Abstract. This paper considers the use of randomly generated directed graphs as neighborhoods for particle swarm optimizers (PSO) using fully informed particles (FIPS), together with dynamic changes to the graph during an algorithm run as a diversity-preserving measure. Different graph sizes, constructed with a uniform out-degree were studied with regard to their effect on the performance of the PSO on optimization problems. Comparisons were made with a static random method, as well as with several canonical PSO and FIPS methods. The results indicate that under appropriate parameter settings, the use of random directed graphs with a probabilistic disruptive re-structuring of the graph produces the best results on the test functions considered.

A key feature of Particle Swarm Optimization algorithms is that fitness information is shared with individuals in a particle's neighborhood. The kind of neighborhood structure that is used affects the rate at which information is disseminated throughout the population. Existing work has studied global and simple local topologies, as well as more complex, but fixed neighborhood structures. This paper looks at randomly generated, directed graph structures in which information flows in one direction only, and also outgoing edges randomly migrate from one source node to another. Experimental evidence indicates that this random dynamic topology, when used with an inertia weight PSO, performs competitively with some existing methods and outperforms others.

Abstract-This paper aims at the rectangle-free coloring of grids using four colors. It has been proven in a well developed theory that there is an upper bound of rectangle-free 4-colorable grids as well as a lower bound of grids for which no rectangle-free color pattern of four colors exist. Between these tight bounds the grids of the size 17 × 17, 17 × 18, 18 × 17, and 18×18 are located for which it is not known until now whether a rectangle-free coloring by four colors exists. We present in this paper an approach that solves all these open problems.From another point of view this paper aims at the solution of a multiple-valued problem having an extremely high complexity. There are 1.16798 * 10 195 different grids of four colors. It must be detected whether at least one of this hardly imaginable large number of patterns satisfies strong additional conditions. In order to solve this highly complex problem, several approaches were taken into account to find out properties of the problem which finally allowed us to calculate the solution.

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