Mishra, SK (2006): Performance of the Barter, the Differential Evolution and the Simulated Annealing Methods of Global Optimization on Some New and Some Old Test Functions.

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Abstract
In this paper we compare the performance of the Barter method, a newly introduced populationbased (stochastic) heuristic to search the global optimum of a (continuous) multimodal function, with that of two other wellestablished and very powerful methods, namely, the Simulated Annealing (SA) and the Differential Evolution (DE) methods of global optimization.
In all, 87 benchmark functions have been optimized 89 times. The DE succeeds in 82 cases, the Barter succeeds in 63 cases, while the Simulated Annealing method succeeds for a modest number of 51 cases. The DE as well as Barter methods are unstable for stochastic functions (YaoLiu#7 and FletcherPowell functions). In particular, Bukin6, Perm2 and Mishra2 functions have been hard for all the three methods.
Seen as such, the barter method is much inferior to the DE, but it performs better than SA. A comparison of the Barter method with the Repulsive Particle Swarm method has indicated elsewhere that they are more or less comparable.
The convergence rate of the Barter method is slower than the DE as well as the SA. This is because of the difficulty of ‘double coincidence’ in bartering. Barter activity takes place successfully in less than one percent trials.
It may be noted that the DE and the SA have a longer history behind them and they have been improved many times. In the present exercise, the DE version used here employs the latest (available) schemes of crossover, mutation and recombination. In comparison to this, the Barter method is a nascent one. We need a thorough investigation into the nature and performance of the Barter method. We have found that when the DE optimizes, the terminal population is homogenous while in case of the Barter method it is not so. This property of the Barter method has several implications with respect to the AgentBased Computational Economics
Item Type:  MPRA Paper 

Original Title:  Performance of the Barter, the Differential Evolution and the Simulated Annealing Methods of Global Optimization on Some New and Some Old Test Functions 
Language:  English 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61  Optimization Techniques; Programming Models; Dynamic Analysis C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63  Computational Techniques; Simulation Modeling 
Item ID:  639 
Depositing User:  Sudhanshu Kumar Mishra 
Date Deposited:  01. Nov 2006 
Last Modified:  13. Feb 2013 09:39 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/639 