APPROXIMATE ALGORITHMS FOR THE MULTIPLE-CHOICE CONTINUOUS KNAPSACK PROBLEMS

Heuristic algorithms for the multiple-choice multidimensional knapsack problem

APPROXIMATE ALGORITHM FOR THE MULTI-DIMENSIONAL KNAPSACK PROBLEM BY USING MULTIPLE CRITERIA DECISION MAKING

In this paper, an interesting and easy method to solve the multi-dimensional  knapsack problem is presented. Although it belongs to the combinatorial optimization, but the proposed method belongs to the decision making field in mathematics. In order to, initially efficiency values for every item is calculated then items are ranked by using Multiple Criteria Decision Making (MCDA).  Finally, ite...

Genetic Algorithms for Multiple-Choice Optimisation Problems

This thesis investigates the use of problem-specific knowledge to enhance a genetic algorithm approach to multiple-choice optimisation problems.It shows that such information can significantly enhance performance, but that the choice of information and the way it is included are important factors for success.Two multiple-choice problems are considered.The first is constructing a feasible nurse ...

The Multiple-choice Knapsack Problem

This paper treats the multiple-choice (continuous) knapsack problem P: n mi n mi maximize L .L cijxijsubjectto(l) I I aij x ij";b,(2)0,,;xij";1,i=I,2, i=l J=l i=l J=1 ... , n, j = 1,2, .... mi and (3) at most one of x il, x i2' ... , x im. is positive for i = 1,2, ., ., n, , where n, mi are positive integers and aij' Cij' bare nonnegative real numbers. Two approximate algorithms and an exact br...

Continuous Knapsack Problems

TIle multiple-choice continuous knapsack problem is dermed as follows: maximize z = ~n ~~i CjJ'XiJ' 1=1 J= 1 subject to (1) ~n ~mi aijXij .;;; b, (2) 0 .;;; Xij .;;; I, i = 1,2, ... , n,j = 1. 2, ... , mi, (3) at most one of Xij G = 1,2, ... , mi) 1=1 J=1 is positive for each i = I, 2, ... , n, where n, mi are positive integers and aij are nonnegative integers. In this paper, it is proved that ...