Science China Information Sciences

, Volume 58, Issue 11, pp 1–17

# Variable solution structure can be helpful in evolutionary optimization

Research Paper

## Abstract

Evolutionary algorithms are a family of powerful heuristic optimization algorithms where various representations have been used for solutions. Previous empirical studies have shown that for achieving a better efficiency of evolutionary optimization, it is often helpful to adopt rich representations (e.g., trees and graphs) rather than ordinary representations (e.g., binary coding). Such a recognition, however, has little theoretical justifications. In this paper, we present a running time analysis on genetic programming. In contrast to previous theoretical efforts focused on simple synthetic problems, we study two classical combinatorial problems, the maximum matching and the minimum spanning tree problems. Our theoretical analysis shows that evolving tree-structured solutions is much more efficient than evolving binary vector encoded solutions, which is also verified by experiments. The analysis discloses that variable solution structure might be helpful in evolutionary optimization when the solution complexity can be well controlled.

### Keywords

evolutionary algorithms genetic programming maximum matching minimum spanning tree running time computational complexity

# 演化优化中可变解结构的效用分析

## 摘要

### 创新点

1. 1.

对于采用可变结构来表示组合优化的解, 以往认为由于表达更加自然从而可帮助演化算法更好的进行优化, 当仅有实验支持、尚缺乏理论支撑, 本文对使用树形解结构的遗传规划算法进行时间复杂度分析, 在最大匹配和最小生成树问题上的分析结果显示了这种可变解结构的有效性, 为可变解结构的使用提供了理论证据。

2. 2.

对于遗传规划算法的时间复杂度分析, 以往主要在人造简单问题上开展, 本文首次给出在组合优化问题上的分析结果, 增进了对遗传规划算法的理论理解。

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