退火基因演算法的收斂分析

Abstract

The Annealing-Genetic(AG) algorithm is a powerful optimization problem. The AG approach was proposed by author two years ago. This approach incorporates genetic algorithms into simulated annealing for improving both the performance of simulated annealing and genetic algorithms. The AG approach has the following features :(1)it can be viewed as a simulated annealing algorithm with the population-based state transition and with the genetic-operator-based quasi-equilibrium control,(2)it can be viewed as a genetic algorithm with the Boltzmann-type selection operator. Empirically, the error rate of the AG algorithm for solving the multiconstraint zero-one knapsack problem is less than 1% for solving the set partitioning problem is less than 0.1% and for solving both the traveling salesman as well as bin-packing problems are around 3%. In all the test cases, the AG approach obtains much better performance than either simulated annealing or genetic algorithm does, In this paper, we present the schemata theory for discussing the efficiency of the AG algorithm.We not only show the global convergence of the AG algorithm but also include the analysis of the convergence behavior and the running time complexity of the algorithm.