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Performance Analysis of Evolutionary Algorithms for Steiner Tree Problems.

Xinsheng Lai¹, Yuren Zhou², Xiaoyun Xia³

¹School of Mathematics and Computer Science, Shangrao Normal University, Shangrao, 334001, China; School of Computer Science and Engineering, South China University of Technology, Guangzhou, 510006, China xsl2011_jx@163.com.

Evolutionary Computation

|December 14, 2016

Summary

This summary is machine-generated.

This study analyzes the (1+1) evolutionary algorithm (EA) for the Steiner tree problem (STP). The (1+1) EA achieves a 3/2-approximation ratio for STP in quasi-bipartite graphs, offering theoretical insights into EA performance.

Keywords:

Steiner tree approximation ratio computational complexity evolutionary algorithms multi-objective

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Area of Science:

Graph theory
Combinatorial optimization
Computer science

Background:

The Steiner tree problem (STP) is an NP-hard optimization problem seeking a minimum weight tree connecting a set of special nodes, potentially using additional Steiner nodes.
While heuristics exist for STP, theoretical analysis of evolutionary algorithms (EAs) for this problem is lacking.
Previous empirical studies suggest EAs are effective for STP.

Purpose of the Study:

To provide the first theoretical analysis of an evolutionary algorithm's performance on the Steiner tree problem.
To investigate the approximation ratio and runtime of the (1+1) EA for STP in a specific graph class.
To compare the (1+1) EA with other heuristics on benchmark instances.

Main Methods:

Theoretical analysis of the (1+1) EA's performance on the Steiner tree problem.
Derivation of an approximation ratio for STP in quasi-bipartite graphs.
Empirical comparison of the (1+1) EA against two other heuristics on two graph instances.

Main Results:

The (1+1) EA achieves a 3/2-approximation ratio for STP in quasi-bipartite graphs with an expected runtime of O(n^2 log n).
The (1+1) EA outperformed two other heuristics on two Steiner tree problem in graphs (GSTP) instances.
A constructed GSTP instance demonstrated potential inefficiency for the (1+1) EA.

Conclusions:

The (1+1) EA offers a theoretically grounded 3/2-approximation for STP in quasi-bipartite graphs.
This work bridges the gap between empirical observations and theoretical understanding of EAs for STP.
Further research is needed to explore EA performance on broader classes of GSTP instances.