Tabu Search for Frequency Assignment in Mobile Radio Networks

The main goal of the Frequency Assignment Problem in mobile radio networks consists of assigning a limited number of frequencies to each radio cell in a cellular network while minimizing electromagnetic interference due to the reuse of frequencies. This problem, known to be NP-hard, is of great importance in practice since better solutions will allow a telecommunications operator to manage larger cellular networks. This paper presents a new Tabu Search algorithm for this application. The algorithm is tested on realistic and large problem instances and compared with other methods based on simulated annealing, constraint programming and graph coloring algorithms. Empirical evidence shows that the Tabu algorithm is very competitive by giving the best solutions to the tested instances.     

Investigation of polynomial algorithms for solving the multicriteria three-index planar assignment problem

Under certain additional conditions imposed on the coefficients of the vector objective function in the three-index planar assignment problem, a large series of computational experiments aimed at the investigation of four polynomial algorithms for finding an asymptotically optimal solution of this problem is carried out.     

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.     

Investigation of polynomial algorithms for solving the three-index planar assignment problem

Under certain additional conditions imposed on the coefficients of the objective function in the three-index planar assignment problem, a large series of computational experiments aimed at the investigation of four polynomial algorithms for finding an asymptotically optimal solution of this problem is conducted.     

A cooperative parallel tabu search algorithm for the quadratic assignment problem

In this study, we introduce a cooperative parallel tabu search algorithm (CPTS) for the quadratic assignment problem (QAP). The QAP is an NP-hard combinatorial optimization problem that is widely acknowledged to be computationally demanding. These characteristics make the QAP an ideal candidate for parallel solution techniques. CPTS is a cooperative parallel algorithm in which the processors exchange information throughout the run of the algorithm as opposed to independent concurrent search strategies that aggregate data only at the end of execution. CPTS accomplishes this cooperation by maintaining a global reference set which uses the information exchange to promote both intensification and strategic diversification in a parallel environment. This study demonstrates the benefits that may be obtained from parallel computing in terms of solution quality, computational time and algorithmic flexibility. A set of 41 test problems obtained from QAPLIB were used to analyze the quality of the CPTS algorithm. Additionally, we report results for 60 difficult new test instances. The CPTS algorithm is shown to provide good solution quality for all problems in acceptable computational times. Out of the 41 test instances obtained from QAPLIB, CPTS is shown to meet or exceed the average solution quality of many of the best sequential and parallel approaches from the literature on all but six problems, whereas no other leading method exhibits a performance that is superior to this.     

Solution of the Cumulative Assignment Problem With a Well-Structured Tabu Search Method

The Cumulative Assignment Problem is an NP-complete problem obtained by substituting the linear objective function of the classic Linear Assignment Problem, with a non-linear cumulative function. In this paper we present a first attempt to solve the Cumulative Assignment Problem with metaheuristic techniques. In particular we consider two standard techniques, namely the Simulated Annealing and the Multi-Start methods, and we describe the eXploring Tabu Search: a new structured Tabu Search algorithm which uses an iterative multi-level approach to improve the search. The new method is analyzed through extensive computational experiments and proves to be more effective than the standard methods.     

Lower bounds for the axial three-index assignment problem

This paper describes new bounding methods for the axial three-index assignment problem (3AP). For calculating 3AP lower bounds, we use a projection method followed by a Hungarian algorithm, based on a new Lagrangian relaxation. We also use a cost transformation scheme, which iteratively transforms 3AP costs in a series of equivalent 3APs, which provides the possibility of improving the 3AP lower bound. These methods produce efficiently computed relatively tight lower bound.     

On the Convergence of Tabu Search

The Tabu Search (TS) meta-heuristic has proved highly successful for solving combinatorial and nonlinear problems. A key aspect of TS consists of using adaptive forms of memory to forbid the search process to revisit solutions already examined unless the trajectory to reach it is different. In Glover (ORSA Journal on Computing, 1990, 2, 4–32) a special memory design was proposed together with a choice rule for handling the situation where the method was compelled to revisit solutions already encountered. This proposal, which specified the exploration should resume from the earliest solution visited in the past, as accompanied by the conjecture that such a choice has implications for finiteness in the zero-one integer program and optimal set membership examples. Up to now numerous applications of TS in various areas of research are available, however, we are aware of only a few results concerning the convergence of TS. In this paper, we prove that Glover's conjecture is true if the neighborhood employed is strongly connected, yielding a reversible path from each solution to every other solution.     

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.     

Cooperative Parallel Tabu Search for Capacitated Network Design

We present a cooperative parallel tabu search method for the fixed charge, capacitated, multicommodity network design problem. Several communication strategies are analyzed and compared. The resulting parallel procedure displays excellent performances in terms of solution quality and solution times. The experiments show that parallel implementations find better solutions than sequential ones. They also show that, when properly designed and implemented, cooperative search outperforms independent search strategies, at least on the class of problems of interest here.     

