Substitution of phosphine ligands in nickel(II) halide complexes by now attractive N-heterocyclic carbene (NHC) ligands is one of the well-known organometallic reactions. New, simple, and easy-to-prepare nickel(II) halides bearing both a phosphine and an NHC ligand, [NiX2(PPh3)(NHC)], were synthesized by the reaction of [NiX2(PPh3)2] (X = Cl and Br) with 1 equiv of a bulky NHC ligand. Rather small NHC ligands did not form NHC/PR3 mixed complexes. Controlling the amount of the NHC ligand and purification led to successful isolation in good to moderate yields and structural determination of these carbene complexes. Studies on catalytic Grignard cross-coupling reactions using three complexes, the NHC/PPh3 mixed complex, a “bis”-carbene complex, and [NiCl2(PPh3)2], revealed that the monocarbene complex catalyzes reactions with the highest activity, but, in comparison, catalysis does not proceed well using the latter two complexes.

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Abstract. This paper proposes a new mating scheme for evolutionary multiobjective optimization (EMO), which simultaneously improves the convergence speed to the Pareto-front and the diversity of solutions. The proposed mating scheme is a two-stage selection mechanism. In the first stage, standard fitness-based selection is iterated for selecting a pre-specified number of candidate solutions from the current population. In the second stage, similarity-based tournament selection is used for choosing a pair of parents among the candidate solutions selected in the first stage. For maintaining the diversity of solutions, selection probabilities of parents are biased toward extreme solutions that are different from prototypical (i.e., average) solutions. At the same time, our mating scheme uses a mechanism where similar parents are more likely to be chosen for improving the convergence speed to the Paretofront. Through computational experiments on multi-objective knapsack problems, it is shown that the performance of recently proposed well-known EMO algorithms (SPEA and NSGA-II) can be improved by our mating scheme.

Abstract. The aim of this paper is to clearly demonstrate the potential ability of a similarity-based mating scheme to dynamically control the balance between the diversity of solutions and the convergence to the Pareto front in evolutionary multiobjective optimization. The similarity-based mating scheme chooses two parents in the following manner. For choosing one parent (say Parent A), first a pre-specified number of candidates (say α candidates) are selected by iterating the standard fitness-based binary tournament selection. Then the average solution of those candidates is calculated in the objective space. The most similar or dissimilar candidate to the average solution is chosen as Parent A. When we want to increase the diversity of solutions, the selection probability of Parent A is biased toward extreme solutions by choosing the most dissimilar candidate. The strength of this diversity-preserving effort is adjusted by the parameter α . We can also bias the selection probability toward center solutions by choosing the most similar candidate when we want to decrease the diversity. The selection probability of the other parent (i.e., the mate of Parent A) is biased toward similar solutions to Parent A for increasing the convergence speed to the Pareto front. This is implemented by choosing the most similar one to Parent A among a pre-specified number of candidates (say β candidates).The strength of this convergence speed-up effort is adjusted by the parameter β . When we want to increase the diversity of solutions, the most dissimilar candidate to Parent A is chosen as its mate. Our idea is to dynamically control the diversity-convergence balance by changing the values of two control parameters α and β during the execution of evolutionary multiobjective optimization algorithms. We examine the effectiveness of our idea through computational experiments on multiobjective knapsack problems.

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