In this paper we propose a novel iterative search procedure for multi-objective optimization problems. The iteration process -though derivative free -utilizes the geometry of the directional cones of such optimization problems, and is capable both of moving toward and along the (local) Pareto set depending on the distance of the current iterate toward this set. Next, we give one possible way of integrating this local search procedure into a given EMO algorithm resulting in a novel memetic strategy. Finally, we present some numerical results on some well-known benchmark problems indicating the strength of both the local search strategy as well as the new hybrid approach.

In this work we study the convergence of generic stochastic search algorithms toward the entire set of approximate solutions of continuous multi-objective optimization problems. Since the dimension of the set of interest is typically equal to the dimension of the parameter space, we focus on obtaining a finite and tight approximation, measured by the Hausdorff distance. Under mild assumptions about the process to generate new candidate solutions, the limit approximation set will be determined entirely by the archiving strategy. We propose and investigate a novel archiving strategy theoretically and empirically. For this, we analyze the convergence behavior of the algorithm, yielding bounds on the obtained approximation quality as well as on the cardinality of the resulting approximation, and present some numerical results.

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When measuring distances between different objects such as different sets the use of metrics has been well established in literature. We investigate here two widely used indicators for the evaluation of Multi-objective Evolutionary Algorithms, the Generational Distance (GD) and the Inverted Generational Distance (IGD), with respect to the properties of a metric. Since the outcome is quite poor, we propose further on a new indicator which is made up of GD and IGD. The novel indicator can be viewed as an 'averaged version' of the Hausdorff distance and forms a pseudo-metric under certain assumptions.