A diversified Tabu search approach for the open-pit mine production scheduling problem with metal uncertainty

This paper presents a metaheuristic solution approach based on Tabu search for the open-pit mine production scheduling problem with metal uncertainty. To search the feasible domain more extensively, two different diversification strategies are used to generate several initial solutions to be optimized by the Tabu search procedure. The first diversification strategy exploits a long-term memory of the search history. The second one relies on the variable neighborhood search method. Numerical results on realistic large-scale instances are provided to indicate the efficiency of the solution approach to produce very good solutions in relatively short computational times.     

A variable selection method based on Tabu search for logistic regression models

A Tabu search method is proposed and analysed for selecting variables that are subsequently used in Logistic Regression Models. The aim is to find from among a set of m variables a smaller subset which enables the efficient classification of cases. Reducing dimensionality has some very well-known advantages that are summarized in literature. The specific problem consists in finding, for a small integer value of p, a subset of size p of the original set of variables that yields the greatest percentage of hits in Logistic Regression. The proposed Tabu search method performs a deep search in the solution space that alternates between a basic phase (that uses simple moves) and a diversification phase (to explore regions not previously visited). Testing shows that it obtains significantly better results than the Stepwise, Backward or Forward methods used by classic statistical packages. Some results of applying these methods are presented.     

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 two-phase tabu search based evolutionary algorithm for the maximum diversity problem

In this paper, we study the maximum diversity problem (MDP) which is equivalent to the quadratic unconstrained binary optimization (QUBO) problem with cardinality constraint. The MDP aims to select a subset of elements with given cardinality such that the sum of pairwise distances between any two elements in the selected subset is maximized. For solving this computationally challenging problem, we propose a two-phase tabu search based evolutionary algorithm (TPTS/EA), which integrates several distinguishing features to ensure the diversity and the quality of the evolution, such as a two-phase tabu search algorithm which consists of a dynamic candidate list (DCL) strategy-based traditional tabu search in the first phase and a solution-based tabu search procedure to refine the search in the second phase, and two path-relinking based recombination operators to generate new offspring solutions. Tested on three sets of totally 140 public instances in the literature, the study demonstrates the efficacy of the proposed TPTS/EA algorithm in terms of both solution quality and computational efficiency. Specifically, our proposed TPTS/EA algorithm is able to improve the previous best known results for 2 instances, while matching the previous best-known solutions for 130 instances. We also provide experimental evidences to highlight the beneficial effect of several important components in our TPTS/EA algorithm.     

General solutions to the single vehicle routing problem with pickups and deliveries

The single vehicle routing problem with pickups and deliveries (SVRPPD) is defined on a graph in which pickup and delivery demands are associated with the customer vertices. The problem consists of designing a least cost route for a vehicle of capacity Q. Each customer is allowed to be visited once for a combined pickup and delivery, or twice if these two operations are performed separately. This article proposes a mixed integer linear programming model for the SVRPPD. It introduces the concept of general solution which encompasses known solution shapes such as Hamiltonian, double-path and lasso. Classical construction and improvement heuristics, as well as a tabu search heuristic, are developed and tested over several instances. Computational results show that the best solutions generated by the heuristics are frequently non-Hamiltonian and may contain up to two customers visited twice.     

POPMUSIC for the point feature label placement problem

Point feature label placement is the problem of placing text labels adjacent to point features on a map so as to maximize legibility. The goal is to choose positions for the labels that do not give rise to label overlaps and that minimize obscuration of features. A practical goal is to minimize the number of overlaps while considering cartographic preferences. This article proposes a new heuristic for solving the point feature label placement problem based on the application of the POPMUSIC frame. Computational experiments show that the proposed heuristic outperformed other recent metaheuristics approaches in the literature. Experiments with problem instances involving up to 10 million points show that the computational time of the proposed heuristic increases almost linearly with the problem size. New problem instances based on real data with more than 13,000 labels are proposed.     

Tabu search for non-permutation flowshop scheduling problem with minimizing total tardiness

This paper deals with the non-permutation flowshop problem which means that the job sequences are allowed to be different on machines. The objective function is minimizing the total tardiness. Firstly, three mixed-integer linear programming (MILP) models for non-permutation flowshop problems are described, and then are analyzed and assessed their relative effectiveness. Secondly, two Tabu search based algorithms, denoted by LH1 and LH2, are proposed to solve the complicated non-permutation flowshop problems. The algorithms are constructed on specific neighborhood structures which enable the searching method effective. Finally, the performance is evaluated against Taillard’s famous benchmark. Computational experiments show that the proposed algorithms, LH1 and LH2, are significantly superior to the L_TS algorithm. And the percentages of improved permutation flowshop instances by LH1 and LH2 algorithms are about 87.8% and 98.3% with respect to total tardiness, respectively. The non-permutation schedules also have achieved significant improvement in four different scenarios of due dates. Consequently, average percentage improvement (API) is 14.52% for flowshop problems with low tardiness factors. It is evident that exploring non-permutation schedule is effective and necessary for low tardiness factors.     

General variable neighborhood search for the continuous optimization

We suggest a new heuristic for solving unconstrained continuous optimization problems. It is based on a generalized version of the variable neighborhood search metaheuristic. Different neighborhoods and distributions, induced from different metrics are ranked and used to get random points in the shaking step. We also propose VNS for solving constrained optimization problems. The constraints are handled using exterior point penalty functions within an algorithm that combines sequential and exact penalty transformations. The extensive computer analysis that includes the comparison with genetic algorithm and some other approaches on standard test functions are given. With our approach we obtain encouraging results.     

