On the Difficulty of Evolving Permutation Codes

TL;DR

This paper explores the challenge of designing permutation codes using evolutionary algorithms, comparing their effectiveness to random search, and highlighting scalability issues in larger problem instances.

Contribution

It introduces an iterative EA-based method for constructing permutation codes with minimum distance constraints, analyzing different fitness functions and policies.

Findings

EA approach outperforms random search in some scenarios

Both methods face scalability issues with larger problems

Different fitness functions impact code quality and growth policies

Abstract

Combinatorial designs provide an interesting source of optimization problems. Among them, permutation codes are particularly interesting given their applications in powerline communications, flash memories, and block ciphers. This paper addresses the design of permutation codes by evolutionary algorithms (EA) by developing an iterative approach. Starting from a single random permutation, new permutations satisfying the minimum distance constraint are incrementally added to the code by using a permutation-based EA. We investigate our approach against four different fitness functions targeting the minimum distance requirement at different levels of detail and with two different policies concerning code expansion and pruning. We compare the results achieved by our EA approach to those of a simple random search, remarking that neither method scales well with the problem size.