Sequencing Cutting Patterns and VLSI Gates by Population Training Algorithms Alexandre C. M. Oliveira • Luiz A. N. Lorena • Departamento de Inform´ atica, Universidade Federal do Maranh˜ ao, Av. Portugueses s/n, Campus do Bacanga, S˜ao Lu ´ is, Maranh˜ ao 65085-580, Brasil Laborat´ orio Associado de Computa¸ c˜ ao Aplicada, Instituto Nacional de Pesquisas Espaciais, Av Astronautas 1758, Jardim da Granja, S˜ao Jos´ e dos Campos, S˜ao Paulo 12227-010, Brasil acmo@deinf.ufma.br • lorena@lac.inpe.br • This paper describes a new way to employ problem-specific heuristics to improve evolutionary algorithms: the Population Training Algorithm (PTA). The PTA keeps stored the individual and its best neighbor in the population for a number of generations inversely proportional to the difference between their evaluation. The population is then ranked by a coefficient that contemplates the double evaluation of individuals, in order that, the best individuals by this rank have greater probability to be selected for recombination and mutation operations. Applications are examined for two sequencing problems: the gate matrix layout and the minimization of open stacks. A 2-Opt-like heuristic and other based upon Faggioli and Bentivoglio’s greedy procedure are employed as training heuristics and their performance are compared, using instances taken from the literature. (Hybrid evolutionary algorithms; Population training; MOSP; GMLP) 1. Introduction Evolutionary algorithms are efficient to explore a wide search space, converging quickly to local minima. However, their lack of exploiting local information is a well-known drawback to reach a global minima. Heuristics and local search procedures has been encapsulated by evolutionary operators to incorporate knowledge about problems’ particularities, driving the evolutionary process to build a population with some desired feature, gaining speed and accuracy. The local search procedures are, in general, applied to only individuals considered elite, avoiding unnecessary objective function calls. For the same reason, problem-specific 1