A multi-objective tabu search for a single-machine scheduling problem with sequence-dependent setup times

An m-objective tabu search algorithm for sequencing of n jobs on a single machine with sequence-dependent setup times is proposed. The algorithm produces a solution set that is reflective of the objectives’ weights and close to the best observed values of the objectives. We also formulate a mixed integer linear program to obtain the optimal solution of a three-objective problem. Numerical examples are used to study the behavior of the proposed m-objective tabu search algorithm and compare its solutions with those of the mixed integer linear program.     

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 two-phase tabu search based evolutionary algorithm for the maximum diversity problem

In this paper, we study the maximum diversity problem (MDP) which is equivalent to the quadratic unconstrained binary optimization (QUBO) problem with cardinality constraint. The MDP aims to select a subset of elements with given cardinality such that the sum of pairwise distances between any two elements in the selected subset is maximized. For solving this computationally challenging problem, we propose a two-phase tabu search based evolutionary algorithm (TPTS/EA), which integrates several distinguishing features to ensure the diversity and the quality of the evolution, such as a two-phase tabu search algorithm which consists of a dynamic candidate list (DCL) strategy-based traditional tabu search in the first phase and a solution-based tabu search procedure to refine the search in the second phase, and two path-relinking based recombination operators to generate new offspring solutions. Tested on three sets of totally 140 public instances in the literature, the study demonstrates the efficacy of the proposed TPTS/EA algorithm in terms of both solution quality and computational efficiency. Specifically, our proposed TPTS/EA algorithm is able to improve the previous best known results for 2 instances, while matching the previous best-known solutions for 130 instances. We also provide experimental evidences to highlight the beneficial effect of several important components in our TPTS/EA algorithm.     

A tabu search algorithm for the Open Shop problem

In this paper we consider the minimum makespan Open Shop problem without preemption. It is well-known that the case with only two machines can be optimally solved in linear time, whereas the problem with an arbitrary number of machines is NP-hard in the strong sense. We propose a tabu search algorithm for the solution of the problem which uses simple list scheduling algorithms to build the starting solutions. The algorithm is extensively tested on randomly generated instances.     

An evolutionary approach for bandwidth multicoloring problems

In this paper we consider some generalizations of the vertex coloring problem, where distance constraints are imposed between adjacent vertices (bandwidth coloring problem) and each vertex has to be colored with more than one color (bandwidth multicoloring problem). We propose an evolutionary metaheuristic approach for the first problem, combining an effective tabu search algorithm with population management procedures. The approach can be applied to the second problem as well, after a simple transformation. Computational results on instances from the literature show that the overall algorithm is able to produce high quality solutions in a reasonable amount of time, outperforming the most effective algorithms proposed for the bandwidth coloring problem, and improving the best known solution of many instances of the bandwidth multicoloring problem.     

Scheduling ambulance crews for maximum coverage

This paper addresses the problem of scheduling ambulance crews in order to maximize the coverage throughout a planning horizon. The problem includes the subproblem of locating ambulances to maximize expected coverage with probabilistic response times, for which a tabu search algorithm is developed. The proposed tabu search algorithm is empirically shown to outperform previous approaches for this subproblem. Two integer programming models that use the output of the tabu search algorithm are constructed for the main problem. Computational experiments with real data are conducted. A comparison of the results of the models is presented.     

A hybrid tabu search based heuristic for the periodic distribution inventory problem with perishable goods

Most of the research on integrated inventory and routing problems ignores the case when products are perishable. However, considering the integrated problem with perishable goods is crucial since any discrepancy between the routing and inventory cost can double down the risk of higher obsolescence costs due to the limited shelf-life of the products. In this paper, we consider a distribution problem involving a depot, a set of customers and a homogeneous fleet of capacitated vehicles. Perishable goods are transported from the depot to customers in such a way that out-of-stock situations never occur. The objective is to simultaneously determine the inventory and routing decisions over a given time horizon such that total transportation cost is minimized. We present a new “arc-based formulation” for the problem which is deemed more suitable for our new tabu search based approach for solving the problem. We perform a thorough sensitivity analysis for each of the tabu search parameters individually and use the obtained gaps to fine-tune the parameter values that are used in solving larger sized instances of the problem. We solve different sizes of randomly generated instances and compare the results obtained using the tabu search algorithm to those obtained by solving the problem using CPLEX and a recently published column generation algorithm. Our computational experiments demonstrate that the tabu search algorithm is capable of obtaining a near-optimal solution in less computational time than the time required to solve the problem to optimality using CPLEX, and outperforms the column generation algorithm for solving the “path flow formulation” of the problem in terms of solution quality in almost all of the considered instances.     

