Many decision making problems can be formulated as multi-objective optimization problems (MOP). There hardly exists the solution that optimizes all objective functions in MOP, and then the concept of Pareto optimal solution (or efficient solution) is introduced. Usually, there exist a lot of Pareto optimal solutions, which are considered as candidates of final decision making solution. It is an...

Under mild conditions, the Pareto set of a continuous multi-objective optimization problem exhibits certain regularity. We have recently advocated taking into consideration such regularity in designing multi-objective evolutionary algorithms. Following our previous work on using Local Principal Component Analysis for capturing the regularity, this paper presents a new approach for acquiring and...

Pareto-optimal solutions are one of the most important and well-studied solution concepts in multi-objective optimization. Often the enumeration of all Pareto-optimal solutions is used to filter out unreasonable trade-offs between different criteria. While in practice, often only few Pareto-optimal solutions are observed, for almost every problem with at least two objectives there exist instanc...

We propose a general methodology for approximating the Pareto front of multi-criteria optimization problems. Our search-based methodology consists of submitting queries to a constraint solver. Hence, in addition to a set of solutions, we can guarantee bounds on the distance to the actual Pareto front and use this distance to guide the search. Our implementation, which computes and updates the d...

We consider a vector minimax Boolean programming problem. The problem consists in finding the set of Pareto optimal solutions. When the problem’s parameters vary then the optimal solution of the problem obtained for some initial parameters may appear non-optimal. We calculate the maximal perturbation of parameters which preseves the optimality of a given solution of the problem. The formula for...

This paper proposes a multiobjective harmony search (MOHS) algorithm for optimal power flow (OPF) problem. OPF problem is formulated as a nonlinear constrained multiobjective optimization problem where different objectives and different constraints have been considered. Fast elitist non dominated sorting and crowding distance have been used to find and manage the Pareto optimal front. Finally, ...

Recent works in evolutionary multiobjective optimization suggest to shift the focus from solely evaluating optimization success in the objective space to also taking the decision space into account. They indicate that this may be a) necessary to express the users requirements of obtaining distinct solutions (distinct Pareto set parts or subsets) of similar quality (comparable locations on the P...

Many real-world optimization problems involve multiple conflicting objectives and the use of evolutionary algorithms to solve the problems has attracted much attention recently. This paper investigates the application of multi-objective optimization technique for the design of a Thyristor Controlled Series Compensator (TCSC)-based controller to enhance the performance of a power system. The des...

In this paper we present a new genetic algorithm (GA) using pareto partitioning method and apply this GA to solving the design problem of the robust PID controller with two degrees of freedom based on the partial model matching approach. This design problem is formulated as two objective minimax optimization problem. Therefore we need to generate a pareto optimal set that is properly distribute...