Optimization strategies gleaned from biological evolution

Abstract

Several problems, in particular the ‘travelling salesman’ problem1 wherein one seeks the shortest route encompassing a randomly distributed group of cities, have been optimized by repeated random alteration (mutation) of a trial solution followed by selection of the cheaper (fitter) solution. Most non-trivial problems have complicated fitness functions, and optimization tends to become stuck in local fitness maxima. A recently introduced strategy to escape (simulated annealing) involves accepting unfavourable mutations with finite probability1–3. Independently, there has been interest in genetic strategies which overcome the problem of fitness maxima in biological evolution4–6, and several authors have applied biological elements to optimization7,8. Here we use computer algorithms to investigate new strategies for the 64-city travelling salesman problem, which combine conventional optimization or ‘quenching’ with biological elements, namely having a population of trial solutions, helping weaker individuals to survive, and an analogue of sexual crossing-over of genes. The new strategies were faster and gave better results than simulated annealing.