Multiobjective Optimization by Nessy Algorithm

This paper presents the extension of the Neural Evolutional Strategy System (Nessy) to the multiobjective optimization case. The neural architecture of the Nessy algorithm is extended by using more than one output neuron, one neuron for each objective. The learning law of Nessy is modified according to the presence of multiple measures of performance. Each hidden neuron of the generation layer randomly selects an objective for one cycle of the network. From this, the multiobjective ranking of the population (or neurons of the solutions layer) is stochastically approximated. The modified Nessy algorithm (Monessy) is able to search for the Pareto set of a multiobjective optimization problem. A test function from literature with well-known Pareto and trade-off set is examined. The newly proposed algorithm effectively searches for the Pareto set by switching between explorational and exploitational search phases. This was compared with random search, which did not hit the Pareto set as nearly as often as the Monessy algorithm. Also, the replacement of a weighted-sum matching measure with multiple matching measures in a framework for texture filter design is considered as a second example.