一种改进的禁忌搜索算法及其在连续全局优化中的应用

禁忌搜索算法是一种元启发式的全局优化算法,是局部搜索算法的一种推广,已被成功地应用于许多组合优化问题中。本文针对有界闭区域上的连续函数全局优化问题,提出了一种改进的禁忌搜索算法,并进行了理论分析和数值实验。数值实验表明,对于连续函数全局优化问题的求解该算法是可行有效的,并且结构简单,迭代次数较少,是一种较好的全局启发式优化算法。     

Design and Evaluation of Tabu Search Algorithms for Multiprocessor Scheduling

Using a simple multiprocessor scheduling problem as a vehicle, we explore the behavior of tabu search algorithms using different tabu, local search and list management strategies. We found that random blocking of the tail of the tabu list always improved performance; but that the use of frequency-based penalties to discourage frequently selected moves did not. Hash coding without conflict resolution was an effective way to represent solutions on the tabu list. We also found that the most effective length of the tabu list depended on features of the algorithm being used, but not on the size and complexity of the problem being solved. The best combination of features included random blocking of the tabu list, tasks as tabus and a greedy local search. An algorithm using these features was found to outperform a recently published algorithm solving a similar problem.     

A Tabu Search Approach for the Resource Constrained Project Scheduling Problem

An appropriate tabu search implementation is designed to solve the resource constrained project scheduling problem. This approach uses well defined move strategies and a structured neighbourhood, defines appropriate tabu status and tenure and takes account of objective function approximation to speed up the search process. A sound understanding of the problem has helped in many ways in designing and enhancing the tabu search methodology. The method uses diversification, intensification and handles infeasibility via strategic oscillation.The above methodology is tested on existing problems from the literature and also on parametrically generated problems with encouraging results. For comparison of results, optimal solutions are used in the former and lower bounds obtained by Lagrangian heuristics are used in the latter.     

A reduction approach to the repeated assignment problem

We consider the repeated assignment problem (RAP), which is a K-fold repetition of the n × n linear assignment problem (LAP), with the additional requirement that no assignment can be repeated more than once. In actual applications K is typically much smaller than n. First, we derive upper and lower bounds respectively by a heuristic together with local search, and an efficient method solving the continuous relaxation. The latter also solves a Lagrangian relaxation, such that the related pegging test, to fix variables at zero or one, decomposes into K independent pegging tests to LAPs. These can be solved exactly by transforming them into all-pairs shortest path problems. Together with these procedures, we also employ a virtual pegging test and reduce RAP in size. Numerical experiments show that the reduced instances, with K ? n, can be solved exactly using standard MIP solvers.     

On Using Tabu Search for Design Automation of VLSI Systems

Tabu search is a meta-heuristic problem solving technique that, when applied carefully, provides near optimal solutions in a very short time. In this paper, we have described the use of tabu search for solving problems related to very large scale integrated (VLSI) circuit design automation. Specifically, we have demonstrated the use for VLSI circuit partitioning and placement. We present a tabu search based circuit bi-partitioning technique that partitions circuits with the goal of minimizing the size of the cutset between the partitions. Then, we use tabu search techniques along with force directed placement techniques to accomplish the physical placement of VLSI circuits on regular two-dimensional arrays with the goal of minimizing the placement time. We use empirical data from partitioning and placement of benchmark circuits to test our techniques. Our methods show improvement when compared to partitioning techniques from the literature and commercially available placement tools. Relative to the literature, our tabu search bi-partitioning technique improves on the best known minimum cuts for several benchmark circuits. Relative to commercially available computer aided design tools, our tabu search based placement approach shows dramatic (20×) speedup in execution time without negative impact on the quality of the solution.     

Parallelizing Tabu Search on a Cluster of Heterogeneous Workstations

In this paper, we present the parallelization of tabu search on a network of workstations using PVM. Two parallelization strategies are integrated: functional decomposition strategy and multi-search threads strategy. In addition, domain decomposition strategy is implemented probabilistically. The performance of each strategy is observed and analyzed. The goal of parallelization is to speedup the search in finding better quality solutions. Observations support that both parallelization strategies are beneficial, with functional decomposition producing slightly better results. Experiments were conducted for the VLSI cell placement, an NP-hard problem, and the objective was to achieve the best possible solution in terms of interconnection length, timing performance (circuit speed), and area. The multiobjective nature of this problem is addressed using a fuzzy goal-based cost computation.     

Tabu Search with Simple Ejection Chains for Coloring Graphs

We present a Tabu Search (TS) method that employs a simple version of ejection chains for coloring graphs. The procedure is tested on a set of benchmark problems. Empirical results indicate that the proposed TS implementation outperforms other metaheuristic methods, including Simulated Annealing, a previous version of Tabu Search and a recent implementation of a Greedy Randomized Adaptive Search Procedure (GRASP).     

Tabu Search heuristics for the Vehicle Routing Problem with Time Windows

This paper surveys the research on the Tabu Search heuristics for the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW can be described as the problem of designing least cost routes for a fleet of vehicles from one depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time interval; all routes start and end at the depot, and the total demands of all points on one particular route must not exceed the capacity of the vehicle. In addition to describing basic features of each method, experimental results for Solomon’s benchmark test problems are presented and analyzed. This work was partially supported by the Emil Aaltonen Foundation, Liikesivistysrahasto Foundation, the Canadian Natural Science and Engineering Research Council and the TOP program funded by the Research Council of Norway. This support is gratefully acknowledged.     

A Tabu Search Approach for the Prize Collecting Traveling Salesman Problem

The Prize Collecting Traveling Salesman Problem is a generalization of the Traveling Salesman Problem. A salesman collects a prize for each visited city and pays a penalty for each non visited city. The objective is to minimize the sum of the travel costs and penalties, but collecting a minimum pre-established amount of prizes. This problem is here addressed by a simple, but efficient tabu search approach which had improved several upper bounds of the considered instances.