simulated annealing algorithm are combined to improve solutions of the problem. In particular, a multi-start strategy is designed to enhance the search capability of the simulated annealing algorithm. Extensive computational experiments on a wide range of benchmark problems from zero-waste to non-zero-waste instances are implemented. Computational results obtained in less than 60 seconds of computation time show that the proposed algorithm outperforms the supposedly excellent algorithms reported recently, on average. It performs particularly better for large instances.     

A hybrid algorithm for the manufacturing cell formation problem

In this paper we compare different heuristic methods for the manufacturing cell formation problem considering part process sequence: a GRASP algorithm, a reactive GRASP algorithm and a hybrid algorithm which combines reactive GRASP and tabu search. All algorithms are tested with a set of instances from the literature. The results from the GRASP algorithm are compared to those of the reactive GRASP in order to evaluate the advantages of automatically adjusting the parameter value within the randomized greedy procedure. Also the reactive GRASP results are compared to those of the hybrid algorithm to evaluate the contribution to solution quality of replacing the local search phase of the GRASP algorithm with tabu search.     

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.     

A hybrid scatter search/electromagnetism meta-heuristic for project scheduling

In the last few decades, several effective algorithms for solving the resource-constrained project scheduling problem have been proposed. However, the challenging nature of this problem, summarised in its strongly NP-hard status, restricts the effectiveness of exact optimisation to relatively small instances. In this paper, we present a new meta-heuristic for this problem, able to provide near-optimal heuristic solutions for relatively large instances. The procedure combines elements from scatter search, a generic population-based evolutionary search method, and from a recently introduced heuristic method for the optimisation of unconstrained continuous functions based on an analogy with electromagnetism theory. We present computational experiments on standard benchmark datasets, compare the results with current state-of-the-art heuristics, and show that the procedure is capable of producing consistently good results for challenging instances of the resource-constrained project scheduling problem. We also demonstrate that the algorithm outperforms state-of-the-art existing heuristics.     

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.     

A reduction approach for solving the rectangle packing area minimization problem

In the rectangle packing area minimization problem (RPAMP) we are given a set of rectangles with known dimensions. We have to determine an arrangement of all rectangles, without overlapping, inside an enveloping rectangle of minimum area. The paper presents a generic approach for solving the RPAMP that is based on two algorithms, one for the 2D Knapsack Problem (KP), and the other for the 2D Strip Packing Problem (SPP). In this way, solving an instance of the RPAMP is reduced to solving multiple SPP and KP instances. A fast constructive heuristic is used as SPP algorithm while the KP algorithm is instantiated by a tree search method and a genetic algorithm alternatively. All these SPP and KP methods have been published previously. Finally, the best variants of the resulting RPAMP heuristics are combined within one procedure. The guillotine cutting condition is always observed as an additional constraint. The approach was tested on 15 well-known RPAMP instances (above all MCNC and GSRC instances) and new best solutions were obtained for 10 instances. The computational effort remains acceptable. Moreover, 24 new benchmark instances are introduced and promising results are reported.     

Tabu search and GRASP for the maximum diversity problem

In this paper, we develop new heuristic procedures for the maximum diversity problem (MDP). This NP-hard problem has a significant number of practical applications such as environmental balance, telecommunication services or genetic engineering. The proposed algorithm is based on the tabu search methodology and incorporates memory structures for both construction and improvement. Although proposed in seminal tabu search papers, memory-based constructions have often been implemented in naïve ways that disregard important elements of the fundamental tabu search proposals. We will compare our tabu search construction with a memory-less design and with previous algorithms recently developed for this problem. The constructive method can be coupled with a local search procedure or a short-term tabu search for improved outcomes. Extensive computational experiments with medium and large instances show that the proposed procedure outperforms the best heuristics reported in the literature within short computational times.     

A tabu search and a genetic algorithm for solving a bicriteria general job shop scheduling problem

This paper deals with a general job shop scheduling problem with multiple constraints, coming from printing and boarding industry. The objective is the minimization of two criteria, the makespan and the maximum lateness, and we are interested in finding an approximation of the Pareto frontier. We propose a fast and elitist genetic algorithm based on NSGA-II for solving the problem. The initial population of this algorithm is either randomly generated or partially generated by using a tabu search algorithm, that minimizes a linear combination of the two criteria. Both the genetic and the tabu search algorithms are tested on benchmark instances from flexible job shop literature and computational results show the interest of both methods to obtain an efficient and effective resolution method.     

