20 years of Greedy Randomized Adaptive Search Procedures with Path Relinking

This is a comprehensive review of the Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic and its hybridization with Path Relinking (PR) over the past two decades. GRASP with PR has become a widely adopted approach for solving hard optimization problems since its proposal in 1999. The paper covers the historical development of GRASP with PR and its theoretical foundations, as well as recent advances in its implementation and application. The review includes a critical analysis of variants of PR, including memory-based and randomized designs, with a total of ten different implementations. It describes these advanced designs both theoretically and practically on two well-known optimization problems, linear ordering and max-cut. The paper also explores the hybridization of GRASP with PR and other metaheuristics, such as Tabu Search and Scatter Search. Overall, this review provides valuable insights for researchers and practitioners seeking to utilize GRASP with PR for solving optimization problems.Comment: 28 pages, 13 figure

GRASP with path relinking for the selective pickup and delivery problem

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A parallel multi-population biased random-key genetic algorithm for electric distribution network reconfiguration

This work presents a multi-population biased random-key genetic algorithm (BRKGA) for the electric distribution network reconfiguration problem (DNR). DNR belongs to the class of network design problems which include transportation problems, computer network restoration and telecommunication network design and can be used for loss minimization and load balancing, being an important tool for distribution network operators. A BRKGA is a class of genetic algorithms in which solutions are encoded as vectors of random keys, i.e. randomly generated real numbers from a uniform distribution in the interval [0, 1). A vector of random keys is translated into a solution of the optimization problem by a decoder. The decoder used generates only feasible solutions by using an efficient codification based upon the fundamentals of graph theory, restricting the search space. The parallelization is based on the single program multiple data paradigm and is executed on the cores of a multi-core processor. Time to target plots, which characterize the running times of stochastic algorithms for combinatorial optimization, are used to compare the performance of the serial and parallel algorithms. The proposed method has been tested on two standard distribution systems and the results show the effectiveness and performance of the parallel algorithm

The minimum length corridor problem : exact, approximative and heuristic algorithms

Orientador: Cid Carvalho de SouzaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Esta dissertação tem como foco a investigação experimental de algoritmos exatos, aproximativos e heurísticos aplicados na resolução do chamado problema do corredor de comprimento mínimo (PCCM). No PCCM recebemos um polígono retilinear P e um conjunto de polígonos retilineares menores formando uma subdivisão S planar conexa de P. Uma solução para este problema, também chamada de corredor, é formada por um conjunto conexo de arestas de S, e tal que cada face interna em S possui pelo menos um ponto em sua borda que pertence a alguma aresta deste conjunto. O objetivo então é encontrar um corredor tal que a soma total dos comprimentos das arestas seja a menor possível. Trata-se de um problema NP-difícil com aplicações em áreas diversas, tais como telecomunicações, engenharia civil e projeto de circuitos VLSI. O PCCM pode ser reduzido polinomialmente a um problema em grafos denominado problema da árvore de Steiner com grupos (PASG). Considerando esta transformação, estudamos e implementamos dois métodos aproximativos, um método exato de branch-and-cut, e um método heurístico baseado na metaheurística GRASP combinada com um evolutionary path relinking (GRASP+EPR). Além disso, propomos três heurísticas de busca local que visam melhorar a qualidade de soluções do PASG. Instâncias do PCCM foram geradas aleatoriamente, nas quais aplicamos os métodos implementados. Analisamos os resultados, e apresentamos as situações onde é interessante utilizar cada método. Verificamos que o método branch-and-cut foi capaz de encontrar soluções ótimas para instâncias que julgamos ser de grande porte em tempos computacionalmente aceitáveis. O melhor algoritmo aproximativo obteve corredores que na média têm comprimento 17% maior que o comprimento ótimo. Se combinarmos este algoritmo com as heurísticas de melhoria propostas este percentual cai para a média de 3,5%. Finalmente, o GRASP+EPR consome mais tempo que este algoritmo aproximativo, entretanto, o comprimento dos corredores obtidos por ele é em média 0,9% maior que o comprimento ótimoAbstract: This dissertation focuses on the experimental investigation of exact, approximation and heuristic algorithms applied to solve the so-called minimum length corridor problem (MLCP). In the MLCP we receive a rectilinear polygon P and a set of minor rectilinear polygons forming a connected planar subdivision S of P. A solution for this problem, also called corridor, is formed by a set of connected edges of S, and such that each inner face of S has at least one point on its your border which belongs to an edge in this set. The goal is to find a corridor such that the sum of lengths of the edges is as small as possible. This is an NP-hard problem with applications in several areas such as telecommunications, civil engineering and design of VLSI circuits. The MLCP can be polynomially reduced to a graph problem known as group Steiner tree problem (GSTP). Based on this transformation, we studied and implemented two approximation methods, an exact branch-and-cut method, and a heuristic method based on the metaheuristic GRASP combined with an evolutionary path relinking (GRASP+EPR). Furthermore, we propose three local search heuristics to improve the quality of GSTP solutions. MLCP instances were randomly generated, in which we apply the methods implemented. We analyzed the results, and present situations where it is interesting to use each method. We found that the branch-and-cut has been able to find optimal solutions for instances that we consider to be large in acceptable computational times. The best approximation algorithm obtained corridors having average length 17% higher than the optimum length. If we combine this algorithm with the improvement heuristics proposed this percentage drops to an average of 3.5%. Finally, the GRASP+EPR spent more time than this approximation algorithm, however, the length of the corridors obtained by the method is, on average, 0.9% higher than the optimum lengthMestradoCiência da ComputaçãoMestre em Ciência da Computaçã

Measuring diversity. A review and an empirical analysis

Maximum diversity problems arise in many practical settings from facility location to social networks, and constitute an important class of NP-hard problems in combinatorial optimization. There has been a growing interest in these problems in recent years, and different mathematical programming models have been proposed to capture the notion of diversity. They basically consist of selecting a subset of elements of a given set in such a way that a measure based on their pairwise distances is maximized to achieve dispersion or representativeness. In this paper, we perform an exhaustive comparison of four mathematical models to achieve diversity over the public domain library MDPLIB, studying the structure of the solutions obtained with each of them. We extend this library by including new Euclidean instances which permit to analyze the geometrical distribution of the solutions. Our study concludes which models are better suited for dispersion and which ones for representativeness in terms of the structure of their solutions, as well as which instances are difficult to solve. We also identify in our conclusions one of the models which is not recommended in any setting. We finalize by proposing two improvements, one related to the models and one to solving methods. The computational testing shows the value of the analysis and merit of our proposals