Iterated Tabu Search Research Articles

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.

Multistart Iterated Tabu Search for Bandwidth Coloring Problem

This paper presents a Multistart Iterated Tabu Search (MITS) algorithm for solving Bandwidth Coloring Problem (BCP) and Bandwidth MultiColoring Problem (BMCP). The proposed MITS algorithm exhibits several distinguishing features, such as integrating an Iterated Tabu Search (ITS) algorithm with a multistart method and a problem specific perturbation operator. Tested on two sets of 66 public benchmark instances widely used in the literature, the MITS algorithm achieves highly competitive results compared with the best performing algorithms, improving the previous best known results for 22 instances while matching the previous best known results for 39 ones. Furthermore, two important features of the proposed algorithm are analyzed.

An implementation of the iterated tabu search algorithm for the quadratic assignment problem

In this paper, we describe an implementation of the iterated tabu search (ITS) algorithm for the quadratic assignment problem (QAP), which is one of the well-known problems in combinatorial optimization. The medium- and large-scale QAPs are not, to this date, practically solvable to optimality, therefore heuristic algorithms are widely used. In the proposed ITS approach, intensification and diversification mechanisms are combined in a proper way. The goal of intensification is to search for good solutions in the neighbourhood of a given solution, while diversification is responsible for escaping from local optima and moving towards new regions of the search space. In particular, the following enhancements were implemented: new formula for fast evaluation of the objective function and efficient data structure; extended intensification mechanisms (including randomized tabu criterion, combination of tabu search and local search, dynamic tabu list maintaining); enhanced diversification strategy using periodic tabu tenure and special mutation procedure. The ITS algorithm is tested on the different instances taken from the QAP library QAPLIB. The results from the experiments demonstrate promising efficiency of the proposed algorithm, especially for the random QAP instances.

A parallel iterated tabu search heuristic for vehicle routing problems

This paper introduces a parallel iterated tabu search heuristic for solving four different routing problems: the classical vehicle routing problem (VRP), the periodic VRP, the multi-depot VRP, and the site-dependent VRP. In addition, it is applicable to the time-window constrained variant of these problems. Using the iterated local search framework, the heuristic combines tabu search with a simple perturbation mechanism to ensure a broad exploration of the search space. We also describe a parallel implementation of the heuristic to take advantage of multiple-core processors. Extensive computational results show that the proposed heuristic outperforms tabu search alone and is competitive with recent heuristics designed for each particular problem.

Metaheuristics for the traveling salesman problem with pickups, deliveries and handling costs

This paper studies the Traveling Salesman Problem with Pickups, Deliveries, and Handling Costs. The subproblem of minimizing the handling cost for a fixed route is analyzed in detail. It is solved by means of an exact dynamic programming algorithm with quadratic complexity and by an approximate linear time algorithm. Three metaheuristics integrating these solution methods are developed. These are based on tabu search, iterated local search and iterated tabu search. The three heuristics are tested and compared on instances adapted from the related literature. The results show that the combination of tabu search and exact dynamic programming performs the best, but using the approximate linear time algorithm considerably decreases the CPU time at the cost of slightly worse solutions.

Lower bounds for the ITC-2007 curriculum-based course timetabling problem

This paper describes an approach for generating lower bounds for the curriculum-based course timetabling problem, which was presented at the International Timetabling Competition (ITC-2007, Track 3). So far, several methods based on integer linear programming have been proposed for computing lower bounds of this minimization problem. We present a new partition-based approach that is based on the “divide and conquer” principle. The proposed approach uses iterative tabu search to partition the initial problem into sub-problems which are solved with an ILP solver. Computational outcomes show that this approach is able to improve on the current best lower bounds for 12 out of the 21 benchmark instances, and to prove optimality for 6 of them. These new lower bounds are useful to estimate the quality of the upper bounds obtained with various heuristic approaches.

METAHEURISTIC APPROACHES FOR THE QUADRATIC MINIMUM SPANNING TREE PROBLEM

Given an undirected graph with costs associated both with its edges and unordered pairs of edges, the quadratic minimum spanning tree problem asks to find a spanning tree that minimizes the sum of costs of all edges and pairs of edges in the tree. We present multistart simulated annealing, hybrid genetic and iterated tabu search algorithms for solving this problem. We report on computational experiments that compare these algorithms on random graphs of size up to 50 vertices. The results indicate that the iterated tabu search algorithm is superior to the other two approaches in terms of both solution quality and computation time.

