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.     

Parallel asynchronous tabu search for multicommodity location-allocation with balancing requirements

We study and compare asynchronous parallelization strategies for tabu search, and evaluate the impact on performance and solution quality of some important algorithmic design parameters: number of processors, handling of exchanged information, etc. Parallelization approaches are implemented and compared by using a tabu search algorithm for multicommodity location-allocation problems with balancing requirements.     

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.     

Genetic and hybrid algorithms for graph coloring

Some genetic algorithms are considered for the graph coloring problem. As is the case for other combinatorial optimization problems, pure genetic algorithms are outperformed by neighborhood search heuristic procedures such as tabu search. Nevertheless, we examine the performance of several hybrid schemes that can obtain solutions of excellent quality. For some graphs, we illustrate that genetic operators can fulfill long-term strategic functions for a tabu search implementation that is chiefly founded on short-term memory strategies.     

An introduction to population approaches for optimization and hierarchical objective functions: A discussion on the role of tabu search

Population approaches suitable for global combinatorial optimization are discussed in this paper. They are composed of a number of distinguishable individuals called "agents", each one using a particular optimization strategy. Periods of independent search follow phases on which the population is restarted from new configurations. Due to its intrinsic parallelism and the asynchronicity of the method, it is particularly suitable for parallel computers. Results on two test problems are presented in this paper. The individual search optimization strategies for each agent have been chosen having the basic characteristics of tabu search. This has been done in order to avoid mixing the hypothesized properties of these population approaches with those of more elaborate tabu search strategies, but remarking on its main characteristics. A set of four test problem "landscapes" is discussed and their use to improve and benchmark the results by using tabu search as the individual optimization strategy within a population heuristic is suggested and explored. The application of tabu search to new problem areas, like molecular biology, is also investigated.     

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.     

Serial and parallel simulated annealing and tabu search algorithms for the traveling salesman problem

This paper describes serial and parallel implementations of two different search techniques applied to the traveling salesman problem. A novel approach has been taken to parallelize simulated annealing and the results are compared with the traditional annealing algorithm. This approach uses abbreviated cooling schedule and achieves a superlinear speedup. Also a new search technique, called tabu search, has been adapted to execute in a parallel computing environment. Comparison between simulated annealing and tabu search indicate that tabu search consistently outperforms simulated annealing with respect to computation time while giving comparable solutions. Examples include 25, 33, 42, 50, 57, 75 and 100 city problems.     

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.     

Parallel Solution of the Helmholtz Equation in a Multilayer Domain

We study time-harmonic wave propagation in layered, heterogeneous media. Solving this relatively complex application problem numerically is a challenging task. The full potential of algorithms, parallel programming models and computer architectures must be exploited. Our aim is to give a broad perspective on the various considerations that come into play. The basic parts of our algorithms consist of finite difference discretizations, domain decomposition and preconditioned iterative methods. We present two serial algorithms with different properties. Then, we discuss parallelization strategies using a local memory model, a shared memory model, or a combination of the two. The numerical experiments highlight the differences between the approaches and show results for three different combinations of algorithm and computer architecture that lead to viable solution methods.     

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 heterogeneous cooperative parallel search of branch-and-bound method and tabu search algorithm

In this study, we present a heterogeneous cooperative parallel search that integrates branch-and-bound method and tabu search algorithm. These two algorithms perform searches in parallel and cooperate by asynchronously exchanging information about the best solutions found and new initial solutions for tabu search. The rapid production of a good solution from the tabu search process provides the branch-and-bound process with a better feasible solution to accelerate the elimination of subproblems that do not contain an optimal solution. The new initial solution produced from the subproblem with a least-cost lower bound of the branch-and-bound method suggests the best potential area for tabu search to explore. We use a master-slave model to reduce the complexity of communication and enhance the performance of data exchange. A branch-and-bound process is used as the master process to control the exchange of information and the termination of computation. Several tabu search processes are executed simultaneously as the slave processes and cooperate by asynchronously exchanging information on the best solutions found and the new initial solutions by the master process of branch-and-bound. Based on the computation experiments of solving traveling salesman problems (TSP), the proposed heterogeneous parallel search algorithm outperforms a conventional parallel branch-and-bound method and a conventional parallel tabu search. We also present the computational results showing the efficiency of heterogeneous cooperative parallel search when we use more processors to accelerate search time. Thus, the proposed heterogeneous parallel search algorithm achieves linear accelerations.     

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 reactive tabu search for the vehicle routing problem

The classical vehicle routing problem (VRP) involves determining a fleet of homogeneous size vehicles and designing an associated set of routes that minimizes the total cost. Our tabu search (TS) algorithm to solve the VRP is based on reactive tabu search (RTS) with a new escape mechanism, which manipulates different neighbourhood schemes in a very sophisticated way in order to get a balanced intensification and diversification continuously during the search process. We compare our algorithm with the best methods in the literature using different data sets and report results including new best known solutions for several well-known benchmark problems.     

Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem

The vehicle routing problem (VRP) under capacity and distance restrictions involves the design of a set of minimum cost delivery routes, originating and terminating at a central depot, which services a set of customers. Each customer must be supplied exactly once by one vehicle route. The total demand of any vehicle must not exceed the vehicle capacity. The total length of any route must not exceed a pre-specified bound. Approximate methods based on descent, hybrid simulated annealing/tabu search, and tabu search algorithms are developed and different search strategies are investigated. A special data structure for the tabu search algorithm is implemented which has reduced notably the computational time by more than 50%. An estimate for the tabu list size is statistically derived. Computational results are reported on a sample of seventeen bench-mark test problems from the literature and nine randomly generated problems. The new methods improve significantly both the number of vehicles used and the total distances travelled on all results reported in the literature.     

Massively parallel analog tabu search using neural networks applied to simple plant location problems

Neural networks and tabu search are two very significant techniques which have emerged recently for the solution of discrete optimization problems. Neural networks possess the desirable quality of implementability in massively parallel hardware while the tabu search metaheuristic shows great promise as a powerful global search method. Tabu Neural Network (TANN) integrates an analog version of the short term memory component of tabu search with neural networks to generate a massively parallel, analog global search strategy that is hardware implementable. In TANN, both the choice of the element to enter the tabu list as well as the maintenance of the decision elements in tabu status is accomplished via neuronal activities. In this paper we apply TANN to the simple plant location problem. Comparisons with the Hopfield-Tank network show an average improvement of about 85% in the quality of solutions obtained.     

Query Optimization in Distributed Relational Databases

The query optimizer is the DBMS (data base management system) component whose task is to find an optimal execution plan for a given input query. Typically, optimization is performed using dynamic programming. However, in distributed execution environments, this approach becomes intractable, due to the increase in the search space incurred by distribution. We propose the use of the tabu search metaheuristic for distributed query optimization. A hashing-based data structure is used to keep track of the search memory, simplifying significantly the implementation of tabu search. To validate this proposal, we implemented the tabu search strategy in the scope of an existing optimizer, which runs several search strategies. We focus our attention on the more difficult problems in terms of the query execution space, in which the solution space includes bushy execution plans and Cartesian products, which are not dealt with very often in the literature. Using a real-life application, we show the effectiveness of tabu search when compared to other strategies.     

Multistart Tabu Search Strategies for the Unconstrained Binary Quadratic Optimization Problem

This paper describes and experimentally compares five rather different multistart tabu search strategies for the unconstrained binary quadratic optimization problem: a random restart procedure, an application of a deterministic heuristic to specially constructed subproblems, an application of a randomized procedure to the full problem, a constructive procedure using tabu search adaptive memory, and an approach based on solving perturbed problems. In the solution improvement phase a modification of a standard tabu search implementation is used. A computational trick applied to this modification – mapping of the current solution to the zero vector – allowed to significantly reduce the time complexity of the search. Computational results are provided for the 25 largest problem instances from the OR-Library and, in addition, for the 18 randomly generated larger and more dense problems. For 9 instances from the OR-Library new best solutions were found.     

Tabu search for discrete–continuous scheduling problems with heuristic continuous resource allocation

Problems of scheduling non-preemptable, independent jobs on parallel identical machines under an additional continuous renewable resource to minimize the makespan are considered. Each job simultaneously requires for its processing a machine and an amount (unknown in advance) of the continuous resource. The processing rate of a job depends on the amount of the resource allotted to this job at a time. The problem is to find a sequence of jobs on machines and, simultaneously, a continuous resource allocation that minimize the makespan. A heuristic procedure for allocating the continuous resource is used. The tabu search metaheuristic to solve the considered problem is presented. The results produced by tabu search are compared with optimal solutions for small instances, as well as with the results generated by simple search methods – multi-start iterative improvement and random sampling for larger instances.     

Protein Conformation of a Lattice Model Using Tabu Search

We apply tabu search techniques to the problem of determining the optimal configuration of a chain of protein sequences on a cubic lattice. The problem under study is difficult to solve because of the large number of possible conformations and enormous amount of computations required. Tabu search is an iterative heuristic procedure which has been shown to be a remarkably effective method for solving combinatorial optimization problems. In this paper, an algorithm is designed for the cubic lattice model using tabu search. The algorithm has been tested on a chain of 27 monomers. Computational results show that our method outperforms previously reported approaches for the same model.     

Solving the flight perturbation problem with meta heuristics

When there is a perturbation in a carefully constructed aircraft schedule, e.g. an aircraft breakdown, it is important to minimize the negative consequences of this disturbance. Here, a tabu search and a simulated annealing approach to the flight perturbation problem are presented. The heuristics use a tree-search algorithm to find new schedules for the aircraft, and utilize a path relinking strategy to explore paths between structurally different solutions. The computational results indicate that the solution strategies, especially the tabu search, can be successfully used to solve the flight perturbation problem.