We apply a multi-color extension of the Beck-Fiala theorem to show that the multiobjective maximum traveling salesman problem is randomized 1/2-approximable on directed graphs and randomized 2/3-approximable on undirected graphs. Using the same technique we show that the multiobjective maximum satisfiabilty problem is 1/2-approximable. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorith...

In this paper, we extend the notions of ( , ρ)-invexity and generalized ( , ρ)invexity to the continuous case and we use these concepts to establish sufficient optimality conditions for the considered class of nonconvexmultiobjective variational control problems. Further, multiobjective variational control mixed dual problem is given for the considered multiobjective variational control problem...

We apply a multi-color extension of the Beck-Fiala theorem to show that the multiobjective maximum traveling salesman problem is randomized 1/2-approximable on directed graphs and randomized 2/3-approximable on undirected graphs. Using the same technique we show that the multiobjective maximum satisfiablilty problem is 1/2-approximable.

The H2/H∞ control problem is well known in the control community. It mixes the results of two powerful control techniques; to balance two objectives: minimizing the H2 norm of the system, while constraining the system’s H∞ norm. In the presence of random noise, this is akin to solving a Nash game with the players’ objectives to minimize the mean of their costs. In this chapter, recent trends in...

The Capacitated Arc Routing Problem (CARP) is a very hard vehicle routing problem raised for instance by urban waste collection. In addition to the total route length (the only criterion minimized in the academic problem), waste management companies seek to minimize also the length of the longest trip. A bi-objective genetic algorithm is presented for this more realistic CARP, never studied bef...

The game-theoretic formulation of the multiobjective multicommodity flow problem is considered. The dynamic version of this problem is studied and an algorithm for its solving, based on the concept of multiobjective games, is proposed. Mathematics Subject Classification 2000: 90B10, 90C35, 90C27, 90C47.

In this work, we deal with obtaining efficient solutions for stochastic multiobjective programming problems. In general, these solutions are obtained in two stages: in one of them, the stochastic problem is transformed into its equivalent deterministic problem, and in the other one, some of the existing generating techniques in multiobjective programming are applied to obtain efficient solution...

The importance of tuning a search algorithm for the specific features of the target search space has been known for quite some time. However, when dealing with multiobjective problems, there are several twists on the conventional notions of fitness landscapes. Multiobjective optimization problems provide additional difficulties for those seeking to study the properties of the search space. Howe...

We present a multiobjective genetic algorithm that incorporates various genetic algorithm techniques that have been proven to be efficient and robust in their problem domain. More specifically, we integrate rank based selection, adaptive niching through coevolutionary sharing, elitist recombination, and non-dominated sorting into a multiobjective genetic algorithm called ERMOCS. As a proof of c...

This paper deals with multiobjective optimization techniques for a class of hybrid optimal control problems in mechanical systems. We deal with general nonlinear hybrid control systems described by boundary-value problems associated with hybrid-type Euler-Lagrange or Hamilton equations. The variational structure of the corresponding solutions makes it possible to reduce the original “mechanical...