Abstract
In real world situations, decision makers prefer to have multiple optimal solutions before making a final decision. Aiming to help the decision makers even if they are non-experts in optimization algorithms, this study proposes a new and simple multimodal optimization (MMO) algorithm called the gravitational particle swarm algorithm (GPSA). Our GPSA is developed based on the concept of “particle clustering in the absence of clustering procedures”. Specifically, it simply replaces the global feedback term in classical particle swarm optimization (PSO) with an inverse-square gravitational force term between the particles. The gravitational force mutually attracts and repels the particles, enabling them to autonomously and dynamically generate sub-swarms in the absence of algorithmic clustering procedures. Most of the sub-swarms gather at the nearby global optima, but a small number of particles reach the distant optima. The niching behavior of our GPSA was tested first on simple MMO problems, and then on twenty MMO benchmark functions. The performance indices (peak ratio and success rate) of our GPSA were compared with those of existing niching PSOs (ring-topology PSO and fitness Euclidean-distance ratio PSO). The basic performance of our GPSA was comparable to that of the existing methods. Furthermore, an improved GPSA with a dynamic parameter delivered significantly superior results to the existing methods on at least 60% of the tested benchmark functions.
Highlights
Multimodal optimization (MMO) algorithms [1] can locate multiple global optima in a single run, which is essential for solving many scientific and engineering optimization problems, e.g., Toyota paradox [2], motor design [3], clustering validity functions [4], network modeling [5], truss-structure design [6], overlay network [7], multi-robot cooperation [8], wireless sensor network [9], object detection [10], and honeycomb core design [11]
After minor improvements, our gravitational particle swarm algorithm (GPSA) significantly outperforms ring-topology PSO (RPSO)
Increasing the pfififfii c2 increases the distance between the particles generating the repulsive flip (dðtÞ 1⁄4 3 c2À þ in (14)), elevating the frequency of repulsive flips and reducing that of the attractive motions. These results clearly demonstrate that the balance between the exploitation and exploration performance of our GPSA can be controlled by c2; a large c2 is suitable for a global searching over a large domain, whereas a small c2 favors local searching over a small domain
Summary
Multimodal optimization (MMO) algorithms [1] ( known as niching methods or techniques) can locate multiple global optima in a single run, which is essential for solving many scientific and engineering optimization problems, e.g., Toyota paradox [2], motor design [3], clustering validity functions [4], network modeling [5], truss-structure design [6], overlay network [7], multi-robot cooperation [8], wireless sensor network [9], object detection [10], and honeycomb core design [11]. The present paper proposes a new, simple, and purely dynamical one-stage method called the gravitational particle swarm algorithm (GPSA) This method replaces the linear feedback term involving the global best in the classical PSO framework with the inverse-square gravitational force between the particles. As our GPSA automatically and dynamically generates the above-mentioned swarm behavior without any clustering algorithms, restart scheme, and taboo archive, it is tractable even for non-experts It requires fewer computational resources and fewer tuning parameters than existing MMO algorithms [22,23,24, 26, 31, 32].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
