Performance of the Barter, the Differential Evolution and the Simulated Annealing Methods of Global Optimization on Some New and Some Old Test Functions

Abstract

In this paper we compare the performance of the Barter method, a newly introduced population-based (stochastic) heuristic to search the global optimum of a (continuous) multi-modal function, with that of two other well-established 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 (Yao-Liu and Fletcher-Powell functions). In particular, Bukin-6, Perm-2 and Mishra-2 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 Agent-Based Computational Economics

Keywords: Global optimization, Simulated Annealing, Differential Evolution, Barter, Pareto optimality, competitive process, Particle Swarm, Agent-Based Computational Economics, Experimental Economics, non-convex functions, Fortran, computer program, benchmark, test functions

JEL Classification: C15, C63