Solving the clique partitioning problem as a maximally diverse grouping problem

In this paper we show that the clique partitioning problem can be reformulated in an equivalent form as the maximally diverse grouping problem (MDGP). We then modify a skewed general variable neighborhood search (SGVNS) heuristic that was first developed to solve the MDGP. Similarly as with the MDGP, significant improvements over the state of the art are obtained when SGVNS is tested on large scale instances. This further confirms the usefulness of a combined approach of diversification afforded with skewed VNS and intensification afforded with the local search in general VNS.     

A hybrid genetic algorithmic approach to the maximally diverse grouping problem

The maximally diverse grouping problem (MDGP) is a NP-complete problem. For such NP-complete problems, heuristics play a major role in searching for solutions. Most of the heuristics for MDGP focus on the equal group-size situation. In this paper, we develop a genetic algorithm (GA)-based hybrid heuristic to solve this problem considering not only the equal group-size situation but also the different group-size situation. The performance of the algorithm is compared with the established Lotfi–Cerveny–Weitz algorithm and the non-hybrid GA. Computational experience indicates that the proposed GA-based hybrid algorithm is a good tool for solving MDGP. Moreover, it can be easily modified to solve other equivalent problems.     

Tabu search for the BWC problem

Given a graph G and positive integers B and W, the BWC problem asks about the existence of a coloring of G, with B black and W white vertices, such that there is no edge between a black and a white vertex. We suggest a heuristic, based on tabu search, which yields quite good results for this problem. We compare the performance of our algorithm to that of several other known heuristics, and also to what one might expect based on some theoretical results we obtained for the checked graphs.     

Tabu search for a multi-objective routing problem

Multi-objective optimization problems deal with the presence of different conflicting objectives. Given that it is not possible to obtain a single solution by optimizing all the objectives simultaneously, a common way to face these problems is to obtain a set of efficient solutions called the non-dominated frontier. In this paper, we address the problem of routing school buses with two objectives: minimize the number of buses, and minimize the longest time a student would have to stay in the bus. The trade-off in this problem is between service level, which is represented by the maximum route length, and operational cost, which is represented by the number of buses in the solution. We present different constructive solution methods and a tabu search procedure to obtain non-dominated solutions. The procedure is coupled with an intensification phase based on the path relinking methodology: a strategy proposed several years ago, which has been rarely used in actual implementations. Computational experiments with real data, in the context of routing school buses in a rural area, establish the effectiveness of our procedure in relation to the approach previously identified to be the best.     

Tabu search for solving the black-and-white travelling salesman problem

The black-and-white travelling salesman problem (BWTSP) is an extension to the well-known TSP by partitioning the set of vertices into black and white vertices, and imposing cardinality and length constraints between two consecutive black vertices in a Hamiltonian tour. BWTSP has various applications in aircraft routing, telecommunication network design and logistics. In this paper, we develop several tabu search (TS) heuristics for solving the BWTSP. Our TS is built upon a new efficient neighbourhood structure, which exploits both the permutation and knapsack features of BWTSP. We also embed our TS as a heuristic procedure to improve the upper bound in a mixed-integer linear programming method. Extensive computational experiment on both benchmark and randomly generated instances shows effectiveness and efficiency of our algorithms. Our algorithms are able to obtain optimal and near optimal solutions to small instances in seconds, and find feasible solutions to large instances that have not been solved by the existing methods in the literature.     

Tabu search and GRASP for the maximum diversity problem

In this paper, we develop new heuristic procedures for the maximum diversity problem (MDP). This NP-hard problem has a significant number of practical applications such as environmental balance, telecommunication services or genetic engineering. The proposed algorithm is based on the tabu search methodology and incorporates memory structures for both construction and improvement. Although proposed in seminal tabu search papers, memory-based constructions have often been implemented in naïve ways that disregard important elements of the fundamental tabu search proposals. We will compare our tabu search construction with a memory-less design and with previous algorithms recently developed for this problem. The constructive method can be coupled with a local search procedure or a short-term tabu search for improved outcomes. Extensive computational experiments with medium and large instances show that the proposed procedure outperforms the best heuristics reported in the literature within short computational times.     

A Tabu search heuristic for the generalized assignment problem

This paper considers the generalized assignment problem (GAP). It is a well-known NP-hard combinatorial optimization problem that is interesting in itself and also appears as a subproblem in other problems of practical importance. A Tabu search heuristic for the GAP is proposed. The algorithm uses recent and medium-term memory to dynamically adjust the weight of the penalty incurred for violating feasibility. The most distinctive features of the proposed algorithm are its simplicity and its flexibility. These two characteristics result in an algorithm that, compared to other well-known heuristic procedures, provides good quality solutions in competitive computational times. Computational experiments have been performed in order to evaluate the behavior of the proposed algorithm.     

Tabu search approaches for solving the two-group classification problem

The two-group classification problem consists in constructing a classifier that can distinguish between the two groups. In this paper, we consider the two-group classification problem which consists in determining a hyperplane that minimizes the number of misclassified points. We assume that the data set is numeric and with no missing data. We develop a tabu search (TS) heuristic for solving this NP-hard problem. The TS approach is based on a more convenient equivalent formulation of the classification problem. We also propose supplementary new intensification phases based on surrogate constraints. The results of the conducted computational experiments show that our TS algorithms produce solutions very close to the optimum and require significantly lower computational effort, so it is a valuable alternative to the MIP approaches. Moreover the tabu search procedures showed in this paper can be extended in a natural way to the general classification problem, which consists of generating more than one separating hyperplanes.     

