A tabu search procedure for multicommodity location/allocation with balancing requirements

We propose a tabu search heuristic for the location/allocation problem with balancing requirements. This problem typically arises in the context of the medium term management of a fleet of containers of multiple types, where container depots have to be selected, the assignment of customers to depots has to be established for each type of container, and the interdepot container traffic has to be planned to account for differences in supplies and demands in various zones of the geographical territory served by a container shipping company. It is modeled as a mixed integer program, which combines zero-one location variables and a multicommodity network flow structure. Extensive computational results on a set of benchmark problems and comparisons with an efficient dual ascent procedure are reported. These show that tabu search is a competitive approach for this class of problems.     

Parallel asynchronous label-correcting methods for shortest paths

We develop parallel asynchronous implementations of some known and some new label-correcting methods for finding a shortest path from a single origin to all the other nodes of a directed graph. We compare these implementations on a shared-memory multiprocessor, the Alliant FX/80, using several types of randomly generated problems. Excellent (sometimes superlinear) speedup is achieved with some of the methods, and it is found that the asynchronous versions of these methods are substantially faster than their synchronous counterparts.The authors acknowledge the director and the staff of CERFACS, Toulouse, France for the use of the Alliant FX/80.This research was supported by the National Science Foundation under Grants 9108058-CCR, 9221293-INT, and 9300494-DMI.     

Parallel tabu search message-passing synchronous strategies for task scheduling under precedence constraints

This paper presents parallelization strategies for a tabu search algorithm for the task scheduling problem on heterogeneous processors under task precedence constraints. Parallelization relies exclusively on the decompostion of the solution space exploration. Four different parallel strategies are proposed and implemented on an asynchronous parallel machine under PVM: the master-slave model, with two different schemes for improved load balancing, and the single-program-multiple-data model, with single-token and multiple-token message passing schemes. The comparative analysis of these strategies shows that the tabu search approach for this problem is very suitable to the parallelization of the neighborhood search, with efficiency results almost always close to one for problems over a certain size.     

A Tabu Search with Slope Scaling for the Multicommodity Capacitated Location Problem with Balancing Requirements

In this paper, a tabu search heuristic is combined with slope scaling to solve a discrete depot location problem, known as the multicommodity location problem with balancing requirements. Although the uncapacitated version of this problem has already been addressed in the literature, this is not the case for the more challenging capacitated version, where each depot has a fixed and finite capacity. The slope scaling approach is used during the initialization phase to provide the tabu search with good starting solutions. Numerical results are reported on various types of large-scale randomly generated instances. The quality of the heuristic is assessed by comparing the solutions obtained with those of a commercial mixed-integer programming code.     

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.     

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.     

A tabu search for Time-dependent Multi-zone Multi-trip Vehicle Routing Problem with Time Windows

We propose a tabu search meta-heuristic for the Time-dependent Multi-zone Multi-trip Vehicle Routing Problem with Time Windows. Two types of neighborhoods, corresponding to the two sets of decisions of the problem, together with a strategy controlling the selection of the neighborhood type for particular phases of the search, provide the means to set up and combine exploration and exploitation capabilities for the search. A diversification strategy, guided by an elite solution set and a frequency-based memory, is also used to drive the search to potentially unexplored good regions and, hopefully, enhance the solution quality. Extensive numerical experiments and comparisons with the literature show that the proposed tabu search yields very high quality solutions, improving those currently published.     

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.     

A tabu search algorithm for scheduling pharmaceutical packaging operations

This paper addresses a practical scheduling problem arising in the packaging department of a pharmaceutical industrial plant. The problem is modeled as a multi-purpose machine scheduling problem with setup and removal times, release and due dates and additional constraints related to the scarce availability of tools and human operators. The objective functions are minimization of makespan and maximum tardiness in lexicographic order. Representing a solution with a directed graph allows us to devise an effective tabu search algorithm to solve the problem. Computational experiments, carried on real and randomly generated instances, show the effectiveness of this approach.     

A tabu search heuristic for the generalized minimum spanning tree problem

This paper describes an attribute based tabu search heuristic for the generalized minimum spanning tree problem (GMSTP) known to be NP-hard. Given a graph whose vertex set is partitioned into clusters, the GMSTP consists of designing a minimum cost tree spanning all clusters. An attribute based tabu search heuristic employing new neighborhoods is proposed. An extended set of TSPLIB test instances for the GMSTP is generated and the heuristic is compared with recently proposed genetic algorithms. The proposed heuristic yields the best results for all instances. Moreover, an adaptation of the tabu search algorithm is proposed for a variation of the GMSTP in which each cluster must be spanned at least once.     

Parallel local search

We present a survey of parallel local search algorithms in which we review the concepts that can be used to incorporate parallelism into local search. For this purpose we distinguish between single-walk and multiple-walk parallel local search and between asynchronous and synchronous parallelism. Within the class of single-walk algorithms we differentiate between multiple-step and single-step parallelism. To describe parallel local search we introduce the concepts of hyper neighborhood structures and distributed neighborhood structures. Furthermore, we present templates that capture most of the parallel local search algorithms proposed in the literature. Finally, we discuss some complexity issues related to parallel local search.     

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.     

