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...

In real world problems, one is often faced with the problem of multiple, possibly competing, goals, which should be optimized simultaneously. These competing goals give rise to a set of compromise solutions, generally denoted as Pareto-optimal. If none of the objectives have preference over the other, none of these trade-off solutions can be said to be better than any other solution in the set....

Using the method of generic continuity of set-valued mappings, this paper studies the stability of weakly Pareto-Nash and Pareto-Nash equilibria for multiobjective population games, when payoff functions are perturbed. More precisely, the paper investigates the continuity properties of the set of weakly Pareto-Nash equilibria and that of the set of Pareto-Nash equilibria under sufficiently smal...

in this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form d_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0x(0)= x'(0)=0, x'(1)=beta x(xi), where $d_{0^{+}}^{alpha}$ denotes the standard riemann-liouville fractional derivative, 0an illustrative example is also presented.

Multi-objective evolutionary algorithms (MOEAs) are widely used to optimize multi-purpose reservoir operations. Considering that most outcomes of MOEAs Pareto optimal sets with a large number incomparable solutions, it is not trivial task for decision-makers (DMs) select compromise solution application purposes. Due the increasing popularity data-driven decision-making, we introduce clustering-...

This paper considers multiobjective linear programming problems (MOLPP) where random fuzzy variables are contained in objective functions and constraints. A new decision making model optimizing possibilistic value at risk (pVaR) is proposed by incorporating the concept of value at risk (VaR) into possibility theory. It is shown that the original MOLPPs involving random fuzzy variables are trans...

Multi-objective optimization is a class of problems with solutions that can be evaluated along two or more incomparable or conflicting objectives. These types of problems differ from standard optimization problems in that the end result is not a single “best solution” but rather a set of alternatives, where for each member of the set, no other solution is completely better (the Pareto set). Mul...

This study explored the application of a multi-objective evolutionary algorithm (MOEA) and Pareto ordering in the multiple-objective automatic calibration of the Soil and Water Assessment Tool (SWAT). SWAT was calibrated in the Calapooia watershed, Oregon, USA, with two different pairs of objective functions in a cluster of 24 parallel computers. The non-dominated sorting genetic algorithm (NSG...

This paper presents a multi-objective optimal power flow technique using particle swarm optimization. Two conflicting objectives, generation cost, and environmental pollution are minimized simultaneously. A multiobjective particle swarm optimization method is used to solve this highly nonlinear and non-convex optimization problem. A diversity preserving technique is incorporated to generate eve...