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2 Stańczak J.

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Optimal control of multistage deterministic, stochastic and fuzzy processes in the fuzzy environment via an evolutionary algorithm

Stańczak J.

Control and Cybernetics

2005

Vol. 34, no 2

525-552

This paper deals with the problem of control of deterministic, stochastic and fuzzy systems with a fixed termination time and fuzzy constraints imposed on controls and states. Constrains imposed on the system are given as membership functions of particular fuzzy sets. Transition functions for controlled systems are given as a matrix of transitions between states for a deterministic object, a matrix of probabilities of transitions for a stochastic object and a matrix of membership functions of transitions for a fuzzy system. An optimal (or sub-optimal) control is obtained using a specialized evolutionary algorithm (EA), which is a development over the previously used methods based on simple genetic algorithm. The specialized EA seems to be a very effective tool for solving such a class of optimization problems, comparing advantageously with the traditional simple genetic algorithm approach and with the previously used solutions like dynamic programming or branch and bound. The specialization of the applied EA is obtained using dedicated problem encoding, the method of ranking of genetic operators and the controlled selection of population members.

Biologically inspired methods for control of evolutionary algorithms

Stańczak J.

Control and Cybernetics

2003

Vol. 32, no 2

411-433

In this paper two methods for evolutionary algorithm control are proposed. The first one is a new method of tuning tlie probabilities of genetic operators. It is assumed in the presented approach that every member of the optimized population conducts his own ranking of genetic operators' qualities. This ranking enables computing the probabilities of execution of genetic operators. This set of probabilities is a basis of experience of every individual and according to this basis the individual chooses the operator in every iteration of the algorithm. Due to this experience one can maximize the chances of his offspring to survive. The second part of the paper deals with a self-adapting method of selection of individuals to a subsequent generation. Methods of selection applied in the evolutionary algorithms are usually inspired by nature and prefer solutions where the main role is played by randomness, competition and struggle among individuals. In the case of evolutionary algorithms, where populations of individuals are usually small, this causes a premature convergence to local minima. In order to avoid this drawback I propose to apply an approach based rather on an agricultural technique. Two new methods of object selection are proposed: a histogram selection and a mixed selection. The methods described were tested using examples based on scheduling and TSP.