Multidimensional Knapsack Problem Based on Uncertain Measure

Abstract

Abstract. The researchers of classical multidimensional knapsack problem have always assumed that the weights, values, and capacities are constant values. However, in the real-life industrial engineering applications, the multidimensional knapsack problem often comes with uncertainty about a lack of information about these parameters. This paper investigates a constrained multidimensional knapsack problem under uncertain environment, in which the relevant parameters are assumed to be uncertain variables. Within the framework of uncertainty theory, two types of uncertain programming models with discount constraints are constructed for the problem with di erent decision criteria, including the expected value criterion and the critical value criterion. Taking full advantage of the operational law for uncertain variables, the proposed models can be transformed into their corresponding deterministic models. After theoretically investigating the properties of the models, we do some numerical experiments. The numerical results illustrate that the proposed models are feasible and e cient for solving the constrained multidimensional knapsack problem with uncertain parameters.

Knapsack problem in fuzzy nature: Different models based on credibility ranking method

“…Abboud et al [2] 1997 Fuzzy goals Mathematical optimization Chen [5] 2009 Object weights Parametric programming Cheng et al [6] 2017 All parameters Chance-constrained programming Kasperski and Kulej [13] 2007 Imprecise profits and imprecise weights of items Bisection approach Lin and Yao [15] 2001 Weight coefficients…”

“…It is applied to solve an investment problem in an imprecise environment. Uncertain multidimensional knapsack problem with different decision criteria was studied by [6]. An Integer Linear Programming Model for Binary Knapsack Problem with Dependent Item Values was demonstrated in [20].…”

Uncertain Multi Level Four Dimensional Multi Item Fractional Transportation Problem

“…A multi item STP under uncertain environment was studied by Dalman [28]. Cheng, Rao and Chen [29] studied about the multi diemensional Knapsack problem which was based on uncertain measures. The model for uncertain multi objective multi item four dimensional fractional transportation problems was studied by Revathi and Mohanaselvi [30].…”

Cycle index of uncertain random graph

“…Nowadays, uncertainty theory has been applied to network optimization ( [15]), supply chain management ( [35]), and supplier selection ( [37]). In this subsection, we briefly state some basic concepts and results about uncertainty theory, which are introduced by Liu [29,30,31] and will be used throughout the paper.…”