Evolutionary Algorithms and Dynamic Programming

TL;DR

This paper explores how evolutionary algorithms can be designed to incorporate dynamic programming techniques, enabling efficient approximation schemes for a broad class of combinatorial optimization problems.

Contribution

It provides a general framework linking evolutionary algorithms with dynamic programming and demonstrates the existence of efficient approximation schemes for DP-benevolent problems.

Findings

Evolutionary algorithms can be constructed to perform dynamic programming steps.

Such algorithms can achieve fully polynomial-time randomized approximation schemes.

Applicable to a wide class of problems with known FPTAS.

Abstract

Recently, it has been proven that evolutionary algorithms produce good results for a wide range of combinatorial optimization problems. Some of the considered problems are tackled by evolutionary algorithms that use a representation which enables them to construct solutions in a dynamic programming fashion. We take a general approach and relate the construction of such algorithms to the development of algorithms using dynamic programming techniques. Thereby, we give general guidelines on how to develop evolutionary algorithms that have the additional ability of carrying out dynamic programming steps. Finally, we show that for a wide class of the so-called DP-benevolent problems (which are known to admit FPTAS) there exists a fully polynomial-time randomized approximation scheme based on an evolutionary algorithm.