A phylogeny is a tree that relates taxonomic units based on their similarity over a set of characteristics. The phylogeny problem under the parsimony criterion consists in finding a phylogeny with a minimum number of evolutionary steps. We propose hybrid heuristic methods - based on GRASP, path-relinking and genetic algorithm methodologies - to build a phylogeny while minimizing parsimony. Computational experiments using benchmark conditions are reported, and the results obtained by the proposed hybrid heuristics are compared with the solutions obtained by a traditional GRASP (without hybridization) heuristic and with previously reported solutions in the literature. The experimental results illustrate that the proposed heuristics are efficient in terms of solution quality and time-to-target-value.

In real optimization problems it is generally desirable to optimize more than one performance criterion (or objective) at the same time. The goal of the multiobjective combinatorial optimization (MOCO) is to optimize simultaneously r > 1 objectives. As in the single-objective case, the use of heuristic/metaheuristic techniques seems to be the most promising approach to MOCO problems because of their efficiency, generality and relative simplicity of implementation. In this work, we develop algorithms based on Greedy Randomized Adaptive Search Procedure (GRASP) and Iterated Local Search (ILS) metaheuristics for the multiobjective knapsack problem. Computational experiments on benchmark instances show that the proposed algorithms are very robust and outperform other heuristics in terms of solution quality and running times.

Este artigo propõe diferentes estratégias de paralelização de um algoritmo GRASP (Greedy Randomized Adaptive Search Procedure) multicritério. O algoritmo paralelo proposto é aplicado ao problema da árvore geradora mínima multicritério, que é NP-difícil. Neste problema, um vetor de custos é definido para cada aresta do grafo e o objetivo é encontrar as árvores geradoras eficientes (soluções Pareto-ótimas). Cada processo encontra um subconjunto de soluções eficientes. Estes subconjuntos são reunidos usando diferentes estratégias para obter o conjunto final de soluções eficientes. O algoritmo proposto é testado em grafos completos com n = 20, 30 e 50 nós e r = 2 e 3 critérios. Os resultados computacionais mostram que a proposta de se paralelizar o algoritmo reduz o tempo de execução e os resultados obtidos pela versão seqüencial foram melhorados.

This paper proposes different strategies of parallelizing a multi-criteria GRASP (Greedy Randomized Adaptive Search Problem) algorithm. The parallel GRASP algorithm is applied to the multi-criteria minimum spanning tree problem, which is NP-hard. In this problem, a vector of costs is defined for each edge of the graph and the goal is to find all the efficient or Pareto optimal spanning trees (Pareto-optimal solutions). Each process finds a subset of efficient solutions. These subsets are joined using different strategies to obtain the final set of efficient solutions. The multi-criteria GRASP algorithm with the different parallel strategies are tested on complete graphs with n = 20, 30 and 50 nodes and r = 2 and 3 criteria. The computational results show that the proposed parallel algorithms reduce the execution time and the results obtained by the sequential version were improved.