Tabu Search directed by direct search methods for nonlinear global optimization

In recent years, there has been a great deal of interest in metaheuristics in the optimization community. Tabu Search (TS) represents a popular class of metaheuristics. However, compared with other metaheuristics like genetic algorithm and simulated annealing, contributions of TS that deals with continuous problems are still very limited. In this paper, we introduce a continuous TS called Directed Tabu Search (DTS) method. In the DTS method, direct-search-based strategies are used to direct a tabu search. These strategies are based on the well-known Nelder–Mead method and a new pattern search procedure called adaptive pattern search. Moreover, we introduce a new tabu list conception with anti-cycling rules called Tabu Regions and Semi-Tabu Regions. In addition, Diversification and Intensification Search schemes are employed. Numerical results show that the proposed method is promising and produces high quality solutions.     

Managing the tabu list length using a fuzzy inference system: an application to examination timetabling

In this paper, we present an application of Tabu Search (TS) to the examination timetabling problem. One of the drawbacks of this meta-heuristic is related to the need of tuning some parameter (like tabu tenure) whose value affects the performance of the algorithm. The importance of developing an automatic procedure is clear considering that most of the users of timetabling software, like academic staff, do not have the expertise to conduct such tuning. The goal of this paper is to present a method to automatically manage the memory in the TS using a Decision Expert System. More precisely a Fuzzy Inference Rule Based System (FIRBS) is implemented to handle the tabu tenure based on two concepts, “Frequency” and “Inactivity”. These concepts are related respectively with the number of times a move is introduced in the tabu list and the last time (in number of iterations) the move was attempted and prevented by the tabu status. Computational results show that the implemented FIRBS handles well the tuning of the tabu status duration improving, as well, the performance of Tabu Search.     

Single-machine scheduling with learning effect and resource-dependent processing times in the serial-batching production

In this paper, we study a single machine scheduling problem by simultaneously considering the processing method of serial-batching, learning effect, resource-dependent processing times, and setup operations. We consider minimizing the makespan as the objective of the studied problem under the constraint that the total resource consumption does not exceed a given limit. For the special case where the resource allocation is given, we first propose the structural properties for job batching policies and batching sequencing, and an optimal batching policy is derived based on these properties. Then, we develop a novel hybrid GSA–TS algorithm which combines the Gravitational Search Algorithm (GSA) and the Tabu Search (TS) algorithm to solve the general case. Computational experiments with different scales show the effectiveness and efficiency of the proposed algorithm.     

A Mixed Heuristic for Circuit Partitioning

As general-purpose parallel computers are increasingly being used to speed up different VLSI applications, the development of parallel algorithms for circuit testing, logic minimization and simulation, HDL-based synthesis, etc. is currently a field of increasing research activity. This paper describes a circuit partitioning algorithm which mixes Simulated Annealing (SA) and Tabu Search (TS) heuristics. The goal of such an algorithm is to obtain a balanced distribution of the target circuit among the processors of the multicomputer allowing a parallel CAD application for Test Pattern Generation to provide good efficiency. The results obtained indicate that the proposed algorithm outperforms both a pure Simulated Annealing and a Tabu Search. Moreover, the usefulness of the algorithm in providing a balanced workload distribution is demonstrated by the efficiency results obtained by a topological partitioning parallel test-pattern generator in which the proposed algorithm has been included. An extented algorithm that works with general graphs to compare our approach with other state of the art algorithms has been also included.     

Diversification-driven tabu search for unconstrained binary quadratic problems

This paper describes a Diversification-Driven Tabu Search (D²TS) algorithm for solving unconstrained binary quadratic problems. D²TS is distinguished by the introduction of a perturbation-based diversification strategy guided by long-term memory. The performance of the proposed algorithm is assessed on the largest instances from the ORLIB library (up to 2500 variables) as well as still larger instances from the literature (up to 7000 variables). The computational results show that D²TS is highly competitive in terms of both solution quality and computational efficiency relative to some of the best performing heuristics in the literature.     

多车场有时间窗的多车型车辆调度及其禁忌算法研究

本文针对物流配送中的多车场车辆调度问题提出了两种多车场的处理方法，介绍了多车场车辆调度问题中容量、时间窗、多车型等多种约束的处理方法，并且根据具体约束情况设计了禁忌算法，对多车场有时间窗的多车型车辆调度问题加以实现，给出了一个具有代表性的算例试验结果和结果分析，通过试验表明了此方法对优化有时间窗的多车型车辆调度问题的有效性．     

Tabu search for the linear ordering problem with cumulative costs

Given a matrix of weights, the Linear Ordering Problem (LOP) consists of finding a permutation of the columns and rows in order to maximize the sum of the weights in the upper triangle. This well known NP-complete problem can also be formulated on a complete weighted graph, where the objective is to find an acyclic tournament that maximizes the sum of arc weights. The variant of the LOP that we target here was recently introduced and adds a cumulative non-linear propagation of the costs to the sum of the arc weights. We first review the previous methods for the LOP and for this variant with cumulative costs (LOPCC) and then propose a heuristic algorithm for the LOPCC, which is based on the Tabu Search (TS) methodology. Our method achieves search intensification and diversification through the implementation of both short and long term memory structures. Our extensive experimentation with 224 instances shows that the proposed procedure outperforms existing methods in terms of solution quality and has reasonable computing-time requirements.     

