The aggregation of objectives in multiple criteria programming is one of the simplest and widely used approach. But it is well known that these techniques sometimes fail in different aspects for determining the Pareto frontier. This paper proposes a new line search based approach for multicriteria optimization. The objectives are aggregated and the problem is transformed into a single objective...

One of the most common approaches for multiobjective optimization is to generate the whole or partial efficient frontier and then decide about the preferred solution in a higher-level decision-making process. In this paper, a new method for generating the efficient frontier for multiobjective problems is developed, called the diversity maximization approach (DMA). This approach is capable of so...

In this paper, a new algorithm is proposed to solve multi-objective optimization problems (MOOPs) through applying the trust-region (TR) method based on local search (LS) techniques; where the MOOP converting to a single objective optimization problem (SOOP) by using reference point method. In the proposed algorithm, some of the points in the search space are generated. For each point the TR al...

The aggregation of objectives in multiple criteria programming is one of the simplest and widely used approach. But it is well known that this technique sometimes fail in different aspects for determining the Pareto frontier. This paper proposes a new approach for multicriteria optimization which aggregates the objective functions and uses a line search method in order to locate an approximate ...

where x is an n-dimensional vector of variables, A is an m × n matrix, b is the RHS vector and the vectors ci (i = 1, ...,m) represent the coefficients of the objective functions (criteria). Let’s denote yi = fi(x), i = 1, ...,m, and let y = (y1, ..., ym) be a vector in the criteria space. The set Y ⊂ Rm composed by all possible criterion vectors y = f(x) when x ∈ X, is known as Feasible Criter...

A multiobjective programming algorithm may find multiple nondominated solutions. If these solutions are scattered more uniformly over the Pareto frontier in the objective space, they are more different choices and hence their quality is better. In this paper, we propose a quality measure called U-measure to measure the uniformity of a given set of nondominated solutions over the Pareto frontier...

One of the most important tasks in multi-objective optimization is "trade-off analysis" which aims to make the total balance among objective functions. The trade-off relation among alternatives can be shown as Pareto frontier. In cases with two or three objective functions, the set of Pareto optimal solutions in the objective function space (i.e., Pareto frontier) can be depicted relatively eas...

This paper deals with three particular models of the bi-criteria {0,1}-knapsack problem: equal weighted items, constant sum of the criteria coe¢cients, and the combination of the two previous models. The con...guration of the Pareto frontier is presented and studied. Several properties on the number and the composition of the e¢cient solutions are devised. The connectedness of the e¢cient solut...

In this paper, a Goal Programming (GP) model is converted into a multi-objective optimization problem (MOO) of minimizing deviations from fixed goals. To solve the resulting MOO problem, a hybrid metaheuristic with two steps is proposed to find the Pareto set’s solutions. First, a Record-to-Record Travel with an adaptive memory is used to find first non-dominated Pareto frontier solutions preem...

One aspect that is often disregarded in evolutionary multiobjective research is the fact that the solution of a problem involves not only search but decision making. Most of approaches concentrate on adapting an evolutionary algorithm to generate the Pareto frontier. In this work we present a new idea to incorporate preferences in MOEA. We introduce a binary fuzzy preference relation that expre...