The weighted sum method of vector objective scalarization is known to generate points on convex Pareto front whose distribution cannot be controlled. This work presents a method of improving the distribution of Pareto points generated by weighted sum method by nonlinear weight selection. Numerical examples are presented to show the effectiveness of the method.

We introduce and analyze a novel scalarization technique and an associated algorithm for generating an approximation of the Pareto front (i.e., the efficient set) of nonlinear multiobjective optimization problems. Our approach is applicable to nonconvex problems, in particular to those with disconnected Pareto fronts and disconnected domains (i.e., disconnected feasible sets). We establish the ...

In the current work, we have formulated the optimal bit-allocation problem for a scalable codec of images or videos as a constrained vector-valued optimization problem and demonstrated that there can be many optimal solutions, called Pareto optimal points. In practice, the Pareto points are derived via the weighted sum scalarization approach. An important question which arises is whether all th...

We determine the power of weighted sum scalarization with respect to computation approximations for general multiobjective minimization and maximization problems. Additionally, we introduce a new multi-factor notion approximation that is specifically tailored case its inherent trade-offs between different objectives. For problems, provide an efficient algorithm computes problem by using exact o...

In this paper, we consider the multiobjective linear programs where coefficients in the objective function belong to uncertainty sets. We introduce the concept of robust efficient solutions to uncertain multiobjective linear programming problems. By using two scalarization methods, the weighted sum method and the ϵ-constraint method, we obtain that the robust efficient solutions for uncertain m...

Today, workforce scheduling programs are being implemented in many production and service centers. These sectors can provide better quality products and/or services to their customers, taking into account employees’ desires and preferences in order to increase sector productivity. In this study, an employee shift scheduling problem in the service sector is discussed. In the problem, the aim is ...

This paper considers supply chain design in green logistics. We formulate the choice of an environmentally conscious chain design as a multi-objective optimization (MOO) problem and approximate the Pareto front using the weighted sum and epsilon constraint scalarization methods as well as with two popular genetic algorithms, NSGA-II and SPEA2. We extend an existing case study of green supply ch...

This paper is concerned with the problem of finding a representative sample of Pareto-optimal points inmulti-objective optimization. The Normal Boundary Intersection algorithm is a scalarization scheme for generating a set of evenly spaced Efficient solutions. A drawback of this algorithm is that Pareto-optimality of solutions is not guaranteed. The contributions of this paper are two-fold. Fir...

In this work, we propose integral global optimality conditions for multiobjective problems not necessarily differentiable. The characterization, already known single objective problems, are extended to by weighted sum and Chebyshev scalarizations. Using last scalarization, an algorithm obtaining approximation of the weak Pareto front whose effectiveness is illustrated solving a collection test ...

We apply a flexible Inexact-Restoration (IR) algorithm to optimization problems with multiobjective constraints under the weighted-sum scalarization approach. In IR methods each iteration has two phases. In the first phase one aims to improve the feasibility and, in the second phase, one minimizes a suitable objective function. We show that with the IR framework there is a natural way to explor...