A Differential Evolution Algorithm to Semivectorial Bilevel Problems
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Semivectorial bilevel problems (SVBLP) deal with the optimization of a single function at the upper level and multiple objective functions at the lower level of hierarchical decisions. Therefore, a set of nondominated solutions to the lower level decision maker (the follower) exists and should be exploited for each setting of decision variables controlled by the upper level decision maker (the leader). This paper presents a new algorithmic approach based on differential evolution to compute a set of four extreme solutions to the SVBLP. These solutions capture not just the optimistic vs. pessimistic leader’s attitude but also possible follower’s reactions more or less favorable to the leader within the lower level nondominated solution set. The differential evolution approach is compared with a particle swarm optimization algorithm. In this experimental comparison we draw attention to pitfalls associated with the interpretation of results and assessment of the performance of algorithms in SVBLP.
KeywordsSemivectorial bilevel problems Differential evolution Particle swarm optimization Optimistic/pessimistic frontiers Optimistic/deceiving solutions Pessimistic/rewarding solutions
This work was supported by projects UID/MULTI/00308/2013 and SAICTPAC/0004/2015-POCI-01-0145-FEDER-016434.
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