Tabu search heuristics for the order batching problem in manual order picking systems

In a manual order picking system, order pickers walk or ride through a distribution warehouse in order to collect items requested by (internal or external) customers. In order to perform these operations efficiently, it is usually required that customer orders be combined into (more substantial) picking orders that are limited in size. The order batching problem considered in this paper deals with the question of how a given set of customer orders should be combined into picking orders such that the total length of all picker tours necessary for all of the requested items to be collected is minimized. For the solution of this problem the authors suggest two approaches based on the tabu search principle. The first is a (classic) tabu search (TS), and the second is the attribute-based hill climber (ABHC). In a series of extensive numerical experiments, these approaches are benchmarked against other solution methods put forward in the current literature. It is demonstrated that the proposed methods are superior to the existing methods and provide solutions which may allow distribution warehouses to operate more efficiently.     

Tabu search for the single row facility layout problem using exhaustive 2-opt and insertion neighborhoods

The single row facility layout problem (SRFLP) is the problem of arranging facilities with given lengths on a line, while minimizing the weighted sum of the distances between all pairs of facilities. The problem is NP-hard. In this paper, we present two tabu search implementations, one involving an exhaustive search of the 2-opt neighborhood and the other involving an exhaustive search of the insertion neighborhood. We also present techniques to significantly speed up the search of the two neighborhoods. Our computational experiments show that the speed up techniques are effective, and our tabu search implementations are competitive. Our tabu search implementations improved previously known best solutions for 23 out of the 43 large sized SRFLP benchmark instances.     

Scatter search for chemical and bio-process optimization

Scatter search is a population-based method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear optimization problems. Based on formulations originally proposed in 1960s for combining decision rules and problem constraints such as the surrogate constraint method, scatter search uses strategies for combining solution vectors that have proved effective in a variety of problem settings. In this paper, we develop a general purpose heuristic for a class of nonlinear optimization problems. The procedure is based on the scatter search methodology and treats the objective function evaluation as a black box, making the search algorithm context-independent. Most optimization problems in the chemical and bio-chemical industries are highly nonlinear in either the objective function or the constraints. Moreover, they usually present differential-algebraic systems of constraints. In this type of problem, the evaluation of a solution or even the feasibility test of a set of values for the decision variables is a time-consuming operation. In this context, the solution method is limited to a reduced number of solution examinations. We have implemented a scatter search procedure in Matlab (Mathworks, 2004) for this special class of difficult optimization problems. Our development goes beyond a simple exercise of applying scatter search to this class of problems, but presents innovative mechanisms to obtain a good balance between intensification and diversification in a short-term search horizon. Computational comparisons with other recent methods over a set of benchmark problems favor the proposed procedure.     

New heuristics for the maximum diversity problem

The maximum diversity problem (MDP) consists of identifying, in a population, a subset of elements, characterized by a set of attributes, that present the most diverse characteristics among the elements of the subset. The identification of such solution is an NP-hard problem. Some heuristics are available to obtain approximate solutions for this problem. In this paper, we propose different GRASP heuristics for the MDP, using distinct construction procedures and including a path-relinking technique. Performance comparison among related work and the proposed heuristics is provided. Experimental results show that the new GRASP heuristics are quite robust and are able to find high-quality solutions in reasonable computational times. G.C. Silva’s work sponsored by CAPES MSc scholarship. L.S. Ochi’s work sponsored by CNPq research grants 304103/2003-9 and 550059/2005-9. S.L. Martins’s work sponsored by CNPq research grant 475124/03-0. A. Plastino’s work sponsored by CNPq research grants 300879/00-8 and 475124/03-0.     

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 decomposed metaheuristic approach for a real-world university timetabling problem

In this paper we present a decomposed metaheuristic approach to solve a real-world university course timetabling problem. Essential in this problem are the overlapping time slots and the irregular weekly timetables. A first stage in the approach reduces the number of subjects through the introduction of new structures that we call ‘pillars’. The next stages involve a metaheuristic search that attempts to solve the constraints one by one, instead of trying to find a solution for all the constraints at once. Test results for a real-world instance are presented.     

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.     

Expanding neighborhood search–GRASP for the probabilistic traveling salesman problem

The Probabilistic Traveling Salesman Problem is a variation of the classic traveling salesman problem and one of the most significant stochastic routing problems. In probabilistic traveling salesman problem only a subset of potential customers need to be visited on any given instance of the problem. The number of customers to be visited each time is a random variable. In this paper, a variant of the well-known Greedy Randomized Adaptive Search Procedure (GRASP), the Expanding Neighborhood Search–GRASP, is proposed for the solution of the probabilistic traveling salesman problem. expanding neighborhood search–GRASP has been proved to be a very efficient algorithm for the solution of the traveling salesman problem. The proposed algorithm is tested on a numerous benchmark problems from TSPLIB with very satisfactory results. Comparisons with the classic GRASP algorithm and with a Tabu Search algorithm are also presented. Also, a comparison is performed with the results of a number of implementations of the Ant Colony Optimization algorithm from the literature and in six out of ten cases the proposed algorithm gives a new best solution.     

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.