A Short Note on the Reducibility of the Collapsing Knapsack Problem
نویسندگان
چکیده
This paper deals with the collapsing knapsack problem. In the literature, to solve the problem, a method incorporating a reduction from the problem to the 0-1 knapsack problem has been proposed. In this paper we show an alternative reduction which produces coefficients smaller than those by the previous. rlOUS. The improvement makes it possible to solve the resulting 0-1 knapsack problem faster than the pre\' On our estimation in a case, the efficiency attains up to 150 times. We also show that the coefficients produced will be the smallest possible.
منابع مشابه
An Efficient Algorithm for Reducing the Duality Gap in a Special Class of the Knapsack Problem
A special class of the knapsack problem is called the separable nonlinear knapsack problem. This problem has received considerable attention recently because of its numerous applications. Dynamic programming is one of the basic approaches for solving this problem. Unfortunately, the size of state-pace will dramatically increase and cause the dimensionality problem. In this paper, an efficient a...
متن کاملAn Efficient Algorithm for Reducing the Duality Gap in a Special Class of the Knapsack Problem
A special class of the knapsack problem is called the separable nonlinear knapsack problem. This problem has received considerable attention recently because of its numerous applications. Dynamic programming is one of the basic approaches for solving this problem. Unfortunately, the size of state-pace will dramatically increase and cause the dimensionality problem. In this paper, an efficient a...
متن کاملA Robust Knapsack Based Constrained Portfolio Optimization
Many portfolio optimization problems deal with allocation of assets which carry a relatively high market price. Therefore, it is necessary to determine the integer value of assets when we deal with portfolio optimization. In addition, one of the main concerns with most portfolio optimization is associated with the type of constraints considered in different models. In many cases, the resulted p...
متن کاملAn employee transporting problem
An employee transporting problem is described and a set partitioning model is developed. An investigation of the model leads to a knapsack problem as a surrogate problem. Finding a partition corresponding to the knapsack problem provides a solution to the problem. An exact algorithm is proposed to obtain a partition (subset-vehicle combination) corresponding to the knapsack solution. It require...
متن کاملSolving a bi-objective project capital budgeting problem using a fuzzy multi-dimensional knapsack
In this paper, the researchers have proposed a multi-dimensional knapsack model for project capital budgeting problem in uncertain situation which has been modeled through fuzzy sets. The optimistic and pessimistic situations were considered and associated deterministic models were yielded. Numerical example has been supplied toillustrate the performance of proposed model. The results were prom...
متن کامل