Controllers design problems are multi objective optimization problems as the controller must satisfy several performance measures that are often conflicting and competing with each other. In multi-objective approach a set of solutions can be generated from which the designer can select a final solution according to his requirement and need. This paper presents the design and analysis Proportion...

In this chapter, we present a new interactive procedure for multiobjective optimization, which is based on the use of a set of value functions as a preference model built by an ordinal regression method. The procedure is composed of two alternating stages. In the first stage, a representative sample of solutions from the Pareto optimal set (or from its approximation) is generated. In the second...

Most existing evolutionary approaches to multiobjective optimization aim at finding an appropriate set of compromise solutions, ideally a subset of the Pareto-optimal set. That means they are solving a set problem where the search space consists of all possible solution sets. Taking this perspective, multiobjective evolutionary algorithms can be regarded as hill-climbers on solution sets: the p...

In this paper, we formulate a multiobjective fuzzy random simple recourse programming problem, in which fuzzy random variables coefficients are involved in equality constraints. In the proposed method, equality constraints with fuzzy random variables are defined on the basis of a possibility measure and and a two-stage programming method. For a given permissible possibility level specified by t...

The common search for a Pareto-optimal set, and the associated front, usually serves as a preprocessing stage for a Multi-Criteria Decision Making (MCDM). In that case the optimization provides information to support the selection of a final solution from a feasible space of solutions. Here, we are interested in a rather different MCDM problem and its associated preprocessing stage. Our study c...

We design a control system for a prosthesis test robot that was previously developed for transfemoral prosthesis design and test. The robot’s control system aims to mimic human walking in the sagittal plane. It has been seen in previous work that trajectory control fails to produce human-like forces. Therefore, we utilize an impedance controller to achieve reasonable tracking of motion and forc...

We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale [Global analysis and economics. I. Pareto optimum and a generalization of Morse theory, in Dynamical Systems, Academic Press, New York, 1973, pp. 531–544]. The method highlights and exploits the underlying manifold structure of the Pareto sets, approximating Pareto optima by mean...

The transit network design problem (TNDP) aims to find a set of routes and corresponding frequencies for an urban public transportation system. We model the TNDP as a multi-objective combinatorial optimization problem whose resolution involves finding a Pareto front that represents different trade-off levels between opposite objectives, the travel and waiting times and the required fleet of bus...

In this paper, we focus on multiobjective fuzzy random programming problems with simple recourse through a fractile optimization model, in which fuzzy random variables coefficients are involved in equality constraints, and random variables coefficients are involved in the objective functions. In the proposed method, equality constraints with fuzzy random variables are defined on the basis of a ...