Designing linear binary block codes: Constructive heuristics and iterated local search

Abstract

Error correcting codes such as linear binary block codes (LBBCs) play an important role, for example, in the transmission of messages over telecommunication networks, or in reading information from digital data media such as DVDs or CDs. The design of LBBCs can be stated as an $NP$-hard combinatorial optimization problem. Due to its hardness several metaheuristic approaches have been proposed in the literature for its solution. In this paper we present different algorithms based on solution construction and on iterated local search. The experimental evaluation shows that a simple multi-start constructive heuristic is often between 2 and 3 orders of magnitude faster than the current state-of-the-art metaheuristics when applied to rather small problem instances. When bigger problem instances are concerned, the proposed iterated local search algorithm has advantages over both the multi-start constructive heuristic and state-of-the-art metaheuristics.