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.
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Notes
- 1.
The inverting step is not considered in Sect. 3.1 because the exchange generators are self-invertible.
- 2.
For the sake of space, its description is not reported here.
- 3.
Additionally, a run terminates also if its CPU time exceeds one hour. However, this criterion has been sporadically met only on the RND150 instances.
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Baioletti, M., Milani, A., Santucci, V. (2016). An Extension of Algebraic Differential Evolution for the Linear Ordering Problem with Cumulative Costs. In: Handl, J., Hart, E., Lewis, P., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds) Parallel Problem Solving from Nature – PPSN XIV. PPSN 2016. Lecture Notes in Computer Science(), vol 9921. Springer, Cham. https://doi.org/10.1007/978-3-319-45823-6_12
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