A phylogenetic tree relates taxonomic units using their similarities over a set of characteristics. Given a set of taxonomic units and their characteristics, the phylogeny problem under the parsimony criterion consists in finding a phylogenetic tree with a minimum number of evolutionary steps. We developed a hybrid genetic algorithm for the problem of building a phylogenetic tree minimizing parsimony. The algorithm combines local search with a crossover strategy based on path-relinking, an intensification technique originally used in the context of other metaheuristics such as scatter search and GRASP. Computational experiments on benchmark and randomly generated instances show that the proposed algorithm is very robust and outperforms other heuristics in terms of solution quality and running times.

A phylogeny is a tree that relates taxonomic units, based on their similarity over a set of characters. The phylogeny problem consists in finding a phylogeny with the minimum number of evolutionary steps. We propose a new neighborhood structure for the phylogeny problem. A greedy randomized adaptive search procedure heuristic based on this neighborhood structure and using variable neighborhood descent for local search is described. Computational results on randomly generated and benchmark instances are reported, showing that the new heuristic is quite robust and outperforms the other algorithms in the literature in terms of solution quality and time‐to‐target value.

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This paper proposes a GRASP (Greedy Randomized Adaptive Search Procedure) algorithm for 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 problem is to find all Pareto optimal or efficient spanning trees (solutions). The algorithm is based on the optimization of different weighted utility functions. In each iteration, a weight vector is defined and a solution is built using a greedy randomized constructive procedure. The found solution is submitted to a local search trying to improve the value of the weighted utility function. We use a drop-and-add neighborhood where the spanning trees are represented by Prufer numbers. In order to find a variety of efficient solutions, we use different weight vectors, which are distributed uniformly on the Pareto frontier.The proposed algorithm is tested on problems with r = 2 and 3 criteria. For non-complete graphs with n = 10, 20 and 30 nodes, the performance of the algorithm is tested against a complete enumeration. For complete graphs with n = 20, 30 and 50 nodes the performance of the algorithm is tested using two types of weighted utility functions. The algorithm is also compared with the multi-criteria version of the Kruskal's algorithm, which generates supported efficient solutions.Keywords GRASP algorithm · Multi-criteria combinatorial optimization · Minimum spanning tree Many practical optimization problems, generally, involve the minimization (or maximization) of several conflicting decision criteria. For example, in the topological network design problem it is desirable to find the best layout of components optimizing performance criteria, such as financial cost, message delay, traffic, link reliability, and so on. These criteria This work was funded by the Municipal Town Hall of Campos dos Goytacazes city. The used computer was acquired with resource of CNPq.