Robust formulations for economic lot-sizing problem with remanufacturing

In this paper, we consider a lot-sizing problem with the remanufacturing option under parameter uncertainties imposed on demands and returns. Remanufacturing has recently been a fast growing area of interest for many researchers due to increasing awareness on reducing waste in production environments, and in particular studies involving remanufacturing and parameter uncertainties simultaneously are very scarce in the literature. We first present a min-max decomposition approach for this problem, where decision maker’s problem and adversarial problem are treated iteratively. Then, we propose two novel extended reformulations for the decision maker’s problem, addressing some of the computational challenges. An original aspect of the reformulations is that they are applied only to the latest scenario added to the decision maker’s problem. Then, we present an extensive computational analysis, which provides a detailed comparison of the three formulations and evaluates the impact of key problem parameters. We conclude that the proposed extended reformulations outperform the standard formulation for a majority of the instances. We also provide insights on the impact of the problem parameters on the computational performance.     

Some effective heuristics for no-wait flowshops with setup times to minimize total completion time

In this work, we consider a complex flowshop scheduling problem in which both no-wait and separate setup times are considered. The optimisation criterion is the minimisation of the total completion time. We propose an effective dominance rule for the four machine case that can also be used for m machines. Five simple and fast heuristics are proposed along with two easy to code stochastic local search methods, one of them being based on Iterated Local Search (ILS). An extensive computational evaluation is carried out with two sets of 5,400 instances. All seven methods are compared to two recent algorithms. The results, confirmed by thorough statistical analyses, show that the proposed methods are more effective and efficient when compared to the best existing algorithms in the literature for the considered problem.     

Expanding Neighborhood GRASP for the Traveling Salesman Problem

In this paper, we present the application of a modified version of the well known Greedy Randomized Adaptive Search Procedure (GRASP) to the TSP. The proposed GRASP algorithm has two phases: In the first phase the algorithm finds an initial solution of the problem and in the second phase a local search procedure is utilized for the improvement of the initial solution. The local search procedure employs two different local search strategies based on 2-opt and 3-opt methods. The algorithm was tested on numerous benchmark problems from TSPLIB. The results were very satisfactory and for the majority of the instances the results were equal to the best known solution. The algorithm is also compared to the algorithms presented and tested in the DIMACS Implementation Challenge that was organized by David Johnson.     

A tabu search heuristic for the generalized minimum spanning tree problem

This paper describes an attribute based tabu search heuristic for the generalized minimum spanning tree problem (GMSTP) known to be NP-hard. Given a graph whose vertex set is partitioned into clusters, the GMSTP consists of designing a minimum cost tree spanning all clusters. An attribute based tabu search heuristic employing new neighborhoods is proposed. An extended set of TSPLIB test instances for the GMSTP is generated and the heuristic is compared with recently proposed genetic algorithms. The proposed heuristic yields the best results for all instances. Moreover, an adaptation of the tabu search algorithm is proposed for a variation of the GMSTP in which each cluster must be spanned at least once.     

No-wait Job Shop Scheduling: Tabu Search and Complexity of Subproblems

This paper deals with the no-wait job shop problem with a makespan objective. We present some new theoretical properties on the complexity of subproblems associated with a well-known decomposition approach. Justified by the complexity results, we implement a fast tabu search algorithm for the problem at hand. It is extensively tested on known benchmark instances and compares favorably to the best existing algorithms for the no-wait job shop as well as the no-wait flow shop.     

带时间窗分车运输同时收发车辆路径问题及其启发式算法

本文结合汽车零部件第三方物流的实际背景,提出了带时间窗的可分车运输同时收发车辆路径问题(简称SVRPSPDTW),并给出了问题的数学模型,同时提出两个求解该问题的启发式算法,最后进行了数值试验.由于没有可以利用的算例,本文在Solomn测试基准库的基础上构建了针对新问题的算例.计算结果表明,所有算例计算时间均不超过1秒,且算法1无论是从车辆的使用数还是从车辆行驶的路径总长度上都明显优于算法2,从而说明算法1是寻找SVRPSPDTW问题初始可行解的较为有效的算法.     

A Particle Swarm Optimization Algorithm with Path Relinking for the Location Routing Problem

This paper introduces a new hybrid algorithmic nature inspired approach based on particle swarm optimization, for solving successfully one of the most popular logistics management problems, the location routing problem (LRP). The proposed algorithm for the solution of the location routing problem, the hybrid particle swarm optimization (HybPSO-LRP), combines a particle swarm optimization (PSO) algorithm, the multiple phase neighborhood search – greedy randomized adaptive search procedure (MPNS-GRASP) algorithm, the expanding neighborhood search (ENS) strategy and a path relinking (PR) strategy. The algorithm is tested on a set of benchmark instances. The results of the algorithm are very satisfactory for these instances and for six of them a new best solution has been found.      