Accelerated tabu search for no-wait flowshop scheduling problem with maximum lateness criterion

For the no-wait flowshop scheduling problem with maximum lateness criterion, properties are developed to speed up three kinds of basic operations generating candidate solutions, i.e., the insertion of a new job into a partial sequence, and the insertion and exchange neighborhood moves. The properties reduce the time to evaluate a candidate from O(nm)$O(\mathit{nm})$ to O  (1) and simplify the implementation of the heuristics based on the basic operations by evaluating candidates before their generation. The properties also reduce from O(n³m)$O(n^{3}m)$ to O(n²)$O(n^2)$ the time complexity of well-known NEH heuristic and the complete evaluation of the insertion and exchange neighborhoods. Tabu search (TS) is applied to the considered problem, since TS tries to find the best neighbor of the current solution in each iteration and therefore can much benefit from the speedups. Three different ways to use insertion and exchange neighborhoods are compared in TS. Computational experiments show that the speedups are more helpful as job number increases and all proposed TS algorithms are more effective and robust than the existing algorithms. Although two- and single-neighborhood TS algorithms are not significantly different, two-neighborhood TS algorithms are more preferable.     

A hybrid of adaptive large neighborhood search and tabu search for the order-batching problem

Given a set of customer orders and a routing policy, the goal of the order-batching problem?(OBP) is to group customer orders to picking orders (batches) such that the total length of all tours through a rectangular warehouse is minimized. Because order picking is considered the most labor-intensive process in warehousing, effectively batching customer orders can result in considerable savings. The OBP is NP-hard if the number of orders per batch is greater than two, and the exact solution methods proposed in the literature are not able to consistently solve larger instances. To address larger instances, we develop a metaheuristic hybrid based on adaptive large neighborhood search and tabu search, called ALNS/TS. In numerical studies, we conduct an extensive comparison of ALNS/TS to all previously published OBP methods that have used standard benchmark sets to investigate their performance. ALNS/TS outperforms all comparison methods with respect to both average solution quality and run-time. Compared to the state-of-the-art, ALNS/TS shows the clearest advantages on the larger instances of the existing benchmark sets, which assume a higher number of customer orders and higher capacities of the picking device. Finally, ALNS/TS is able to solve newly generated large-scale instances with up to 600 customer orders and six articles per customer order with reasonable run-times and convincing scaling behavior and robustness.     

Iterated tabu search for the circular open dimension problem

This paper investigates the circular open dimension problem (CODP), which consists of packing a set of circles of known radii into a strip of fixed width and unlimited length without overlapping. The objective is to minimize the length of the strip. In this paper, CODP is solved by a series of sub-problems, each corresponding to a fixed strip length. For each sub-problem, an iterated tabu search approach, named ITS, is proposed. ITS starts from a randomly generated solution and attempts to gain improvements by a tabu search procedure. After that, if the obtained solution is not feasible, a perturbation operator is subsequently employed to reconstruct the incumbent solution and an acceptance criterion is implemented to determine whether or not accept the perturbed solution. As a supplementary method, the length of the strip is determined in monotonously decreasing way, with the aid of some post-processing techniques. The search terminates and returns the best found solution after the allowed computation time has been elapsed. Computational experiments based on numerous well-known benchmark instances show that ITS produces quite competitive results, with respect to the best known results, while the computational time remains reasonable for each instance.     

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.     

Using the tabu search method for the distribution of supplies in a hospital

Two supply delivery systems in a hospital are compared. In order to evaluate the number of carriers required by the new system, an operational research model has been developed and solved by the tabu search method. The results indicate that the new system is better except on weekend days.This work has been achieved while the second author was visiting the Université de Montréal.     

A tabu search algorithm for maximum parsimony phylogeny inference

Phylogeny reconstruction is too complex a combinatorial problem for an exhaustive search, because the number of possible solutions increases exponentially with the number of taxa involved. In this paper, we adopt the parsimony principle and design a tabu search algorithm for finding a most parsimonious phylogeny tree. A special array structure is employed to represent the topology of trees and to generate the neighboring trees. We test the proposed tabu search algorithm on randomly selected data sets obtained from nuclear ribosomal DNA sequence data. The experiments show that our algorithm explores fewer trees to reach the optimal one than the commonly used program “dnapenny” (branch-and-bound based) while it generates much more accurate results than the default options of the program “dnapars” (heuristic search based). The percentage of search space needed to find the best solution for our algorithm decreased rapidly as the number of taxa increased. For a 20-taxon phylogeny problem, it needs on average to examine only 3.92 × 10⁻¹⁵% of the sample space.     

Bounds for short covering codes and reactive tabu search

Given a prime power q, c_q(n,R) denotes the minimum cardinality of a subset H in such that every word in this space differs in at most R coordinates from a multiple of a vector in H. In this work, two new classes of short coverings are established. As an application, a new optimal record-breaking result on the classical covering code is obtained by using short covering. We also reformulate the numbers c_q(n,R) in terms of dominating set on graphs. Departing from this reformulation, the reactive tabu search (a variation of tabu search heuristics) is developed to obtain new upper bounds on c_q(n,R). The algorithm is described and conclusions on the results are drawn; they identify the advantages of using the reactive mechanism for this problem. Tables of lower and upper bounds on c_q(n,R), q=3,4, n≤7, and R≤3, are also presented.     

A tabu search heuristic for the vehicle routing problem with private fleet and common carrier

This paper describes a tabu search heuristic for a vehicle routing problem where the owner of a private fleet can either visit a customer with one of his vehicles or assign the customer to a common carrier. The owner’s objective is to minimize the variable and fixed costs for operating his fleet plus the total costs charged by the common carrier. The proposed tabu search is shown to outperform the best approach reported in the literature on 34 benchmark instances with a homogeneous fleet.