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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]

Abstract: In this paper we study a problem that arises in the competitive facility location field. Facilities and customers are represented by points of a planar Euclidean domain. We associate a weighted distance to each facility to reflect that customers select facilities depending on distance and importance. We define, by considering weighted distances, the k-influence region of a facility as the set of points of the domain that has the given facility among their k-nearest/farthest neighbors. On the other hand, we partition the domain into subregions so that each subregion has a non-negative weight associated to it which measures a characteristic related to the area of the subregion. Given a weighted partition of the domain, the k-influence region problem finds the points of the domain where are new facility should be opened. This is done considering the known weight associated to the new facility and ensuring a minimum weighted area of its k-influence region. We present a GPU parallel approach, designed under CUDA architecture, for approximately solving the k-influence region problem. In addition, we describe how to visualize the solutions, which improves the understanding of the problem and reveals complicated structures that would be hard to capture otherwise. Integration of computation and visualization facilitates decision makers with an iterative what-if analysis process, to acquire more information to obtain an approximate optimal location. Finally, we provide and discuss experimental results showing the efficiency and scalability of our approach. [Copyright &y& Elsevier]