Vegetation Buffer Strips Design Using an Optimization Approach for Non-Point Source Pollutant Control of an Agricultural Watershed

Management of agriculture-induced water quality problems requires an integrated approach involving selection of the most suitable and economical Best Management Practices (BMP). Vegetation Buffer Strips (VBS), one of the commonly used off-field structural BMPs, when designed and placed correctly, can significantly improve the water quality. However, VBS takes up agricultural land used for crop production and the implementation/maintenance costs are of concern. Currently, the standards for design of VBS (location and width) are normally set on field study basis, and they do not involve science-based approach to guarantee their efficiency under regional variations, geological and economical conditions. The present study proposes a new approach which integrates computational modeling of watershed processes, fluvial processes and modern heuristic optimization techniques to design a cost effective VBSs in a watershed. The watershed model AnnAGNPS (Annual AGricultural Non-Point Source Pollution Model) and channel network model CCHE1D (Center for Computational Hydroscience and Engineering One(1) Dimensional Model) are linked together to simulate the sediment/pollutant transport processes. Based on the computational results, a multi-objective function is set up, which aims to minimize soil losses, nutrient concentrations as well as total costs associated with installation and maintenance of VBS, while the production profits from agriculture production are being maximized. The solution procedure involves the use of iterative Tabu Search (TS) algorithm to flip VBS design parameters (switching from one alternative to another). The search for the optimal solution follows an iterative procedure. An illustrative case study of USDA’s Goodwin Creek experimental watershed located in Northern Mississippi is used to demonstrate the capabilities of the proposed approach. The results show that the optimized design of VBS using an integrated approach at the watershed level can provide efficient and cost-effective conservation of the environmental quality by taking into account productivity and profitability.

Solving the Fleet Size and Mix Vehicle Routing Problem with Time Windows via Adaptive Memory Programming

This paper presents a novel Adaptive Memory Programming (AMP) solution approach for the Fleet Size and Mix Vehicle Routing Problem with Time Windows (FSMVRPTW). The FSMVRPTW seeks to design a set of depot returning vehicle routes to service a set of customers with known demands, for a heterogeneous fleet of vehicles with different capacities and fixed costs. Each customer is serviced only once by exactly one vehicle, within fixed time intervals that represent the earliest and latest times during the day that service can take place. The objective is to minimize the total transportation costs, or similarly to determine the optimal fleet composition and dimension following least cost vehicle routes. The proposed method utilizes the basic concept of an AMP solution framework equipped with a probabilistic semi-parallel construction heuristic, a novel solution re-construction mechanism, an innovative Iterated Tabu Search algorithm tuned for intensification local search and frequency-based long term memory structures. Computational experiments on well-known benchmark data sets illustrate the efficiency and effectiveness of the proposed method. Compared to the current state-of-the-art, the proposed method improves the best reported cumulative and mean results over most problem instances with reasonable computational requirements.

Iterated tabu search for identifying community structure in complex networks

This paper presents an iterated tabu search (denoted by ITS) algorithm for optimizing the modularity of community structure in complex networks. The proposed algorithm follows a general framework composed of two phases: basic optimization and postrefinement. When the basic optimization cannot improve the modularity any more, a postrefinement procedure is employed to further optimize the objective function with a global view. For both these two phases, iterated tabu search algorithm is employed to optimize the objective function. Computational results show the high effectiveness of the proposed ITS algorithm compared with six state-of-the-art algorithms in the literature. In particular, our ITS algorithm improves the previous best known modularity for several small and medium size networks.

A new bounding procedure and an improved exact algorithm for the Max-2-SAT problem

Given a CNF (conjunctive normal form) Boolean expression with clauses of size at most two, the Max-2-SAT problem asks to find a truth assignment to the Boolean variables that makes true the maximum number of clauses. In this paper, we describe an innovative upper bound computation procedure which is centered around the use of equations and inequalities that are satisfied by all solutions to the problem. The procedure is incorporated in a branch-and-bound algorithm for Max-2-SAT. An initial solution to the problem is provided by an iterated tabu search heuristic. We present computational experience on the Max-2-SAT benchmark instances from the Max-SAT Evaluation 2007. The results show that the developed branch-and-bound algorithm is very competitive with the best previously reported techniques.

List-graph colouring for multiple depot vehicle scheduling

This article addresses a multiple depot vehicle scheduling problem (MDVSP) arising in public transportation. The general problem consists in assigning vehicles to trips while minimising the number of scheduled vehicles and the operational costs. The MDVSP considered here takes into account heterogeneous types of vehicles with complex relations among them. This special feature matches well situations encountered in practice, but makes the problem particularly difficult. We introduce a new formulation based on list-graph colouring, from which an iterative tabu search is developed for vehicle minimisation. The approach is assessed on seven real-world benchmarks and yields highly satisfactory results in terms of solution quality and computation time.

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.

Iterated tabu search for the maximum diversity problem

In this paper, we deal with the maximum diversity problem (MDP), which asks to select a specified number of elements from a given set so that the sum of distances between the selected elements is as large as possible. We develop an iterated tabu search (ITS) algorithm for solving this problem. We also present a steepest ascent algorithm, which is well suited in application settings where solutions of satisfactory quality are required to be provided very quickly. Computational results for problem instances involving up to 5000 elements show that the ITS algorithm is a very attractive alternative to the existing approaches. In particular, we demonstrate the outstanding performance of ITS on the MDP instances taken from the literature. For 69 such instances, new best solutions were found.

