We study a concept in multicriteria optimization called compromise solutions (introduced in 1973 by Yu [20]) and a generalized version of this, termed reference point solutions. Our main result shows the power of this concept: Approximating reference point solutions is polynomially equivalent to constructing an approximate Pareto set as in [16]. A reference point solution is the solution closes...

For continuous multi-objective optimization problems there exists an infinite number of solutions on the Paretooptimal front. A multi-objective evolutionary algorithm attempts to find a representative set of the Pareto-optimal solutions. In the case of multi-objective multi-modal problems, there exist multiple decision vectors which map to identical objective vectors on Pareto front. Many multi...

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...

Pareto local search (PLS) methods are local search algorithms for multiobjective combinatorial optimization problems based on the Pareto dominance criterion. PLS explores the Pareto neighbourhood of a set of non-dominated solutions until it reaches a local optimal Pareto front. In this paper, we discuss and analyse three different Pareto neighbourhood exploration strategies: best, first, and ne...

In general, Multi-objective Evolutionary Algorithms do not guarantee find solutions in the Pareto-optimal set. We propose a new approach for solving decomposable deceptive multi-objective problems that can find all solutions of the Pareto-optimal set. Basically, the proposed approach starts by decomposing the problem into subproblems and, then, combining the found solutions. The resultant appro...

Many real-world optimization problems have several, usually conflicting objectives. Evolutionary multi-objective optimization usually solves this predicament by searching for the whole Pareto-optimal front of solutions, and relies on a decision maker to finally select a single solution. However, in particular if the number of objectives is large, the number of Pareto-optimal solutions may be hu...

Evolutionary algorithms (EAs) have been well acknowledged as a promising paradigm for solving optimisation problems with multiple conflicting objectives in the sense that they are able to locate a set of diverse approximations of Pareto optimal solutions in a single run. EAs drive the search for approximated solutions through maintaining a diverse population of solutions and by recombining prom...

The Pareto set of a multiobjective optimization problem consists of the solutions for which one or more objectives can not be improved without deteriorating one or more other objectives. We consider problems with linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large...

In real world problems, one is often faced with the problem of multiple, possibly competing, goals, which should be optimized simultaneously. These competing goals give rise to a set of compromise solutions, generally denoted as Pareto-optimal. If none of the objectives have preference over the other, none of these trade-off solutions can be said to be better than any other solution in the set....

This paper proposes a practical methodology for the solution of multi-objective system reliability optimization problems. The new method is based on the sequential combination of multi-objective evolutionary algorithms and data clustering on the prospective solutions to yield a smaller, more manageable sets of prospective solutions. Existing methods for multiple objective problems involve eithe...