The probability models for combinatorial optimization problems

probabilistic models, EDA algorithms, Bayesian networks

In the last few years there has been a growing interest in the field of Estimation of Distribution Algorithms (EDAs), where crossover and mutation genetic operators are replaced by probability estimation and sampling techniques. The Bayesian Optimization Algorithm incorporates methods for learning Bayesian networks and uses these to model the promising solutions and generate new ones. The aim of this paper is to propose the parallel version of this algorithm, where the optimization time decreases linearly with the number of processors. During the parallel construction of network, the explicit topological ordering of variables is used to keep the model acyclic. The performance of the optimization process seems to be not affected by this constraint and our version of algorithm was successfully tested for the discrete combinatorial problem represented by graph partitioning as well as for deceptive functions.

In the last few years there has been a growing interest in the field of Estimation of Distribution Algorithms (EDAs), where crossover and mutation genetic operators are replaced by probability estimation and sampling techniques. The Bayesian Optimization Algorithm incorporates methods for learning Bayesian networks and uses these to model the promising solutions and generate new ones. The aim of this paper is to propose the parallel version of this algorithm, where the optimization time decreases linearly with the number of processors. During the parallel construction of network, the explicit topological ordering of variables is used to keep the model acyclic. The performance of the optimization process seems to be not affected by this constraint and our version of algorithm was successfully tested for the discrete combinatorial problem represented by graph partitioning as well as for deceptive functions.