A combined local search and integer programming approach to the traveling tournament problem

The traveling tournament problem is a well-known combinatorial optimization problem with direct applications to sport leagues scheduling, that sparked intensive algorithmic research over the last decade. With the Challenge Traveling Tournament Instances as an established benchmark, the most successful approaches to the problem use meta-heuristics like tabu search or simulated annealing, partially heavily parallelized. Integer programming based methods on the other hand are hardly able to tackle larger benchmark instances. In this work we present a hybrid approach that draws on the power of commercial integer programming solvers as well as the speed of local search heuristics. Our proposed method feeds the solution of one algorithm phase to the other one, until no further improvements can be made. The applicability of this method is demonstrated experimentally on the galaxy instance set, resulting in currently best known solutions for most of the considered instances.     

Multi-neighborhood tabu search for the maximum weight clique problem

Given an undirected graph G=(V,E) with vertex set V={1,??,n} and edge set E?V×V. Let w:V??Z ⁺ be a weighting function that assigns to each vertex i??V a positive integer. The maximum weight clique problem (MWCP) is to determine a clique of maximum weight. This paper introduces a tabu search heuristic whose key features include a combined neighborhood and a dedicated tabu mechanism using a randomized restart strategy for diversification. The proposed algorithm is evaluated on a total of 136 benchmark instances from different sources (DIMACS, BHOSLIB and set packing). Computational results disclose that our new tabu search algorithm outperforms the leading algorithm for the maximum weight clique problem, and in addition rivals the performance of the best methods for the unweighted version of the problem without being specialized to exploit this problem class.     

Strategic oscillation for the capacitated hub location problem with modular links

The capacitated single assignment hub location problem with modular link capacities is a variant of the classical hub location problem in which the cost of using edges is not linear but stepwise, and the hubs are restricted in terms of transit capacity rather than in the incoming traffic. We propose a metaheuristic algorithm based on strategic oscillation, a methodology originally introduced in the context of tabu search. Our method incorporates several designs for constructive and destructive algorithms, together with associated local search procedures, to balance diversification and intensification for an efficient search. Computational results on a large set of instances show that, in contrast to exact methods that can only solve small instances optimally, our metaheuristic is able to find high-quality solutions on larger instances in short computing times. In addition, the new method, which joins tabu search strategies with strategic oscillation, outperforms the previous tabu search implementation.     

An Ant Colony Optimization Algorithm for Shop Scheduling Problems

We deal with the application of ant colony optimization to group shop scheduling, which is a general shop scheduling problem that includes, among others, the open shop scheduling problem and the job shop scheduling problem as special cases. The contributions of this paper are twofold. First, we propose a neighborhood structure for this problem by extending the well-known neighborhood structure derived by Nowicki and Smutnicki for the job shop scheduling problem. Then, we develop an ant colony optimization approach, which uses a strong non-delay guidance for constructing solutions and which employs black-box local search procedures to improve the constructed solutions. We compare this algorithm to an adaptation of the tabu search by Nowicki and Smutnicki to group shop scheduling. Despite its general nature, our algorithm works particularly well when applied to open shop scheduling instances, where it improves the best known solutions for 15 of the 28 tested instances. Moreover, our algorithm is the first competitive ant colony optimization approach for job shop scheduling instances.     

Hierarchical approach for survivable network design

A central design challenge facing network planners is how to select a cost-effective network configuration that can provide uninterrupted service despite edge failures. In this paper, we study the Survivable Network Design (SND) problem, a core model underlying the design of such resilient networks that incorporates complex cost and connectivity trade-offs. Given an undirected graph with specified edge costs and (integer) connectivity requirements between pairs of nodes, the SND problem seeks the minimum cost set of edges that interconnects each node pair with at least as many edge-disjoint paths as the connectivity requirement of the nodes. We develop a hierarchical approach for solving the problem that integrates ideas from decomposition, tabu search, randomization, and optimization. The approach decomposes the SND problem into two subproblems, Backbone design and Access design, and uses an iterative multi-stage method for solving the SND problem in a hierarchical fashion. Since both subproblems are NP-hard, we develop effective optimization-based tabu search strategies that balance intensification and diversification to identify near-optimal solutions. To initiate this method, we develop two heuristic procedures that can yield good starting points. We test the combined approach on large-scale SND instances, and empirically assess the quality of the solutions vis-à-vis optimal values or lower bounds. On average, our hierarchical solution approach generates solutions within 2.7% of optimality even for very large problems (that cannot be solved using exact methods), and our results demonstrate that the performance of the method is robust for a variety of problems with different size and connectivity characteristics.     

