This paper considers a bi-criteria planning problems on single machine, with the goal of minimizing total square time duration and maximizing earliness. To solve this problem we have to find Pareto set. We introduced strong relation between lower bound, upper bound number efficient solutions via theorem which shows also that is near optimal solution if small.

A problem of axiomatic construction of a social decision function is studied for the case when individual opinions of agents are given as m-graded preferences with arbitrary integer m ≥ 3. It is shown that the only rule satisfying the introduced axioms of Pairwise Compensation, Pareto Domination and Noncompensatory Threshold and Contraction is the threshold rule.

This paper presents an improved multi-objective group search optimizer (IMGSO) that is based on Pareto theory that is designed to handle multi-objective optimization problems. The optimizer includes improvements in three areas: the transition-feasible region is used to address constraints, the Dealer’s Principle is used to construct the non-dominated set, and the producer is updated using a tab...

We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, Academic Press, New York (1973) 531– 544). We speak about synthetic approach because the optimal set is natively approximated by means of a compound geometrical object, i.e., a simplicial complex, rather than by an unstructured scatter of individual optima. Th...

A genetic algorithm for multiobjective optimization is presented which tries to evolve an evenly distributed set of solutions belonging to the Pareto set by: (i) ranking the population according to nondomination properties; (ii) defining a filter to retain Pareto set solutions and (iii) using adequate operators: exclusion, addition and single-objective operator which improves the individuals fr...

The Pareto stability is one of solution concepts in two-sided matching markets with ties. It is known that there always exists a Pareto stable matching in the many-to-many setting. In this paper, we consider the following generalization of the Pareto stable matching problem in the many-to-many setting. Each agent v of one side has a matroid defined on the set of edges incident to v, and the set...