Multiobjective Stochastic Linear Programming: An Overview

Abstract

Many Optimization problems in engineering and economics involve the challenging task of pondering both conflicting goals and random data. In this paper, we give an up-to-date overview of how important ideas from optimization, probability theory and multicriteria decision analysis are interwoven to address situations where the presence of several objective functions and the stochastic nature of data are under one roof in a linear optimization context. In this way users of these models are not bound to caricature their problems by arbitrarily squeezing different objective functions into one and by blindly accepting fixed values in lieu of imprecise ones.

Some New Trends in Multiobjective Programming Problems Under Uncertainty

“…Findings from several research works [5] leave no doubt about the fact that these values may be useful in providing the range of possible outcomes. Nevertheless, they ignore such important factors as the size and the probability of deviation outside the likely range as well as other aspects concerning the dispersions of involved probabilities.…”

Modeling Community Influence in Social Networks with Markov Chains

“…From literature [21][22][23], we know that if the transition probability matrix P is irreducible and non-periodic, From definition 1, 3, 4, 5 and equation (7), we can see that the matrix P is positive transition matrix, hence, matrix P is irreducible and non-periodic [24], therefore, CI will converge to a reasonable value.…”

Adaptive Strategies for Accelerating the Convergence of Average Cost Markov Decision Processes Using a Moving Average Digital Filter

“…An elegant way to find the optimal control actions for each state is provided by the classical value or policy iteration algorithms [1][2][3][4][5][6][7][8][9][10][11]. The value iteration (VI) algorithm is arguably the most popular algorithm, in part because of its simplicity and ease of implementation.…”