Comparison of metaheuristic algorithms for Examination Timetabling Problem

SA, TS, GA and ACS are four of the main algorithms for solving challenging problems of intelligent systems. In this paper we consider Examination Timetabling Problem that is a common problem for all universities and institutions of higher education. There are many methods to solve this problem, In this paper we use Simulated Annealing, Tabu Search, Genetic Algorithm and Ant Colony System in their basic frameworks for solving this problem and compare results of them with each other.     

A Metaheuristic to Solve a Location-Routing Problem with Non-Linear Costs

The paper deals with a location-routing problem with non-linear cost functions. To the best of our knowledge, a mixed integer linear programming formulation for the addressed problem is proposed here for the first time. Since the problem is NP-hard exact algorithms are able to solve only particular cases, thus to solve more general versions heuristics are needed. The algorithm proposed in this paper is a combination of a p-median approach to find an initial feasible solution and a metaheuristic to improve the solution. It is a hybrid metaheuristic merging Variable Neighborhood Search (VNS) and Tabu Search (TS) principles and exploiting the synergies between the two. Computational results and conclusions close the paper.     

Tabu Search for the planar three-index assignment problem

Tabu Search is a very effective method for approximately solving hard combinatorial problems. In the current work we implement Tabu Search for solving the Planar Three-Index Assignment Problem. The problem deals with finding the minimum cost assignment between elements of three distinct sets demanding that every pair of elements, each representing a different set, appears in the same solution exactly once. The solutions of the problems correspond to Latin squares. These structures form the basis of the move generation mechanism employed by the Tabu Search procedures. Standard Tabu Search ideas such as candidate move list, variable tabu list size, and frequency-based memory are tested. Computational results for a range of problems of varying dimensions are presented.     

Financial Applications of a Tabu Search Variable Selection Model

We illustrate how a comparatively new technique, a Tabu search variable selection model [Drezner, Marcoulides and Salhi (1999)], can be applied efficiently within finance when the researcher must select a subset of variables from among the whole set of explanatory variables under consideration. Several types of problems in finance, including corporate and personal bankruptcy prediction, mortgage and credit scoring, and the selection of variables for the Arbitrage Pricing Model, require the researcher to select a subset of variables from a larger set. In order to demonstrate the usefulness of the Tabu search variable selection model, we: (1) illustrate its efficiency in comparison to the main alternative search procedures, such as stepwise regression and the Maximum R 2 procedure, and (2) show how a version of the Tabu search procedure may be implemented when attempting to predict corporate bankruptcy. We accomplish (2) by indicating that a Tabu Search procedure increases the predictability of corporate bankruptcy by up to 10 percentage points in comparison to Altman's (1968) Z-Score model.     

Three new stochastic local search algorithms for continuous optimization problems

This paper introduces three new stochastic local search metaheuristics algorithms namely, the Best Performance Algorithm (BPA), the Iterative Best Performance Algorithm (IBPA) and the Largest Absolute Difference Algorithm (LADA). BPA and IBPA are based on the competitive nature of professional athletes, in them desiring to improve on their best recorded performances. LADA is modeled on calculating the absolute difference between two numbers. The performances of the algorithms have been tested on a large collection of benchmark unconstrained continuous optimization functions. They were benchmarked against two well-known local-search metaheuristics namely, Tabu Search (TS) and Simulated Annealing (SA). Results obtained show that each of the new algorithms delivers higher percentages of the best and mean function values found, compared to both TS and SA. The execution times of these new algorithms are also comparable. LADA gives the best performance in terms of execution time.     

The development of a multi-objective Tabu Search algorithm for continuous optimisation problems

While there have been many adaptations of some of the more popular meta-heuristics for continuous multi-objective optimisation problems, Tabu Search has received relatively little attention, despite its suitability and effectiveness on a number of real-world design optimisation problems. In this paper we present an adaptation of a single-objective Tabu Search algorithm for multiple objectives. Further, inspired by path relinking strategies common in discrete optimisation problems, we enhance our algorithm to allow it to handle problems with large numbers of design variables. This is achieved by a novel parameter selection strategy that, unlike a full parametric analysis, avoids the use of objective function evaluations, thus keeping the overall computational cost of the procedure to a minimum. We assess the performance of our two Tabu Search variants on a range of standard test functions and compare it to a leading multi-objective Genetic Algorithm, NSGA-II. The path relinking-inspired parameter selection scheme gives a clear performance improvement over the basic multi-objective Tabu Search adaptation and both variants perform comparably with the NSGA-II.     

