摘要

思维进化计算是模拟人类思维过程提出的一种很有潜力的新型演化算法。思维进化计算已成功应用于求解数值优化问题，对TSP、常微分方程组建模和Job-shop调度问题等非数值优化问题也做了一定的研究，但目前思维进化计算尚未有关于非数值优化问题的通用算法框架。

本文针对解空间为有限空间的非数值优化问题，提出了求解这些问题的思维进化计算通用算法框架。首先针对这些非数值优化问题的特点，抽象出它们的通用编码。然后引入特征、信息矩阵的概念，提出了通用信息抽取和个体学习策略，从而实现了思维进化的趋同和异化操作，给出了通用的思维进化计算框架，并运用组合原理和马尔可夫链理论证明了该算法框架的全局收敛性。最后通过应用该算法框架求解顶点着色问题、Job-shop调度问题验证了该算法框架的可行性、有效性。该算法框架具有较强的通用性，适合于TSP、顶点着色问题、Job-shop调度问题、神经网络结构优化问题、系统建模等一大类非数值优化问题。实际应用中将具体非数值优化问题合理转化，设计编码与解码策略，定义该问题的特征和信息矩阵等概念，就可以直接应用该框架。本文研究为求解复杂的非数值优化问题提供了一种新的有效途径。

关键词：非数值优化问题，思维进化计算，趋同，异化，信息矩阵

ABSTRACT

Mind Evolutionary Computation(MEC) was proposed by simulating the processes of human mind. It is a new potential evolutionary algorithm. MEC has been applied to numerical optimization problems, and some non-numerical optimization problems, for example traveling salesman problem, job-shop scheduling, and Modeling for Systems of Ordinary Differential Equations, are solved successfully with MEC. But the all-purpose algorithm of MEC for non-numerical problems doesn’t exist.

In this paper, MEC algorithm is introduced for a kind of non-numeric optimization problems which solution space is limit. First an all-purpose coding method is induced according to the common characteristics of those problems. Then a series of concepts ,for example character ,information matrix，etc，are introduced. So an all-purpose similartaxis and dissimilation operations of MEC for those problems are designed. Consequently MEC algorithm for a kind of non-numeric optimization problems is introduced and its global convergence is proved with combinatorial theory and Markov chain. We solve vertex coloring problem and job-shop scheduling with this algorithm. Our experiments show that this algorithm is feasible and effective. This algorithm is all-purpose and it is fitted for traveling salesman problem, job-shop scheduling, vertex coloring problem, the optimization of the artificial neural network architecture and Modeling for Systems, etc. When we solve a non-numerical problem with this algorithm, if this problem is converted reasonably and the character and information matrix of this problem are defined, then this algorithm can work. The MEC algorithm offers a new all-purpose and effective method for a kind of non-numerical problems.

Keywords：non-numerical problem，Mind Evolutionary Computation，similartaxis，dissimilation，information matrix

thanks for your help!