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Multi-modal optimization is an active research topic that has attracted increasing attention from evolutionary computation community. Particle swarm optimization (PSO) with niching technique is one of the most effective approaches for multi-modal optimization. However, in existing PSO with niching methods, the number of particles around different niches varies distinctly from each other, which makes it difficult for the algorithm to find high-quality solutions in all niches. To address this issue, this paper proposes a new niching PSO with equilibrium factor named E-SPSO. Different from the existing niching PSOs, the numbers of particles in different niches have been kept in balance in E-SPSO. The velocity of each particle is influenced by not only the personal best particle and the global best particle, but also an equilibrium factor (EF). By using the equilibrium factor to update the velocities of particles, the particles can be allocated uniformly among the niches. In this way, the computation resources can be assigned to the niches in a more balanced manner, so that the algorithm can gain more population diversity and find high-quality solutions in all niches. Experimental results on eleven benchmark problems show that the proposed mechanism not only increases the number of optima found, but also improves the search efficiency. [ABSTRACT FROM AUTHOR]

In this paper we propose and solve common influence region problems. These problems are related to the simultaneous influence, or the capacity to attract customers, of two sets of facilities of different types. For instance, while a facility of the first type competes with the other facilities of the first type, it cooperates with several facilities of the second type. The problems studied can be applied, for example, to decision-making support systems for marketing and/or locating facilities. We present parallel algorithms, to be run on a Graphics Processing Unit, for approximately solving the problems considered here. We also provide experimental results and discuss the efficiency and scalability of our approach. Finally, we present the speedup ratios obtained when the running times of the parallel proposed algorithms using a GPU are compared with those obtained from their respective efficient sequential CPU versions. [ABSTRACT FROM AUTHOR]