BioSystems 38 (1996) 29-43 Hybrid evolutionary programming problems for heavily constrained Hyun Myung, Jong-Hwan Kim* Department of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST) 373-l Kusung-dong. Yusung-gu, Taejon-shi 305-701, Republic of Korea Received 18 January 1995; revision received 25 April 1995; accepted 21 July 1995 Abstract A hybrid of evolutionary programming (EP) and a deterministic optimization procedure is applied to a series of non- linear and quadratic optimization problems. The hybrid scheme is compared with other existing schemes such as EP alone, two-phase (TP) optimization, and EP with a non-stationary Penalty function (NS-EP). The results indicate that the hybrid method can outperform the other methods when addressing heavily constrained optimization problems in terms of computational efficiency and solution accuracy. Keywordr: Hybrid evolutionary programming; Deterministic optimization; Computational efficiency; Solution accuracy 1. Introduction Evolutionary programming (EP) is a general, robust optimization technique. The method has been proven to possess global asymptotic con- vergence properties (Fogel, 1995, Ch.4), and re- sults from work in evolution strategies suggest that EP produces geometric rates of convergence on strongly-convex functions (B&k et al., 1993; Fogel, 1995, Ch.4). Empirical evidence suggests its utility on a broad range of discrete and continuous function optimization problems (Fogel, 1988, 1995; Angeline et al., 1994; Sebald and Schlenzig, ?? Corresponding author, E-mail: johkim@vivaldi.kaist. ac.kr 1994; and many others). But EP, more than any evolutionary optimization algorithm, is likely to not be the best optimization procedure for any specific function in terms of efficiency, con- vergence rate, etc.; its robustness comes at the sac- ritice of domain specificity. For example, if the function to be minimized is a quadratic bowl, then Newton-Gauss optimization will generate the minimum point in one iteration from any starting location. In turn, Newton-Gauss will generally fail to find the minima of multimodal surfaces because it relies heavily on gradient and higher-order statistics of the function to be minimized. In- tuitively, a two-stage procedure of first using evo- lutionary optimization to overcome multiple min- ima, followed by more traditional optimization 0303-2647/96/$15.00 0 1996 Elsevier Science Ireland Ltd. All rights reserved SSDI 0303-2647(95)01564-2