Some new test functions for global optimization and performance of repulsive particle swarm method

Mishra, Sudhanshu (2006): Some new test functions for global optimization and performance of repulsive particle swarm method.

Abstract

In this paper we introduce some new test functions to assess the performance of global optimization methods. These functions have been selected partly because several of them are aesthetically appealing and partly because a few of them are really difficult to optimize, while all the functions are multi-modal. Each function has been graphically presented to appreciate its geometrical appearance. To optimize these functions we have used the Repulsive Particle Swarm (RPS) method. We have also appended a computer program of the RPS method. Except two functions, namely the 'crowned cross' and the 'cross-legged table' functions all other new test functions are optimized by the RPS program.The program has also been tested with success on a number of well-established benchmark functions. However, the program fails miserably in optimizing the Bukin and a couple of other functions.

Note: Readers should beware of the plagiarism by one Mr. Sanjeev K Singh, Tezpur University, Assam, who, in his article "A Comparative Study of Genetic Algorithm, Improved-Repulsive Particle Swarm Optimization and Simulated Annealing" published in the proceedings of Advances in Computational Optimization and Analysis of Systems (COSA 2007), 6-9 February, 2007 Outreach Centre, IIT, Kanpur, attributes introduction of some new functions (Bird function, Penholder function, Cross function, etc) and the improved Particle Swarm method to himself.

• Item Type: MPRA Paper
• Institution: North-Eastern Hill University, Shillong (India)
• Language: English
• Keywords: Repulsive particle swarm method; Global optimization; New test functions; Bird function; Pen-holder function; Crowned cross function; Cross-legged table function; Cross function; Cross in tray function; Carrom table function; Holder table function; Test-tube holder function
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C88 - Other Computer Software; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis

References

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