Maximally diverse grouping: an iterated tabu search approach

The maximally diverse grouping problem (MDGP) consists of finding a partition of a set of elements into a given number of mutually disjoint groups, while respecting the requirements of group size constraints and diversity. In this paper, we propose an iterated tabu search (ITS) algorithm for solving this problem. We report computational results on three sets of benchmark MDGP instances of size up to 960 elements and provide comparisons of ITS to five state-of-the-art heuristic methods from the literature. The results demonstrate the superiority of the ITS algorithm over alternative approaches. The source code of the algorithm is available for free download via the internet.     

Solving the maximum clique problem using a tabu search approach

We describe two variants of a tabu search heuristic, a deterministic one and a probabilistic one, for the maximum clique problem. This heuristic may be viewed as a natural alternative implementation of tabu search for this problem when compared to existing ones. We also present a new random graph generator, the -generator, which produces graphs with larger clique sizes than comparable ones obtained by classical random graph generating techniques. Computational results on a large set of test problems randomly generated with this new generator are reported and compared with those of other approximate methods.The authors are grateful to the Quebec Government (Fonds F.C.A.R.) and to the Canadian Natural Sciences and Engineering Research Council (grant 0GP0038816) for financial support.     

A tabu search tutorial based on a real-world scheduling problem

We apply a tabu search method to a scheduling problem of a company producing cables for cars: the task is to determine on what machines and in which order the cable jobs should be produced in order to save production costs. First, the problem is modeled as a combinatorial optimization problem. We then employ a tabu search algorithm as an approach to solve the specific problem of the company, adapt various intensification as well as diversification strategies within the algorithm, and demonstrate how these different implementations improve the results. Moreover, we show how the computational cost in each iteration of the algorithm can be reduced drastically from O(n ³) (naive implementation) to O(n) (smart implementation) by exploiting the specific structure of the problem (n refers to the number of cable orders).     

A tabu search approach for proportionate multiprocessor open shop scheduling

In the multiprocessor open shop scheduling problem, jobs are to be processed on a set of processing centers—each having one or more parallel identical machines, while jobs do not have a pre-specified obligatory route. A special case is the proportionate multiprocessor open shop scheduling problem (PMOSP) in which the processing time on a given center is not job-dependent. Applications of the PMOSP are evident in health care systems, maintenance and repair shops, and quality auditing and final inspection operations in industry. In this paper, a tabu search (TS) approach is presented for solving the PMOSP with the objective of minimizing the makespan. The TS approach utilizes a neighborhood search function that is defined over a network representation of feasible solutions. A set of 100 benchmark problems from the literature is used to evaluate the performance of the developed approach. Experimentations show that the developed approach outperforms a previously developed genetic algorithm as it produces solutions with an average of less than 5 % deviation from a lower bound, and 40 % of its solutions are provably optimal.     

A two-phase tabu search approach to the location routing problem

In many distribution systems, the location of the distribution facilities and the routing of the vehicles from these facilities are interdependent. Although this interdependence has been recognized by academics and practitioners alike, attempts to integrate these two decisions have been limited. The location routing problem (LRP), which combines the facility location and the vehicle routing decisions, is NP-hard. Due to the problem complexity, simultaneous solution methods are limited to heuristics. This paper presents a two-phase tabu search architecture for the solution of the LRP. First introduced in this paper, the two-phase approach offers a computationally efficient strategy that integrates facility location and routing decisions. This two-phase architecture makes it possible to search the solution space efficiently, thus producing good solutions without excessive computation. An extensive computational study shows that the TS algorithm achieves significant improvement over a recent effective LRP heuristic.     

A composite-neighborhood tabu search approach to the traveling tournament problem

The Traveling Tournament Problem (TTP) is a combinatorial problem that combines features from the traveling salesman problem and the tournament scheduling problem. We propose a family of tabu search solvers for the solution of TTP that make use of complex combination of many neighborhood structures. The different neighborhoods have been thoroughly analyzed and experimentally compared. We evaluate the solvers on three sets of publicly available benchmarks and we show a comparison of their outcomes with previous results presented in the literature. The results show that our algorithm is competitive with those in the literature.     

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.     

A tabu search approach for the single machine mean tardiness problem

In this paper, a tabu search approach is proposed for solving the single machine mean tardiness scheduling problem. Simulation experiment results obtained from the tabu search approach and three other heuristics are compared. Although computation time is increased, the results indicate that the proposed approach provides a much better solution than the other three approaches.     

A hybridized tabu search approach for the minimum weight vertex cover problem

The minimum weight vertex cover problem is a basic combinatorial optimization problem defined as follows. Given an undirected graph and positive weights for all vertices the objective is to determine a subset of the vertices which covers all edges such that the sum of the related cost values is minimized. In this paper we apply a modified reactive tabu search approach for solving the problem. While the initial concept of reactive tabu search involves a random walk we propose to replace this random walk by a controlled simulated annealing. Numerical results are presented outperforming previous metaheuristic approaches in most cases.     

Multi-objective tabu search using a multinomial probability mass function

A tabu search approach to solve multi-objective combinatorial optimization problems is developed in this paper. This procedure selects an objective to become active for a given iteration with a multinomial probability mass function. The selection step eliminates two major problems of simple multi-objective methods, a priori weighting and scaling of objectives. Comparison of results on an NP-hard combinatorial problem with a previously published multi-objective tabu search approach and with a deterministic version of this approach shows that the multinomial approach is effective, tractable and flexible.     

