In multicriteria optimization, a compromise solution is a feasible solution whose cost vector minimizes the distance to the ideal point w.r.t. a given norm. The coordinates of the ideal point are given by the optimal values for the single optimization problem for each criterion. We show that the concept of compromise solutions fits nicely into the existing notion of Pareto optimality: For a hug...

In the multi objective optimization, in the case when generated set of Pareto optimal solutions is large, occurs the problem to select of the best solution from this set. In this paper is suggested a method to order of Pareto set. Ordering the Pareto optimal set carried out in conformity with the introduced distance function between each solution and selected reference point, where the referenc...

This paper focuses on a multi-objective derivation of branch-and-bound procedures. Such a procedure aims to provide the set of Pareto optimal solutions of a multi-objective combinatorial optimization problem. Unlike previous works on this issue, the bounding is performed here via a set of points rather than a single ideal point. The main idea is that a node in the search tree can be discarded i...

In this paper, the authors consider a single machine scheduling problem with rejection. In traditional research, it is assumed all jobs must be processed. However, in the real-world situation, certain jobs can be rejected. In this study, the jobs can be either accepted and scheduled or be rejected at the cost of a penalty. Two objective functions are considered simultaneously: (1) minimization ...

A novel approach of differential evolution (DE) by incorporating the Pareto-optimal set is presented for optimising train movement through tuning fuzzy membership functions in mass transit systems. The Pareto-optimal based multiobjective optimisation approach uniquely provides a set of optimal non-dominated solutions to the decision-maker. From the set, the decision-maker selects satisfactory s...

In recent years, the research focus in multi-objective optimization has shifted from approximating the Pareto optimal front in its entirety to identifying solutions that are well-balanced among their objectives. Proper Pareto optimality is an established concept for eliminating Pareto optimal solutions that exhibit unbounded tradeoffs. Imposing a strict tradeoff bound allows specifying how many...

This paper presents a solution methodology for multiobjective optimization problems in the context of models for the placement of components on printed wiring boards (PWB’s). The methodology combines the use of a flow and heat transfer solver, a genetic algorithm for the adaptive search of optimal or near-optimal solutions, and a multiobjective optimization strategy [Pareto optimization or mult...