The improvement in the performance of computers and mathematical programming techniques has led to the development of a new class of algorithms called matheuristics. Associated with an improvement of Mixed Integer Programming (MIP) solvers, these methods have successfully solved plenty of combinatorial optimization problems. This paper presents a matheuristic approach that hybridizes local search based metaheuristics and mathematical programming techniques to solve the capacitated p-median problem. The proposal considers reduced mathematical models obtained by a heuristic elimination of variables that are unlikely to belong to a good or optimal solution. In addition, a partial optimization algorithm based on the reduction is proposed. All mathematical models are solved by an MIP solver. Computational experiments on five sets of instances confirm the good performance of our approach.The first work on the CPMP appeared in scientific literature in the 1980s (Mulvey and Beck, 1984;Pirkul, 1987). Osman and Christofides (1994) used a hybrid approach that combines simulated annealing and tabu search and randomly generated 20 instances with size ranging from 50 to 100 customers to test the proposed methods. Maniezzo et al. (1998) presented an evolutionary method and an effective local search technique to solve the CPMP. Computational results showed the effectiveness of the proposed approach on five sets of instances, including those proposed by Osman and Christofides. More recently, Baldacci et al. (2002) proposed a new method based on a set partitioning formulation. The authors presented computational results on instances from the literature and proposed new sets of test problems with additional constraints: bounds on the cluster cardinality and incompatibilities between entities. Senne (2002, 2004) presented a column-generation method integrated to Lagrangean/surrogate relaxation to calculate lower bounds. Their proposed method identifies new productive columns, accelerating the computational process. Computational results were presented on instances generated based on a geographic database from the city São José dos Campos. Ahmadi and Osman (2005) proposed a combination of metaheuristics in a framework called GRAMPS (greedy random adaptive memory search method). A scatter search approach was proposed by Scheuerer and Wendolsky (2006), who evaluated it on instances from the literature, obtaining several new best solutions. Díaz and Fernández (2006) presented a hybrid scatter search and path relinking algorithm. The authors have run a series of computational experiments evaluating the proposed methods on instances from the literature, including instances corresponding to 737 cities in Spain. Both algorithms were evaluated separately; however, the combination of path relinking and scatter search gave the best results. Fleszar and Hindi (2008) solved the CPMP using variable neighborhood search to define sets of medians and the CPLEX package to solve assignment problems. Chaves et al. (2007) presented a hybrid heuristic ...

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Population growth and the massive production of automotive vehicles have lead to the increase of traffic congestion problems. Traffic congestion today is not limited to large metropolitan areas, but is observed even in medium-sized cities and highways. Traffic engineering can contribute to lessen these problems. One possibility, explored in this paper, is to assign tolls to streets and roads, with the objective of inducing drivers to take alternative routes, and thus better distribute traffic across the road network. This assignment problem is often referred to as the tollbooth problem and it is NP-hard. In this paper, we propose mathematical formulations for two versions of the tollbooth problem that use piecewise- 123Ann Oper Res linear functions to approximate congestion cost. We also apply a biased random-key genetic algorithm on a set of real-world instances, analyzing solutions when computing shortest paths according to two different weight functions. Experimental results show that the proposed piecewise-linear functions approximate the original convex function quite well and that the biased random-key genetic algorithm produces high-quality solutions.

Cloud computing has recently emerged as a new technology for hosting and supplying services over the Internet. This technology has brought many benefits, such as eliminating the need for maintaining expensive computing hardware and allowing business owners to start from small and increase resources only when there is a rise in service demand. With an increasing demand for cloud computing, providing performance guarantees for applications that run over cloud become important. Applications can be abstracted into a set of virtual machines with certain guarantees depicting the quality of service of the application. In this paper, we consider the placement of these virtual machines across multiple data centers, meeting the quality of service requirements while minimizing the bandwidth cost of the data centers. This problem is a generalization of the NP-hard Generalized Quadratic Assignment Problem (GQAP). We formalize the problem and propose a novel algorithm based on a biased random-key genetic algorithm (BRKGA) to find nearoptimal solutions for the problem. The experimental results show that the proposed algorithm is effective in quickly finding feasible solutions and it produces better results than a baseline aproach provided by a commercial solver and a multi-start algorithm.

In this paper we study the unrelated parallel machine scheduling problem with sequence and machine-dependent setup times. We consider the objective of minimizing the maximum completion time of the latest job, usually referred to as makespan. We propose a new MIP-based heuristic combining atomic moves such as insertion, ejection and closure, in order to generate sequences of such atomic moves minimizing the makespan. This heuristic employs a commercial solver to search the neighborhood in a multi-start algorithm. Our approach performed well in computational experiments targeting two sets of benchmark instances previously used in the literature Keywords: MIP-based neighborhood, hybrid metaheuristics, unrelated parallel machine scheduling problem, makespan. heurística baseada em programação matemática para o problema de programação de tarefas em máquinas paralelas não relacionadas com tempo de preparação dependente da sequência e da máquina.