A Cutting Plane Based Algorithm for the Multiple Knapsack Problem

نویسندگان

  • C. E. Ferreira
  • A. Martin
  • R. Weismantel
چکیده

In this paper we describe a cutting plane based algorithm for the multiple knapsack problem. We use our algorithm to solve some practical problem instances arising in the layout of electronic circuits and in the design of main frame computers, and we report on our computational experience. This includes a discussion and evaluation of separation algorithms, an LP-based primal heuristic and some implementation details. The paper is based on the polyhedral theory for the multiple knapsack polytope developed in our companion paper FMW93] and meant to turn this theory into an algorithmic tool for the solution of practical problems.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

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...

متن کامل

On the minimum cost multiple-source unsplittable flow problem

The minimum cost multiple-source unsplittable flow problem is studied in this paper. A simple necessary condition to get a solution is proposed. It deals with capacities and demands and can be seen as a generalization of the well-known semi-metric condition for continuous multicommdity flows. A cutting plane algorithm is derived using a superadditive approach. The inequalities considered here a...

متن کامل

Approximation Algorithms for Knapsack Problems with Cardinality Constraintsy

We address a variant of the classical knapsack problem in which an upper bound is imposed on the number of items that can be selected. This problem arises in the solution of real-life cutting stock problems by column generation, and may be used to separate cover inequalities with small support within cutting plane approaches to integer linear programs. We focus our attention on approximation al...

متن کامل

Upper bounds for the binary quadratic knapsack problem

We address the binary quadratic knapsack problem (QKP) of selecting from a set of items, a subset with maximum profit, and whose overall weight does not exceed a given capacity c. The objective function of the problem, which measures the profit of the selection, is a nonconvex quadratic function, and the QKP is naturally formulated as a quadratic binary problem. Several works have proposed rela...

متن کامل

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 کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1993