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.     

Heuristic Techniques for Single Line Train Scheduling

Optimising a train schedule on a single line track is known to be NP-Hard with respect to the number of conflicts in the schedule. This makes it difficult to determine optimum solutions to real life problems in reasonable time and raises the need for good heuristic techniques. The heuristics applied and compared in this paper are a local search heuristic with an improved neighbourhood structure, genetic algorithms, tabu search and two hybrid algorithms. When no time constraints are enforced on solution time, the genetic and hybrid algorithms were within five percent of the optimal solution for at least ninety percent of the test problems.     

A graph-based hyper-heuristic for educational timetabling problems

This paper presents an investigation of a simple generic hyper-heuristic approach upon a set of widely used constructive heuristics (graph coloring heuristics) in timetabling. Within the hyper-heuristic framework, a tabu search approach is employed to search for permutations of graph heuristics which are used for constructing timetables in exam and course timetabling problems. This underpins a multi-stage hyper-heuristic where the tabu search employs permutations upon a different number of graph heuristics in two stages. We study this graph-based hyper-heuristic approach within the context of exploring fundamental issues concerning the search space of the hyper-heuristic (the heuristic space) and the solution space. Such issues have not been addressed in other hyper-heuristic research. These approaches are tested on both exam and course benchmark timetabling problems and are compared with the fine-tuned bespoke state-of-the-art approaches. The results are within the range of the best results reported in the literature. The approach described here represents a significantly more generally applicable approach than the current state of the art in the literature. Future work will extend this hyper-heuristic framework by employing methodologies which are applicable on a wider range of timetabling and scheduling problems.     

Meta-heuristic approaches with memory and evolution for a multi-product production/distribution system design problem

We consider a multi-product two-stage production/distribution system design problem (PDSD) where a fixed number of capacitated distribution centers are to be located with respect to capacitated suppliers (plants) and retail locations (customers) while minimizing the total costs in the system. We present a mixed-integer problem formulation that facilitates the development of efficient heuristic procedures. We provide meta-heuristic procedures, including a population-based scatter search with path relinking and trajectory-based local and tabu search, for the solution of the problem. We also develop efficient construction heuristics and transshipment heuristics that are incorporated into the heuristic procedures for the solution of subproblems. We present extensive computational results that show the high performance of the solution approaches. We obtain smaller than 1.0% average optimality gaps with acceptable runtimes, even for relatively large problems. The computational results also demonstrate the effectiveness of the construction and transshipment heuristics that impact the solution quality and overall runtimes.     

An Improved Petal Heuristic for the Vehicle Routeing Problem

Solutions produced by the first generation of heuristics for the vehicle routeing problem are often far from optimal. Recent adaptations of local search improvement heuristics, like tabu search, produce much better solutions but require increased computing time. However there are situations where good solutions must be obtained quickly. The algorithm proposed in this paper yields solutions almost as good as those produced by tabu search adaptations, but at only a small fraction of their computing time. This heuristic can be seen as an improved version of the original petal heuristic. On 14 benchmark test problems, the proposed heuristic yields solutions whose values lie on average within 2.38% of that of the best known solutions.     

An Application of Tabu Search Heuristic for the Maximum Edge-Weighted Subgraph Problem

The purpose of this article is to describe an efficient search heuristic for the Maximum Edge-weighted Subgraph (MEwS) problem. This problem requires to find a subgraph such that the sum of the weights associated with the edges of the subgraph is maximized subject to a cardinality constraint. In this study a tabu search heuristic for the MEwS problem is proposed. Different algorithms to obtain an initial solution are presented. One neighborhood search strategy is also proposed. Preliminary computational results are reported for randomly generated test problems of MEwS problem with different densities and sizes. For most of test problems, the tabu search heuristic found good solutions. In addition, for large size test problems, the tabu search outperformed the local search heuristic appearing in the literature.     