Large-scale controlled rounding using tabu search with strategic oscillation

When publishing tabular data, the United States Bureau of the Census must sometimes round fractional data to integer values or round integer data to multiples of a prespecified base. Data integrity can be maintained by rounding tabular data subject to additivity constraints while minimizing the overall perturbation of the data. In this paper, we describe a heuristic based on tabu search with strategic oscillation for solving this NP-hard problem. A lower-bounding technique is developed in order to evaluate the quality of the solutions and provide a starting solution for the tabu search. Numerical results demonstrate the effectiveness of the procedure when applied to extremely large tables with up to 27,000 randomly generated entries. Additionally, the algorithm is shown to perform extremely well when applied to actual data obtained from the United States Bureau of the Census.     

Tabu search variants for the mix fleet vehicle routing problem

The Mix Fleet Vehicle Routing Problem (MFVRP) involves the design of a set of minimum cost routes, originating and terminating at a central depot, for a fleet of heterogeneous vehicles with various capacities, fixed costs and variable costs to service a set of customers with known demands. This paper develops new variants of a tabu search meta-heuristic for the MFVRP. These variants use a mix of different components, including reactive tabu search concepts; variable neighbourhoods, special data memory structures and hashing functions. The reactive concept is used in a new way to trigger the switch between simple moves for intensification and more complex ones for diversification of the search strategies. The special data structures are newly introduced to efficiently search the various neighbourhood spaces. The combination of data structures and strategic balance between intensification and diversification generates an efficient and robust implementation, which is very competitive with other algorithms in the literature on a set of benchmark instances for which some new best-known solutions are provided.     

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.     

Tabu search applied to the general fixed charge problem

Recent successes in applying tabu search to a wide variety of classical optimization problems have motivated the investigation of applying tabu search to the well-known general fixed charge problem (GFCP). In this paper, an adaptation of tabu search to GFCP is described and computational results are given. In addition, the computational results are compared with those obtained from SWIFT-2, the most well-known and frequently used heuristic method for GFCP. As will be shown, the results are very encouraging.     

Maximally diverse grouping: an iterated tabu search approach

The maximally diverse grouping problem (MDGP) consists of finding a partition of a set of elements into a given number of mutually disjoint groups, while respecting the requirements of group size constraints and diversity. In this paper, we propose an iterated tabu search (ITS) algorithm for solving this problem. We report computational results on three sets of benchmark MDGP instances of size up to 960 elements and provide comparisons of ITS to five state-of-the-art heuristic methods from the literature. The results demonstrate the superiority of the ITS algorithm over alternative approaches. The source code of the algorithm is available for free download via the internet.     

Creating lasso-solutions for the traveling salesman problem with pickup and delivery by Tabu search

We consider the Traveling Salesman Problem with Pickup and Delivery (TSPPD) where the same costumers might require both deloverie of goods and pickup of other goods. All the goods should be transported from/to the same depot. A vehicle on a TSPPD-tour could often get some practical problems when arranging the load. Even if the vehicle has enough space for all the pickups, one has to consider that they are stored in a way that doesn't block the delivery for the next customer. In real life problems this occurs for instance for breweries when they deliver bottles of beer or mineral water and collects empty bottles from the same customers on the same tour. In these situations we could relax the constraints of only checking Hamiltonian tours, and also try solutions that can visit customers in a way giving rise to a ‘alsso’ model. A solution which first only delivers bottles until the vehicle is partly unloaded, then do both delivery and pickup at the remaining customers and at last picks up the empty bottle from the first visited customers, could in these situations be better than a pure Hamiltonian tour, at least in a practical setting. To find such solutions, we will use the metaheuristic Tabu Search on some well known TSPPD-problems, and compare them to other kinds of solutions on the same problems.     

Tabu search with ejection chains for the vehicle routing problem with private fleet and common carrier

The problem reported in this paper is a variant of the classical vehicle routing problem, where customer requests for a transportation company can be served either by its private fleet of vehicles or assigned to an external common carrier. The latter case occurs if the demand exceeds the total capacity of the private fleet or if it is more economical to do so. Accordingly, the objective is to minimize the variable and fixed costs of the private fleet plus the costs charged by the common carrier. A tabu search heuristic with a neighbourhood structure based on ejection chains is proposed to solve this problem. It is empirically demonstrated that this algorithm outperforms the best approaches reported in the literature on a set of benchmark instances with both homogeneous and heterogeneous fleets.     

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.     

Tabu search embedded simulated annealing for the shortest route cut and fill problem

The shortest route cut and fill problem proposed by Henderson et al ¹ is studied in this paper where we extend the model to include multiple vehicles and a makespan objective. A new tabu search embedded simulated annealing algorithm for both models is developed. Computational experiments show that the new approach is robust and achieves better solutions when compared with those found using Henderson et al's algorithm for larger test cases within significantly shorter times.     

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 graph partitioning

In this paper, we develop a tabu search procedure for solving the uniform graph partitioning problem. Tabu search, an abstract heuristic search method, has been shown to have promise in solving several NP-hard problems, such as job shop and flow shop scheduling, vehicle routing, quadratic assignment, and maximum satisfiability. We compare tabu search to other heuristic procedures for graph partitioning, and demonstrate that tabu search is superior to other solution approaches for the uniform graph partitioning problem both with respect to solution quality and computational requirements.