In this paper, a new general scalarization technique for solving multiobjective optimization problems is presented. After studying the properties of this formulation, two problems as special cases of this general formula are considered. It is shown that some well-known methods such as the weighted sum method, the -constraint method, the Benson method, the hybrid method and the elastic -constrai...

This paper considers an artificial noise (AN)-aided transmit design for multi-user MIMO systems with integrated services. Specifically, two sorts of service messages are combined and served simultaneously: one multicast message intended for all receivers and one confidential message intended for only one receiver and required to be perfectly secure from other unauthorized receivers. Our interes...

We consider the problem of constructing an approximation of the Pareto curve associated with the multiobjective optimization problem minx∈S{(f1(x), f2(x))}, where f1 and f2 are two conflicting polynomial criteria and S ⊂ Rn is a compact basic semialgebraic set. We provide a systematic numerical scheme to approximate the Pareto curve. We start by reducing the initial problem into a scalarized po...

Abstract In a single-objective setting, nonconvex quadratic problems can equivalently be reformulated as convex over the cone of completely positive matrices. small dimensions this equals matrices which are entrywise nonnegative and semidefinite, so reformulation solved via SDP solvers. Considering multiobjective problems, naturally question arises, whether advantage reformulations extends to m...

Abstract In engineering applications one often has to trade-off among several objectives as, for example, the mechanical stability of a component, its efficiency, weight and cost. We consider biobjective shape optimization problem maximizing ceramic component under tensile load while minimizing volume. Stability is thereby modeled using Weibull-type formulation probability failure external load...

We introduce a new flexible Inexact-Restoration (IR) algorithm and an application to problems with multiobjective constraints (MOCP) 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. This is done in such a way to ensure bounded d...

In multi-objective reinforcement learning (MORL) the agent is provided with multiple feedback signals when performing an action. These signals can be independent, complementary or conflicting. Hence, MORL is the process of learning policies that optimize multiple criteria simultaneously. In this abstract, we briefly describe our extensions to single-objective multi-armed bandits and reinforceme...

Web service composition combines available services to provide new functionality. The various available services have different quality-of-service (QoS) attributes. Building a QoS-optimal web service composition is a multi-criteria NP-hard problem. Most of the existing approaches reduce this problem to a single-criterion problem by aggregating different criteria into a unique global score (scal...

Indicator-based evolutionary algorithms are amongst the best performing methods for solving multi-objective optimization (MOO) problems. In reinforcement learning (RL), introducing a quality indicator in an algorithm’s decision logic was not attempted before. In this paper, we propose a novel on-line multi-objective reinforcement learning (MORL) algorithm that uses the hypervolume indicator as ...

In this paper, we study risk-averse models for multicriteria optimization problems under uncertainty. We use a weighted sum-based scalarization and take a robust approach by considering a set of scalarization vectors to address the ambiguity and inconsistency in the relative weights of each criterion. We model the risk aversion of the decision makers via the concept of multivariate conditional ...