Heuristic Procedures for the Capacitated Vehicle Routing Problem

In this paper we present two new heuristic procedures for the Capacitated Vehicle Routing Problem (CVRP). The first one solves the problem from scratch, while the second one uses the information provided by a strong linear relaxation of the original problem. This second algorithm is designed to be used in a branch and cut approach to solve to optimality CVRP instances. In both heuristics, the initial solution is improved using tabu search techniques. Computational results over a set of known instances, most of them with a proved optimal solution, are given.     

Iterated tabu search for the car sequencing problem

This paper introduces an iterated tabu search heuristic for the daily car sequencing problem in which a set of cars must be sequenced so as to satisfy requirements from the paint shop and the assembly line. The iterated tabu search heuristic combines a classical tabu search with perturbation operators that help escape from local optima. The resulting heuristic is flexible, easy to implement, and fast. It has produced very good results on a set of test instances provided by the French car manufacturer Renault.     

Simple assembly line balancing—Heuristic approaches

In this paper heuristics for Type 1 and Type 2 of the Simple Assembly Line Balancing Problem (SALBP) are described. Type 1 of SALBP (SALBP-1) consists of assigning tasks to work stations such that the number of stations is minimized for a given production rate whereas Type 2 (SALBP-2) is to maximize the production rate, or equivalently, to minimize the sum of idle times for a given number of stations. In both problem types, precedence constraints between the tasks have to be considered.We describe bidirectional and dynamic extensions to heuristic priority rules widely used for SALBP-1. For the solution of SALBP-2 we present search methods which involve the repetitive application of procedures for SALBP-1. Furthermore, improvement procedures for SALBP-2 are developed and combined with tabu search, a recent strategy to overcome local optimality. Several optional elements of tabu search are discussed. Finally, the application of a nontraditional tabu search approach to solve SALBP-1 is investigated. Computational experiments validate the effectiveness of our new approaches.     

A tabu thresholding algorithm for arc crossing minimization in bipartite graphs

Acyclic directed graphs are commonly used to model complex systems. The most important criterion to obtain a readable map of an acyclic graph is that of minimizing the number of arc crossings. In this paper, we present a heuristic for solving the problem of minimizing the number of arc crossings in a bipartite graph. It consists of a novel and easier implementation of fundamental tabu search ideas without explicit use of memory structures (a tabu thresholding approach). Computational results are reported on a set of 250 randomly generated test problems. Our algorithm has been compared with the two best heuristics published in the literature and with the optimal solutions for the test problems, size permitting.This research was partially supported by the C.I.C.Y.T. with code tap92-0639.     

Variable neighborhood search for harmonic means clustering

Harmonic means clustering is a variant of minimum sum of squares clustering (which is sometimes called K-means clustering), designed to alleviate the dependance of the results on the choice of the initial solution. In the harmonic means clustering problem, the sum of harmonic averages of the distances from the data points to all cluster centroids is minimized. In this paper, we propose a variable neighborhood search heuristic for solving it. This heuristic has been tested on numerous datasets from the literature. It appears that our results compare favorably with recent ones from tabu search and simulated annealing heuristics.     

Tabu search for graph partitioning

In this paper, we develop a tabu search procedure for solving the uniform graph partitioning problem. Tabu search, an abstract heuristic search method, has been shown to have promise in solving several NP-hard problems, such as job shop and flow shop scheduling, vehicle routing, quadratic assignment, and maximum satisfiability. We compare tabu search to other heuristic procedures for graph partitioning, and demonstrate that tabu search is superior to other solution approaches for the uniform graph partitioning problem both with respect to solution quality and computational requirements.     

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.     

