Multi-objective optimisation problems normally have not one but a set of solutions, which are called Pareto-optimal solutions or non-dominated solutions. Once a Pareto-optimal set has been obtained, the decision-maker faces the challenge of analysing a potentially large set of solutions. Selecting one solution over others can be quite a challenging task because the Pareto set can contain an unm...

In this paper, several new set quality metrics are introduced that can be used to evaluate the ‘‘goodness’’ of an observed Pareto solution set. These metrics, which are formulated in closed-form and geometrically illustrated, include hyperarea difference, Pareto spread, accuracy of an observed Pareto frontier, number of distinct choices and cluster. The metrics should enable a designer to eithe...

this study proposes a combination of a fuzzy sliding mode controller (fsmc) with integral-proportion-derivative switching surface based superconducting magnetic energy storage (smes) and pid tuned by a multi-objective optimization algorithm to solve the load frequency control in power systems. the goal of design is to improve the dynamic response of power systems after load demand changes. in t...

suspension system as one of the most important key elements of vehicle has always been considered by research centres and auto makers over the world and this issue is more important on sport cars which have special sensitive working conditions and even the smallest defect can strongly affect their performances. in this study, optimization of effective handling parameters of a sport car with thr...

In multidisciplinary optimization a designer solves a problem where there are different criteria usually contradicting each other. In general, the solution of such a problem is not unique. When seeking an optimal design, it is natural to exclude from the consideration any design solution which can be improved without deterioration of any discipline and violation of the constraints; in other wor...

In this paper we consider two-person games in strategic form in cases in which each player has only two moves. The related Nash competitive and cooperative solution and Nash equilibria are presented. Nash cooperative solution is the only solution such that the corresponding payoffs respect three properties (belonging to feasible set, Pareto optimality and symmetry) together with two technical a...

Abstract: In multi-objective optimization problems, the optimization target is to obtain a set of non-dominated solutions. Comparing solution sets is crucial in evaluating the performances of different optimization algorithms. The use of performance indicators is common in comparing those sets and, subsequently, optimization algorithms. A good solution set must be close to the Pareto-optimal fr...

In this paper, a new evolutionary technique for detecting continuous Pareto optimal sets is proposed. The technique is designed for functions of one real variable but it can be extended for several variables functions. In this approach an individual (a solution) is either a closed interval or a point. Each solution in the final population corresponds to a decision region of Pareto optimal set. ...

In [5] an evolutionary algorithm for detecting continuous Pareto optimal sets has been proposed. In this paper we propose a new evolutionary elitist approach combing a non-standard solution representation and an evolutionary optimization technique. The proposed method permits detection of continuous decision regions. In our approach an individual (a solution) is either a closed interval or a po...