Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...

A procedure to approximate the nondominated set for general (continuous) bi-criteria programs is proposed. The piecewise approximation is composed of quadratic curves, each of which is developed locally in a neighborhood of a nondominated point of interest and based on primal-dual relationships associated with the weighted-Tchebycheff scalarization of the original problem. The approximating qua...

We present a new interactive hybrid approach for solving multicriteria optimization problems where features of approximation methods and interactive approaches are incorporated. We produce rough approximations of the nondominated set and let the decision maker indicate with the help of reference points where to refine the approximation. In this way, (s)he iteratively directs the search towards ...

In this paper, we consider the problem of searching nondominated alternatives in a discrete multiple criteria problem. The search procedure is based on the use of a reference direction. A reference direction reflects the desire of the decision maker (DM) to specify a search direction. To find a set of given alternatives related somehow to the reference direction specified by the DM, the referen...

In multi-objective convex optimization it is necessary to compute an infinite set of nondominated points. We propose a method for approximating the nondominated set of a multi-objective nonlinear programming problem, where the objective functions and the feasible set are convex. This method is an extension of Benson’s outer approximation algorithm for multi-objective linear programming problems...

We present a new algorithm for optimizing a linear function over the set of efficient solutions of a multiobjective integer program MOIP. The algorithm’s success relies on the efficiency of a new algorithm for enumerating the nondominated points of a MOIP, which is the result of employing a novel criterion space decomposition scheme which (1) limits the number of subspaces that are created, and...

‎In this paper‎, ‎we present an algorithm for generating approximate nondominated points of a multiobjective optimization problem (MOP)‎, ‎where the constraints and the objective functions are convex‎. ‎We provide outer and inner approximations of nondominated points and prove that inner approximations provide a set of approximate weakly nondominated points‎. ‎The proposed algorithm can be appl...

General multi-objective optimization problems are often solved by a sequence of parametric single objective problems, so-called scalarizations. If the set of nondominated points is finite, and if an appropriate scalarization is employed, the entire nondominated set can be generated in this way. In the bicriteria case it is well known that this can be realized by an adaptive approach which, give...

In this paper, we investigate the problem of time series forecasting using single hidden layer feedforward neural networks (SLFNs), which is optimized via multiobjective evolutionary algorithms. By utilizing the adaptive differential evolution (JADE) and the knee point strategy, a nondominated sorting adaptive differential evolution (NSJADE) and its improved version knee point-based NSJADE (KP-...

This paper addresses the problem of capturing nondominated points on convex Pareto frontiers, which are encountered in invex multi-objective programming problems. An algorithm to find a piecewise linear approximation of the nondominated set of convex Pareto frontier are applied. Index Term-Approximation, Nondominated points, Invex multi-objective problems, Block norms.