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 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...

Scalarization of the multiobjective programming problems with fuzzy coefficients using the embedding theorem and the concept of convex cone (ordering cone) is proposed in this paper. Since the set of all fuzzy numbers can be embedded into a normed space, this motivation naturally inspires us to invoke the scalarization techniques in vector optimization problems to evaluate the multiobjective pr...

A general duality framework in convex multiobjective optimization is established using the scalarization with K-strongly increasing functions and the conjugate duality for composed convex cone-constrained optimization problems. Other scalarizations used in the literature arise as particular cases and the general duality is specialized for some of them, namely linear scalarization, maximum(-line...

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 ...

The paper presents main features of the conic scalarization method in multiobjective optimization. The conic scalarization method guarantee to generate all proper efficient solutions and does not require any kind of cenvexity or boundedness conditions. In addition the preference and reference point information of the decision maker is taken into consideretion by this method. Also in this paper,...

The main purpose of this paper is to obtain sufficient conditions for existence of points of coincidence and common fixed points for a pair of self mappings satisfying some expansive type conditions in $b$-metric spaces. Finally, we investigate that the equivalence of one of these results in the context of cone $b$-metric spaces cannot be obtained by the techniques using scalarization function....

‎A common approach to determine efficient solutions of a multiple objective optimization problem‎ ‎is reformulating it to a parameter dependent scalar optimization problem‎. ‎This reformulation is called scalarization approach‎. Here, a well-known scalarization approach named Pascoletti-Serafini scalarization is considered‎. First, some difficulties of this scalarization are discussed and then ...

Array syntax, existed in many languages, adds expressive power by allowing operations on and assignments to the array sections. When compiling to a uniprocessor machine, the array statement must be converted into a loop that maintains the correct semantics, by a process called scalarization. Scalarization presents a significant technical problem because an array assignment needs to be implement...