An Extension of Algebraic Differential Evolution for the Linear Ordering Problem with Cumulative Costs

Abstract

In this paper we propose an extension to the algebraic differential evolution approach for permutation based problems (DEP). Conversely from classical differential evolution, DEP is fully combinatorial and it is extended in two directions: new generating sets based on exchange and insertion moves are considered, and the case \(F>1\) is now allowed for the differential mutation operator. Moreover, also the crossover and selection operators of the original DEP have been modified in order to address the linear ordering problem with cumulative costs (LOPCC). The new DEP schemes are compared with the state-of-the-art LOPCC algorithms using a widely adopted benchmark suite. The experimental results show that DEP reaches competitive performances and, most remarkably, found 21 new best known solutions on the 50 largest LOPCC instances.