Continuous ant colony system and tabu search algorithms hybridized for global minimization of continuous multi-minima functions

A new hybrid optimization method, combining Continuous Ant Colony System (CACS) and Tabu Search (TS) is proposed for minimization of continuous multi-minima functions. The new algorithm incorporates the concepts of promising list, tabu list and tabu balls from TS into the framework of CACS. This enables the resultant algorithm to avoid bad regions and to be guided toward the areas more likely to contain the global minimum. New strategies are proposed to dynamically tune the radius of the tabu balls during the execution and also to handle the variable correlations. The promising list is also used to update the pheromone distribution over the search space. The parameters of the new method are tuned based on the results obtained for a set of standard test functions. The results of the proposed scheme are also compared with those of some recent ant based and non-ant based meta-heuristics, showing improvements in terms of accuracy and efficiency.     

Hybrid scatter tabu search for unconstrained global optimization

The problem of finding a global optimum of an unconstrained multimodal function has been the subject of intensive study in recent years, giving rise to valuable advances in solution methods. We examine this problem within the framework of adaptive memory programming (AMP), focusing particularly on AMP strategies that derive from an integration of Scatter Search and Tabu Search. Computational comparisons involving 16 leading methods for multimodal function optimization, performed on a testbed of 64 problems widely used to calibrate the performance of such methods, disclose that our new Scatter Tabu Search (STS) procedure is competitive with the state-of-the-art methods in terms of the average optimality gap achieved.     

Matheuristics for solving a multi-attribute collection problem for a charity organisation

This paper studies a real-life multi-attribute profit collecting vehicle routing problem, arising in the collection operations of a charity organisation in the United Kingdom. The problem involves a heterogeneous fleet of vehicles of different capacities, mandatory visits to a subset of vertices, time windows, rest requirements associated with maximum driving and working times, and partial collection. A mixed integer programming formulation of the problem is described, along with three matheuristics based on Tabu Search and Large Neighbourhood Search. Computational results on instances derived from the case study are presented, and insights are given from a practical implementation.     

Truck dock assignment problem with operational time constraint within crossdocks

In this paper, we consider a truck dock assignment problem with an operational time constraint in crossdocks where the number of trucks exceeds the number of docks available. The problem feasibility is affected by three factors: the arrival and departure time window of each truck, the operational time for cargo shipment among the docks, and the total capacity available to the crossdock. The objective is to find an optimal assignment of trucks that minimizes the operational cost of the cargo shipments and the total number of unfulfilled shipments at the same time. We combine the above two objectives into one term: the total cost, a sum of the total dock operational cost and the penalty cost for all the unfulfilled shipments. The problem is then formulated as an integer programming (IP) model. We find that as the problem size grows, the IP model size quickly expands to an extent that the ILOG CPLEX Solver can hardly manage. Therefore, two meta-heuristic approaches, Tabu Search (TS) and genetic algorithm (GA), are proposed. Computational experiments are conducted, showing that meta-heuristics, especially the Tabu search, dominate the CPLEX Solver in nearly all test cases adapted from industrial applications.     

“MOSS” multiobjective scatter search applied to non-linear multiple criteria optimization

This paper introduces a multiple criteria scatter search to deal with bounded constrained non-linear continuous vector optimization problems of high dimension, applying a MultiStart Tabu Search (TS) as a diversification generation method, each TS works with its own starting point, recency memory, and aspiration threshold. Frequency memory is used to diversify the search and it is shared between the TS. A Pareto relation is applied in order to designate a subset of the best generated solutions to be reference solutions. A choice function called Kramer Choice function is used to divide the reference solutions in two subsets. The Euclidean distance is used as a measure of dissimilarity in order to find diverse solutions to be combined. Linear combinations of the reference solutions are used as a solution combination method. “Balls” in the decision space and the objective space are used to avoid duplications. Different tabu sets with different tabu tenures are employed in the scatter phase to enhance the diversity of the search. The performance of our approach is compared with Pareto-optimal frontiers and three other state-of-the-art MOEAs for a suite test problems taken from the literature.     

基于PSO-MAs算法的产品组合问题研究

针对多约束的产品组合问题,提出一种基于PSO的Memetic算法。该算法首先运用约束理论识别并剔除非瓶颈约束,然后基于伪效用比率设计了一个局部搜索算法,并将其加入到PSO算法的种群进化中,以增强PSO算法的局部学习能力。通过对算法在小规模和大规模算例中测试,表明该算法在小规模问题中优于许多已有算法,同时能在相对较短地时间内更有效地求解较大规模产品组合问题。因此本文提出的基于PSO的Memetic算法可以用来有效地求解实际中的产品组合问题。     

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.