The conical area evolutionary algorithm (CAEA) has a very high run-time efficiency for bi-objective optimization, but it can not tackle problems with more than two objectives. In this letter, a conical hypervolume evolutionary algorithm (CHEA) is proposed to extend the CAEA to a higher dimensional objective space. CHEA partitions objective spaces into a series of conical subregions and retains only one elitist individual for every subregion within a compact elitist archive. Additionally, each offspring needs to be compared only with the elitist individual in the same subregion in terms of the local hypervolume scalar indicator. Experimental results on 5-objective test problems have revealed that CHEA can obtain the satisfactory overall performance on both run-time efficiency and solution quality.

A partitioning parallelization of the multi-objective evolutionary algorithm based on decomposition, pMOEA/D, is proposed in this letter to achieve significant time reductions for expensive bi-objective optimization problems (BOPs) on message-passing clusters. Each sub-population of pMOEA/D resides on a separate processor in a cluster and consists of a non-overlapping partition and some extra overlapping individuals for updating neighbors. Additionally, sub-populations cooperate across separate processors by the hybrid migration of elitist individuals and utopian points. Experimental results on two benchmark BOPs and the wireless sensor network layout problem indicate that pMOEA/D achieves satisfactory performance in terms of speedup and quality of solutions on message-passing clusters.

A conical area evolutionary algorithm (CAEA) is presented to further improve computational efficiencies of evolutionary algorithms for bi-objective optimization. CAEA partitions the objective space into a number of conical subregions and then solves a scalar subproblem in each subregion that uses a conical area indicator as its scalar objective. The local Pareto optimality of the solution with the minimal conical area in each subregion is proved. Experimental results on bi-objective problems have shown that CAEA offers a significantly higher computational efficiency than the multi-objective evolutionary algorithm based on decomposition (MOEA/D) while CAEA competes well with MOEA/D in terms of solution quality.