The hazard of being an English football league manager: empirical estimates for three recent league seasons

This paper uses data drawn from the English Football League to model separate hazard rates for club managers for the 2001/2, 2002/3 and 2003/4 seasons. On average over the three seasons, approximately one-third of managers involuntarily exited employment status with their club. We model the hazard using a standard logistic model exploiting information on the spell at risk rather than the individual. The role of neglected heterogeneity is also examined using random and fixed effects logistic models within a discrete-time setting. League position at the start of the spell at risk is found to be the most important determinant of a manager's involuntary exit. A variety of individual specific human capital and other covariates are found to be unimportant in determining the hazard and no role for unobservable heterogeneity as captured by random effects is detected.     

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 priority list based heuristic for the job shop problem: part 2 tabu search

Following a recent paper by the same author, a priority list-based tabu search heuristic is compared with the leading schedule-based tabu search heuristic of Nowicki and Smutnicki. More search neighbourhoods are required to achieve a given average makespan, but each priority list neighbourhood is searched much faster than the corresponding neighbourhood in the space of feasible schedules. Priority list-based tabu search therefore outperforms schedule-based tabu search in terms of elapsed CPU time.     

A tabu search algorithm for a two-dimensional non-guillotine cutting problem

In this paper we study a two-dimensional non-guillotine cutting problem, the problem of cutting rectangular pieces from a large stock rectangle so as to maximize the total value of the pieces cut. The problem has many industrial applications whenever small pieces have to be cut from or packed into a large stock sheet. We propose a tabu search algorithm. Several moves based on reducing and inserting blocks of pieces have been defined. Intensification and diversification procedures, based on long-term memory, have been included. The computational results on large sets of test instances show that the algorithm is very efficient for a wide range of packing and cutting problems.     

Reducing the bandwidth of a sparse matrix with tabu search

The bandwidth of a matrix A={a_ij} is defined as the maximum absolute difference between i and j for which a_ij≠0. The problem of reducing the bandwidth of a matrix consists of finding a permutation of the rows and columns that keeps the nonzero elements in a band that is as close as possible to the main diagonal of the matrix. This NP-complete problem can also be formulated as a labeling of vertices on a graph, where edges are the nonzero elements of the corresponding symmetrical matrix. Many bandwidth reduction algorithms have been developed since the 1960s and applied to structural engineering, fluid dynamics and network analysis. For the most part, these procedures do not incorporate metaheuristic elements, which is one of the main goals of our current development. Another equally important goal is to design and test a special type of candidate list strategy and a move mechanism to be embedded in a tabu search procedure for the bandwidth reduction problem. This candidate list strategy accelerates the selection of a move in the neighborhood of the current solution in any given iteration. Our extensive experimentation shows that the proposed procedure outperforms the best-known algorithms in terms of solution quality consuming a reasonable computational effort.     

Optimization of a high-speed placement machine using tabu search algorithms

Combinatorial optimization represents a wide range of real-life manufacturing optimization problems. Due to the high computational complexity, and the usually high number of variables, the solution of these problems imposes considerable challenges. This paper presents a tabu search approach to a combinatorial optimization problem, in which the objective is to maximize the production throughput of a high-speed automated placement machine. Tabu search is a modern heuristic technique widely employed to cope with large search spaces, for which classical search methods would not provide satisfactory solutions in a reasonable amount of time. The developed TS strategies are tailored to address the different issues caused by the modular structure of the machine. This revised version was published online in June 2006 with corrections to the Cover Date.     

Routing and scheduling in a flexible job shop by tabu search

A hierarchical algorithm for the flexible job shop scheduling problem is described, based on the tabu search metaheuristic. Hierarchical strategies have been proposed in the literature for complex scheduling problems, and the tabu search metaheuristic, being able to cope with different memory levels, provides a natural background for the development of a hierarchical algorithm. For the case considered, a two level approach has been devised, based on the decomposition in a routing and a job shop scheduling subproblem, which is obtained by assigning each operation of each job to one among the equivalent machines. Both problems are tackled by tabu search. Coordination issues between the two hierarchical levels are considered. Unlike other hierarchical schemes, which are based on a one-way information flow, the one proposed here is based on a two-way information flow. This characteristic, together with the flexibility of local search strategies like tabu search, allows to adapt the same basic algorithm to different objective functions. Preliminary computational experience is reported.     

A dynamic neighborhood based tabu search algorithm for real-world flight instructor scheduling problems

The multi-objective flight instructor scheduling problem is an optimization problem that schedules instructors to teach a set of pilot training events. The objectives of the problem are to minimize labor cost, maximize workload consistency and maximize flight instructor satisfaction of their assignments. The problem is further complicated by various hard and soft constraints. We study a multi-objective cost function and convert it to a scalar-weighted objective function using a priori weighting scheme. We then design an efficient dynamic neighborhood based tabu search meta-heuristic to solve the problem. The algorithm exploits the special properties of different types of neighborhood moves. We also address issues of solution domination, tabu short-term memory, dynamic tabu tenure and aspiration rule. The application of the algorithm in a major US airline carrier is reported and the results show that our algorithm achieves significant benefits in practice.     

The continuous reactive tabu search: Blending combinatorial optimization and stochastic search for global optimization

A novel algorithm for the global optimization of functions (C-RTS) is presented, in which a combinatorial optimization method cooperates with a stochastic local minimizer. The combinatorial optimization component, based on the Reactive Tabu Search recently proposed by the authors, locates the most promising boxes, in which starting points for the local minimizer are generated. In order to cover a wide spectrum of possible applications without user intervention, the method is designed with adaptive mechanisms: the box size is adapted to the local structure of the function to be optimized, the search parameters are adapted to obtain a proper balance of diversification and intensification. The algorithm is compared with some existing algorithms, and the experimental results are presented for a variety of benchmark tasks.