This paper presents the first convergence result for random search algorithms to a subset of the Pareto set of given maximum size k with bounds on the approximation quality ǫ. The core of the algorithm is a new selection criterion based on a hypothetical multilevel grid on the objective space. It is shown that, when using this criterion for accepting new search points, the sequence of solution ...

Many real-world problems have a multiobjective character. A-posteriori techniques such as multiobjective evolutionary algorithms (MOEA) generate best compromise solution sets, i.e. Pareto-fronts and Pareto-sets. Classic MOEA are able to find quite efficiently good approximations of the complete Pareto-fronts also for very complex problems. In real-world applications only small sections of the c...

In spite of the recent quick growth of the Evolutionary Multi-objective Optimization (EMO) research field, there has been few trials to adapt the general variation operators to the particular context of the quest for the Pareto-optimal set. The only exceptions are some mating restrictions that take in account the distance between the potential mates – but contradictory conclusions have been rep...

In this paper, a new algorithm is proposed to solve multi-objective optimization problems (MOOPs) through applying the trust-region (TR) method based on local search (LS) techniques; where the MOOP converting to a single objective optimization problem (SOOP) by using reference point method. In the proposed algorithm, some of the points in the search space are generated. For each point the TR al...

in this paper, we first present a new important property for bouligand tangent cone (contingent cone) of a star-shaped set. we then establish optimality conditions for pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.

Given a range of traffic related sustainability problems, policy makers need to know which measures should be taken to reach their objectives as much as possible. Multi-objective optimisation is useful to support these decisions, because it results in an overview of possibly optimal solutions. This Pareto set can be very large, especially if more than two (mainly opposed) objectives are involve...

A multiobjective model-based predictive control approach is presented for solving a dial-a-ride problem. The dynamic objective function considers two dimensions: user and operator costs. As those two components are usually aimed at opposite goals, the problem is formulated and solved through multiobjective model predictive control. When a new call asking for service is received, the method firs...

Multi-objective problems are often solved by modifying them into equivalent single objective problems using pre-defined weights or utility functions. Then, a multi-objective problem is solved similar to a single objective problem returning a single solution. These methods can be problematic because assigning appropriate numerical values (i.e., weights) to an objective function can be challengin...

In this paper, we propose a sufficient condition for a solution to be optimal for a 2-additive Choquet integral in the context of multiobjective combinatorial optimization problems. A 2-additive Choquet optimal solution is a solution that optimizes at least one set of parameters of the 2-additive Choquet integral. We also present a method to generate 2-additive Choquet optimal solutions of mult...

In spite of the recent quick growth of the Evolutionary Multi-objective Optimization (EMO) research field, there has been few trials to adapt the general variation operators to the particular context of the quest for the Pareto-optimal set. The only exceptions are some mating restrictions that take in account the distance between the potential mates – but contradictory conclusions have been rep...