ITERATED TABU SEARCH: AN IMPROVEMENT TO STANDARD TABU SEARCH

The goal of this paper is to discuss the tabu search (TS) meta-heuristic and its enhancement for combinatorial optimization problems. Firstly, the issues related to the principles and specific features of the standard TS are concerned. Further, a promising extension to the classical tabu search scheme is introduced. The most important component of this extension is a special kind of diversification mechanism. We give the paradigm of this new improved TS strategy, which is called an iterated tabu search (ITS). ITS was applied to the difficult combinatorial optimization problems, the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). The results of the experiments with the TSP and QAP show the high efficiency of the ITS strategy. The outstanding performance of ITS is also demonstrated by the fact that the new record-breaking solutions were found for the hard QAP instances - tai80a and tai100a.

Iterated Tabu Search for the Unconstrained Binary Quadratic Optimization Problem

Given a set of objects with profits (any, even negative, numbers) assigned not only to separate objects but also to pairs of them, the unconstrained binary quadratic optimization problem consists in finding a subset of objects for which the overall profit is maximized. In this paper, an iterated tabu search algorithm for solving this problem is proposed. Computational results for problem instances of size up to 7000 variables (objects) are reported and comparisons with other up-to-date heuristic methods are provided.

ITERATED TABU SEARCH FOR THE TRAVELING SALESMAN PROBLEM: NEW RESULTS

In this paper, we present some new results obtained for the traveling salesman problem (TSP) by using the iterated tabu search (ITS) meta-heuristic. ITS is a promising extension to the ordinary tabu search scheme. It seeks near-optimal solutions by combining intensification (standard tabu search) and diversification (perturbation of solutions) in a proper way. For the TSP, the main effect is achieved due to decomposition of the solution neighbourhood structure and considerably speeding-up the tabu search process, which is used, namely, in the role of intensification. This fast-iterated tabu search (FITS) technique resulted in quite encouraging solutions for the TSP instances from the TSP instance library TSPLIB. FITS obviously outperformed the other heuristic algorithms used in the experimentation, especially, on the smaller TSP instances.

An improved hybrid genetic algorithm: new results for the quadratic assignment problem

Genetic algorithms (GAs) have been proven to be among the most powerful intelligent techniques in various areas of the computer science, including difficult optimization problems. In this paper, we propose an improved hybrid genetic algorithm (IHGA). It uses a robust local improvement procedure (a limited iterated tabu search (LITS)) as well as an effective restart (diversification) mechanism that is based on so-called “shift mutations”. IHGA has been applied to the well-known combinatorial optimization problem, the quadratic assignment problem (QAP). The results obtained from the numerous experiments on different QAP instances from the instances library QAPLIB show that the proposed algorithm appears to be superior to other modem heuristic approaches that are among the best algorithms for the QAP. The high efficiency of our algorithm is also corroborated by the fact that the new, recordbreaking solutions were obtained for a number of large real-life instances.

Local search algorithms for the min-max loop layout problem

In the min-max loop layout problem, machines are to be arranged around a loop of conveyor belt. The ordering of the machines dictates the number of circuits of the conveyor belt required to manufacture each of several products. The goal is to find an ordering of the machines that minimises the maximum number of circuits required for the manufacture of any of the products. Since the problem is strongly NP-hard, the study of heuristic methods is of interest. This paper proposes iterated descent and tabu search algorithms, and a randomised insertion algorithm. Results of extensive computational tests show that all of our algorithms outperform a previously known algorithm that applies a greedy heuristic to the solution of a linear programming relaxation. The best quality solutions are obtained with iterated descent. This adds further evidence to the belief that iterated descent can produce high quality solutions to a variety of combinatorial optimisation problems. Moreover, unlike some other local search algorithms, iterated descent does not require much tuning in order to be competitive.

Tabu Search for Vehicle Routing Problems (VRPs)

Vehicle Routing Problems (VRPs) considered in this paper involve a set of engineers operating from one base and a set of geographically distributed jobs or services to be performed by them under the given technological and temporal constraints. All engineers have different time-windows for their working and the technological constraints specify their competence to do jobs which can be performed within the given time-windows. A solution to a VRP is the scheduling of jobs among different engineers so that these jobs can be performed in minimum cost with all the temporal and technological constraints satisfied. The objective is to maximize the work done measured in terms of total number of jobs completed and minimize the total distance travelled by all the engineers. Three types of VRPs considered are under, critically and over resourced VRPs. VRPs belong to the class of NP-Complete problems. This paper investigates experimentally the application of an iterative method Tabu Search (TS) [5] in solving all the three types of randomly generated VRPs. The performance of TS is measured in terms of the number of unallocated jobs left and the cost of the solution measured in terms of total distance travelled by all the engineers. Starting with a given initial solution, TS attempts to obtain a near optimal solution containing the minimum number of unallocated jobs and the minimum cost. It is compared with the Hill-Climbing (HC) algorithm also used to solve same VRPs. In almost all cases, TS performs better than HC. However, in some cases, HC is found to give better results in terms of number of unallocated jobs.