Image registration with iterated local search

This contribution is devoted to the application of iterated local search to image registration, a very complex, real-world problem in the field of image processing. To do so, we first re-define this parameter estimation problem as a combinatorial optimization problem, then analyze the use of image-specific information to guide the search in the form of an heuristic function, and finally propose its solution by iterated local search. Our algorithm is tested by comparing its performance to that of two different baseline algorithms: iterative closest point, a well-known, image registration technique, a hybrid algorithm including the latter technique within a simulated annealing approach, a multi-start local search procedure, that allows us to check the influence of the search scheme considered in the problem solving, and a real coded genetic algorithm. Four different problem instances are tackled in the experimental study, resulting from two images and two transformations applied on them. Three parameter settings are analyzed in our approach in order to check three heuristic information scenarios where the heuristic is not used at all, is partially used or almost completely guides the search process, as well as two different number of iterations in the algorithms outer-inner loops. This work was partially supported by the Spanish Ministerio de Ciencia y Tecnología under project TIC2003-00877 (including FEDER fundings) and under Network HEUR TIC2002-10866-E.     

带有资源转移时间的RCPSP资源流模型及算法

本文在传统资源受限项目调度问题(resource-constrained project scheduling problem, RCPSP)中引入资源转移时间,为有效获得问题的最优解,采用资源流编码方式表示可行解,建立了带有资源转移时间的RCPSP资源流优化模型,目标为最小化项目工期。根据问题特征设计了改进的资源流重构邻域算子,分别设计了改进的禁忌搜索算法和贪心随机自适应禁忌搜索算法求解模型。数据实验结果表明,相较于现有文献中的方法,所提两种算法均可针对更多的项目实例求得最优解,并且得到最优解的时间更短,求解效率更高。此外,分析了算法在求解具有不同特征的项目实例时的性能,所得结果为项目经理结合项目特征评价算法适用性提供了指导。     

New convergent heuristics for 0–1 mixed integer programming

Several hybrid methods have recently been proposed for solving 0–1 mixed integer programming problems. Some of these methods are based on the complete exploration of small neighborhoods. In this paper, we present several convergent algorithms that solve a series of small sub-problems generated by exploiting information obtained from a series of relaxations. These algorithms generate a sequence of upper bounds and a sequence of lower bounds around the optimal value. First, the principle of a linear programming-based algorithm is summarized, and several enhancements of this algorithm are presented. Next, new hybrid heuristics that use linear programming and/or mixed integer programming relaxations are proposed. The mixed integer programming (MIP) relaxation diversifies the search process and introduces new constraints in the problem. This MIP relaxation also helps to reduce the gap between the final upper bound and lower bound. Our algorithms improved 14 best-known solutions from a set of 108 available and correlated instances of the 0–1 multidimensional Knapsack problem. Other encouraging results obtained for 0–1 MIP problems are also presented.     

A tabu search algorithm for the minmax regret minimum spanning tree problem with interval data

This paper deals with the strongly NP-hard minmax regret version of the minimum spanning tree problem with interval costs. The best known exact algorithms solve the problem in reasonable time for rather small graphs. In this paper an algorithm based on the idea of tabu search is constructed. Some properties of the local minima are shown. Exhaustive computational tests for various classes of graphs are performed. The obtained results suggest that the proposed tabu search algorithm quickly outputs optimal solutions for the smaller instances, previously discussed in the existing literature. Furthermore, some arguments that this algorithm performs well also for larger instances are provided.     

An Application of a Multi-Objective Tabu Search Algorithm to a Bicriteria Flowshop Problem

This paper proposes a new tabu search algorithm for multi-objective combinatorial problems with the goal of obtaining a good approximation of the Pareto-optimal or efficient solutions. The algorithm works with several paths of solutions in parallel, each with its own tabu list, and the Pareto dominance concept is used to select solutions from the neighborhoods. In this way we obtain at each step a set of local nondominated points. The dispersion of points is achieved by a clustering procedure that groups together close points of this set and then selects the centroids of the clusters as search directions. A nice feature of this multi-objective algorithm is that it introduces only one additional parameter, namely, the number of paths. The algorithm is applied to the permutation flowshop scheduling problem in order to minimize the criteria of makespan and maximum tardiness. For instances involving two machines, the performance of the algorithm is tested against a Branch-and-Bound algorithm proposed in the literature, and for more than two machines it is compared with that of a tabu search algorithm and a genetic local search algorithm, both from the literature. Computational results show that the heuristic yields a better approximation than these algorithms.