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 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 heuristic for the dynamic transportation of patients between care units

The problem studied in this paper stems from a real application to the transportation of patients in the Hospital Complex of Tours (France). The ambulance central station of the Hospital Complex has to plan the transportation demands between care units which require a vehicle. Some demands are known in advance and the others arise dynamically. Each demand requires a specific type of vehicle and a vehicle can transport only one person at a time. The demands can be subcontracted to a private company which implies high cost. Moreover, transportations are subject to particular constraints, among them priority of urgent demands, disinfection of a vehicle after the transportation of a patient with contagious disease and respect of the type of vehicle needed. These characteristics involve a distinction between the vehicles and the crews during the modeling phase. We propose a modeling for solving this difficult problem and a tabu search algorithm inspired by Gendreau et al. (1999). This method supports an adaptive memory and a tabu search procedure. Computational experiments on a real-life instance and on randomly generated instances show that the method can provide high-quality solutions for this dynamic problem with a short computation time.     

A tabu search scheme for abstract problems, with applications to the computation of fixed points

We present a general tabu search iterative algorithm to solve abstract problems on metric spaces. At each iteration, if the current solution turns out to be unacceptable then a neighborhood of unacceptable solutions is determined and excluded for further exploration, in such a way that, under mild assumptions, an acceptable solution is asymptotically reached. Thus our algorithm makes a crucial use of memory to avoid visiting unacceptable solutions more than once. We also present a specialization of our general method to the computation of fixed points.     

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.     

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.     

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 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.     

A user's guide to tabu search

We describe the main features of tabu search, emphasizing a perspective for guiding a user to understand basic implementation principles for solving combinatorial or nonlinear problems. We also identify recent developments and extensions that have contributed to increasing the efficiency of the method. One of the useful aspects of tabu search is the ability to adapt a rudimentary prototype implementation to encompass additional model elements, such as new types of constraints and objective functions. Similarly, the method itself can be evolved to varying levels of sophistication. We provide several examples of discrete optimization problems to illustrate the strategic concerns of tabu search, and to show how they may be exploited in various contexts. Our presentation is motivated by the emergence of an extensive literature of computational results, which demonstrates that a well-tuned implementation makes it possible to obtain solutions of high quality for difficult problems, yielding outcomes in some settings that have not been matched by other known techniques.The research of this paper has been supported in part by the joint Air Force Office of Scientific Research and Office of Naval Research Contract No. F49620-90-C-0033, at the University of Colorado and by the Swiss National Research Council Grant No. 20-27926.89.     

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.     

An integrated tabu search algorithm for the lot streaming problem in job shops

In this paper, we focus on solving the lot streaming problem in a job shop environment, where consistent sublots are considered. The presented three-phase algorithm incorporates the predetermination of sublot sizes, the determination of schedules based on tabu search and the variation of sublot sizes. With regard to tabu search implementation, a constructive multi-level neighbourhood is developed, which effectively connects three isolated neighbourhood functions. Moreover, enhancements of the basic version of tabu search are conducted. Combined with the procedure for varying sublot sizes, the algorithm further exploits the improvement potential. All tested instances show a rapid convergence to their lower bounds. The well-known difficult benchmark problems also achieve substantial makespan reduction. In addition, the performance of specific components is intensively examined in our study.     

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.     

A tabu search algorithm for the single machine total weighted tardiness problem

In this study, a tabu search (TS) approach to the single machine total weighted tardiness problem (SMTWT) is presented. The problem consists of a set of independent jobs with distinct processing times, weights and due dates to be scheduled on a single machine to minimize total weighted tardiness. The theoretical foundation of single machine scheduling with due date related objectives reveal that the problem is NP-hard, rendering it a challenging area for meta-heuristic approaches. This paper presents a totally deterministic TS algorithm with a hybrid neighborhood and dynamic tenure structure, and investigates the strength of several candidate list strategies based on problem specific characteristics in increasing the efficiency of the search. The proposed TS approach yields very high quality results for a set of benchmark problems obtained from the literature.     

An efficient implementation of the robust tabu search heuristic for sparse quadratic assignment problems

We propose and develop an efficient implementation of the robust tabu search heuristic for sparse quadratic assignment problems. The traditional implementation of the heuristic applicable to all quadratic assignment problems is of O(N²) complexity per iteration for problems of size N. Using multiple priority queues to determine the next best move instead of scanning all possible moves, and using adjacency lists to minimize the operations needed to determine the cost of moves, we reduce the asymptotic (N → ∞) complexity per iteration to O(N log N). For practical sized problems, the complexity is O(N).     

A new neighborhood and tabu search for the Blocking Job Shop

The Blocking Job Shop is a version of the job shop scheduling problem with no intermediate buffers, where a job has to wait on a machine until being processed on the next machine. We study a generalization of this problem which takes into account transfer operations between machines and sequence-dependent setup times. After formulating the problem in a generalized disjunctive graph, we develop a neighborhood for local search. In contrast to the classical job shop, there is no easy mechanism for generating feasible neighbor solutions. We establish two structural properties of the underlying disjunctive graph, the concept of closures and a key result on short cycles, which enable us to construct feasible neighbors by exchanging critical arcs together with some other arcs. Based on this neighborhood, we devise a tabu search algorithm and report on extensive computational experience, showing that our solutions improve most of the benchmark results found in the literature.     

Simulated annealing and tabu search approaches for the Corridor Allocation Problem

In the Corridor Allocation Problem, we are given n facilities to be arranged along a corridor. The arrangements on either side of the corridor should start from a common point on the left end of the corridor. In addition, no space is allowed between two adjacent facilities. The problem is motivated by applications such as the arrangement of rooms in office buildings, hospitals, shopping centers or schools. Tabu search and simulated annealing algorithms are presented to minimize the sum of weighted distances between every pair of facilities. The algorithms are evaluated on several instances of different sizes either randomly generated or available in the literature. Both algorithms reached the optimal (when available) or best-known solutions of the instances with n ? 30. For larger instances with size 42 ? n ? 70, the simulated annealing implementation obtained smaller objective values, while requiring a smaller number of function evaluations.     

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.     

TSPACK: A two-level tabu search for the three-dimensional bin packing problem

Three-dimensional orthogonal bin packing is a problem NP-hard in the strong sense where a set of boxes must be orthogonally packed into the minimum number of three-dimensional bins. We present a two-level tabu search for this problem. The first-level aims to reduce the number of bins. The second optimizes the packing of the bins. This latter procedure is based on the Interval Graph representation of the packing, proposed by Fekete and Schepers, which reduces the size of the search space. We also introduce a general method to increase the size of the associated neighborhoods, and thus the quality of the search, without increasing the overall complexity of the algorithm. Extensive computational results on benchmark problem instances show the effectiveness of the proposed approach, obtaining better results compared to the existing ones.