We propose a general-purpose algorithm APS (Adaptive Pareto-Sampling) for determining the set of Pareto-optimal solutions of bicriteria combinatorial optimization (CO) problems under uncertainty, where the objective functions are expectations of random variables depending on a decision from a finite feasible set. APS is iterative and population-based and combines random sampling with the soluti...

This study proposes a combination of a fuzzy sliding mode controller (FSMC) with integral-proportion-Derivative switching surface based superconducting magnetic energy storage (SMES) and PID tuned by a multi-objective optimization algorithm to solve the load frequency control in power systems. The goal of design is to improve the dynamic response of power systems after load demand changes. In t...

This article reports an experimental analysis on stochastic local search for approximating the Pareto set of bi-objective unconstrained binary quadratic programming problems. First, we investigate two scalarizing strategies that iteratively identify a high-quality solution for a sequence of sub-problems. Each sub-problem is based on a static or adaptive definition of weighted-sum aggregation co...

We introduce an unconstrained multicriteria optimization problem and discuss its relation to various well-known scalar robust optimization problems with a finite uncertainty set. Specifically, we show that a unique solution of a robust optimization problem is Pareto optimal for the unconstrained optimization problem. Furthermore, it is demonstrated that the set of weakly Pareto optimal solution...

This paper presents efficient CO2 abatement levels for 135 countries and identifies reasons for the absence of worldwide greenhouse gas emission reductions. Based on individual marginal cost and benefit functions for emission abatement we compare the Pareto-optimal Samuelson solution with the Nash equilibrium. We found that the Pareto-optimal solution would require status quo world emissions to...

Shapley value is a popular way to compute payoffs in cooperative games where the agents are assumed to have deterministic, risk-neutral (linear) utilities.This paper explores a class of Multi-agent constantsum cooperative games where the payoffs are random variables. We introduce a new model based on Borch’s Theorem from the actuarial world of re-insurance, to obtain a Pareto optimal allocation...

Operations research applications often pose multicriteria problems. Mathematical research on multicriteria problems predominantly revolves around the set of Pareto optimal solutions, while in practice, methods that output a single solution are more widespread. In real-world multicriteria optimization, reference point methods are widely used and successful examples of such methods. A reference p...

Path planning is one of the most vital elements of mobile robotics, providing the agent with a collision-free route through the workspace. The global path plan can be calculated with a variety of informed search algorithms, most notably the A* search method, guaranteed to deliver a complete and optimal solution that minimizes the path cost. D* is widely used for its dynamic replanning capabilit...

The decomposition-based method has been recognized as a major approach for multiobjective optimization. It decomposes a multi-objective optimization problem into several singleobjective optimization subproblems, each of which is usually defined as a scalarizing function using a weight vector. Due to the characteristics of the contour line of a particular scalarizing function, the performance of...