Optimizing heuristic search in forest planning

Heuristic search methods are being used more and more in forest planning since the current formulations of exact methods such as linear programming are not suitable to all today's planning problems. A practical problem with most heuristics is that their performance greatly depends on the parameters that guide their search process. The effect of parameters is hard to know without extensive tests, but these tests cannot be conducted in forest planning practice, because of lacking time and experience. This study presented a method that uses Hooke and Jeeves direct search to optimize the parameters of a heuristic, taking into account the allowed computing time. The method was used to optimize three local-improvement heuristics in a non-spatial and a spatial forest planning problem, and with a short and long computing time. The heuristics were simulated annealing, threshold accepting, and tabu search, all of which are used in forestry. The results were logical and showed that while the optimal values of some parameters were rather constant the others were sensitive to problem type, allowed computing time, or problem size. The objective function value of the forest planning problem was not sensitive to small changes in the parameters of the heuristics. However, because computing time was very sensitive to many parameters, there was not much freedom to set the parameters if both the quality of the solution and speed of the algorithm had to be maintained.     

A tabu search algorithm for solving economic lot scheduling problem

The economic lot scheduling problem has driven considerable amount of research. The problem is NP-hard and recent research is focused on finding heuristic solutions rather than searching for optimal solutions. This paper introduces a heuristic method using a tabu search algorithm to solve the economic lot scheduling problem. Diversification and intensification schemes are employed to improve the efficiency of the proposed Tabu search algorithm. Experimental design is conducted to determine the best operating parameters for the Tabu search. Results show that the tabu search algorithm proposed in this paper outperforms two well known benchmark algorithms.     

A tabu search approach for solving a difficult forest harvesting machine location problem

This paper deals with two main problems in forest harvesting. The first is that of selecting the locations for the machinery to haul logs from the points where they are felled to the roadside. The second consists in designing the access road network connecting the existing road network with the points where machinery is installed. Their combination induces a very important and difficult problem to solve in forest harvesting. It can be formulated as a combination of two difficult optimization problems: a plant location problem and a fixed charge network flow problem. In this paper, we propose a solution approach based on tabu search. The proposed heuristic includes several enhancements of the basic tabu search framework. The main difficulty lies in evaluating neighboring solutions, which involves decisions related to location of machinery and to road network arcs. Hence, the neighborhood is more complex than in typical applications of metaheuristics. Minimum spanning tree algorithms and Steiner tree heuristics are used to deal with this problem. Numerical results indicate that the heuristic approach is very attractive and leads to better solutions than those provided by state-of-the-art integer programming codes in limited computation times, with solution times significantly smaller. The numerical results do not vary too much when typical parameters such as the tabu tenure are modified, except for the dimension of neighborhood.     

Heuristics for the dynamic facility layout problem with unequal-area departments

The dynamic facility layout problem (DFLP) is the problem of finding positions of departments on the plant floor for multiple periods (material flows between departments change during the planning horizon) such that departments do not overlap, and the sum of the material handling and rearrangement costs is minimized. In this paper, the departments may have unequal-areas and free orientations, and the layout for each period is generated on the continuous plant floor. Because of the complexity of the problem, only small-size problems can be solved in reasonable time using exact techniques. As a result, a boundary search (construction) technique, which places departments along the boundaries of already placed departments, is developed for the DFLP. The solution is improved using a tabu search heuristic. The heuristics were tested on some instances from the DFLP and static facility layout problem (SFLP) literature. The results obtained demonstrate the effectiveness of the heuristics.     

Diversification strategies in tabu search algorithms for the maximum clique problem

The purpose of this study is to develop some understanding of the benefits that can be derived from the inclusion of diversification strategies in tabu search methods. To do so, we discuss the implementation of various diversification strategies in several tabu search heuristics developed for the maximum clique problem. Computational results on a large set of randomly generated test problems are reported and compared to assess the impact of these techniques on solution quality and running time.     

An efficient tabu search procedure for the p-Median Problem

In this paper we present a new solution heuristic for the p-Median Problem. The algorithm is based on tabu search principles, and uses short term and long term memory, as well as strategic oscillation and random tabu list sizes. Our proposed procedure is compared with two other move heuristics: a well-known interchange heuristic and a recent hybrid heuristic. In computational tests on networks ranging in size up to 500 nodes the new heuristic is found to be superior with respect to the quality of solutions produced.     

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.