混合启发式算法求解多配送人员车辆路径问题

为解决带时间窗和多配送人员的车辆路径问题,本文采用混合启发式算法对其进行求解。该算法主要由整数规划重组、局部搜索算法和模拟退火算法三部分组成。在算法中,整数规划重组有效提高了解的质量,局部搜索算法和模拟退火算法保证了算法搜索的深入性和广泛性。通过与CPLEX和禁忌搜索算法进行对比,证实了混合启发式算法实用价值更高,求解效果更好。     

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。     

Performance of simulated annealing-based heuristic for the unconstrained binary quadratic programming problem

The unconstrained binary quadratic programming problem (BQP) is known to be NP-hard and has many practical applications. This paper presents a simulated annealing (SA)-based heuristic for the BQP. The new SA heuristic for the BQP is based on a simple (1-opt) local search heuristic and designed with a simple cooling schedule, but the multiple annealing processes are adopted. To show practical performances of the SA, we test on publicly available benchmark instances of large size ranging from 500 to 2500 variables and compare them with other heuristics such as multi-start local search, the previous SA, tabu search, and genetic algorithm incorporating the 1-opt local search. Computational results indicate that our SA leads to high-quality solutions with short times and is more effective than the competitors particularly for the largest benchmark set. Furthermore, the values of new best-known solutions found by the SA for several large instances are also reported.     

Reinforcement learning enhanced multi-neighborhood tabu search for the max-mean dispersion problem

This paper presents a highly effective reinforcement learning enhancement of multi-neighborhood tabu search for the max-mean dispersion problem. The reinforcement learning component uses the Q-learning mechanism that incorporates the accumulated feedback information collected from the actions performed during the search to guide the generation of diversified solutions. The tabu search component employs 1-flip and reduced 2-flip neighborhoods to collaboratively perform the neighborhood exploration for attaining high-quality local optima. A learning automata method is integrated in tabu search to adaptively determine the probability of selecting each neighborhood. Computational experiments on 80 challenging benchmark instances demonstrate that the proposed algorithm is favorably competitive with the state-of-the-art algorithms in the literature, by finding new lower bounds for 3 instances and matching the best known results for the other instances. Key elements and properties are also analyzed to disclose the source of the benefits of our integration of learning mechanisms and tabu search.     

Heuristics for multiple facility location in a network using the variance criterion

In cyclic networks the p-variance location problem is NP-hard, and therefore it is suitable to use heuristic methods to find approximate solutions to the problem. To this end, two strategies are explored, the first using combinatorial search procedures over the vertex set, whereas the second searches for the solution over the entire network. The initial vertex set solutions are generated by using tabu search, variable neighbourhood search and interchange procedures. The heuristics have been tested on instances of up to 30 vertices and 70 edges, and their performances compared.     

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.     

A parallel multi-neighborhood cooperative tabu search for capacitated vehicle routing problems

This paper presents a parallel tabu search algorithm that utilizes several different neighborhood structures for solving the capacitated vehicle routing problem. Single neighborhood or neighborhood combinations are encapsulated in tabu search threads and they cooperate through a solution pool for the purpose of exploiting their joint power. The computational experiments on 32 large scale benchmark instances show that the proposed method is highly effective and competitive, providing new best solutions to four instances while the average deviation of all best solutions found from the collective best results reported in the literature is about 0.22%. We are also able to associate the beneficial use of special neighborhoods with some test instance characteristics and uncover some sources of the collective power of multi-neighborhood cooperation.     

A tabu search heuristic for ship routing and scheduling

The purpose of this paper is to solve a planning problem faced by many shipping companies dealing with the transport of bulk products. These shipping companies are committed to carrying some contract cargoes and will try to derive additional revenue from optional spot cargoes. An efficient tabu search algorithm has been developed to ensure quick decision support for the planners. The solutions generated by the tabu search heuristic are compared with those produced by a previously published multi-start local search heuristic. Computational results show that the tabu search heuristic yields optimal or near-optimal solutions to real-life instances within reasonable time. For large and tigthly constrained cases, the tabu search heuristic provides much better solutions than the multi-start local search heuristic. A version of the tabu search heuristic will be integrated as an improved solver in a prototype decision support system used by several shipping companies.