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A factor graph based genetic algorithm

Helmi B. H., Rahmani A. T., Pelikan M.

International Journal of Applied Mathematics and Computer Science

2014

Vol. 24, no. 3

621--633

We propose a new linkage learning genetic algorithm called the Factor Graph based Genetic Algorithm (FGGA). In the FGGA, a factor graph is used to encode the underlying dependencies between variables of the problem. In order to learn the factor graph from a population of potential solutions, a symmetric non-negative matrix factorization is employed to factorize the matrix of pair-wise dependencies. To show the performance of the FGGA, encouraging experimental results on different separable problems are provided as support for the mathematical analysis of the approach. The experiments show that FGGA is capable of learning linkages and solving the optimization problems in polynomial time with a polynomial number of evaluations.

Study Actuality of Immune Optimization Algorithm

Shi W., Yang H., Miao Y., Hu Y.

Przegląd Elektrotechniczny

2013

R. 89, nr 3b

98--100

In this paper, an optimization algorithm base immune principle is expatiated, explain its basic theory and process. And discuss immune algorithm’s advantage than other heuristic algorithms, such as: genetic algorithm and evolution strategy. And introduce several better algorithms base immune algorithm, present application in optimization problems. At last we propose immune algorithm’s further development in optimization problems’ application.

W artykule przedstawiono algorytm optymalizacji oparty na układzie odpornościowym. Opisano podstawy teoretyczne i zasady działania. Dokonano porównania z innymi algorytmami heurystycznymi, jak genetyczny i ewolucyjny. Omówiono także potencjalne zastosowanie algorytmów bazujących na proponowanym rozwiązaniu.

On some optimization problem related to economic equilibrium

Naniewicz Z.

Control and Cybernetics

2002

Vol. 31, no 1

141-165

The paper considers an optimization problem in which the minima of a finite collection of objective functions satisfy some unilateral constraints and are linked together by a certain subdifferential relationship. The governing relations are stated as a variational inequality defined on a nonconvex feasible set. By the reduction to the variational inequality involving nonmonotone multivalued mapping, defined over nonnegative orthant, the existence of solutions is examined. The prototype is the general economic equilibrium problem. The exemplification of the theory for the quadratic multi-objective function is provided.