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  1. Applied Mathematics-A Journal of Chinese Universities
  2. Applied Mathematics-A Journal of Chinese Universities : Volume 17
  3. Applied Mathematics-A Journal of Chinese Universities : Volume 17, Issue 2, June 2002
  4. Semi-definite relaxation algorithm of multiple knapsack problem
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Applied Mathematics-A Journal of Chinese Universities : Volume 32
Applied Mathematics-A Journal of Chinese Universities : Volume 31
Applied Mathematics-A Journal of Chinese Universities : Volume 30
Applied Mathematics-A Journal of Chinese Universities : Volume 29
Applied Mathematics-A Journal of Chinese Universities : Volume 28
Applied Mathematics-A Journal of Chinese Universities : Volume 27
Applied Mathematics-A Journal of Chinese Universities : Volume 26
Applied Mathematics-A Journal of Chinese Universities : Volume 25
Applied Mathematics-A Journal of Chinese Universities : Volume 24
Applied Mathematics-A Journal of Chinese Universities : Volume 23
Applied Mathematics-A Journal of Chinese Universities : Volume 22
Applied Mathematics-A Journal of Chinese Universities : Volume 21
Applied Mathematics-A Journal of Chinese Universities : Volume 20
Applied Mathematics-A Journal of Chinese Universities : Volume 19
Applied Mathematics-A Journal of Chinese Universities : Volume 18
Applied Mathematics-A Journal of Chinese Universities : Volume 17
Applied Mathematics-A Journal of Chinese Universities : Volume 17, Issue 4, December 2002
Applied Mathematics-A Journal of Chinese Universities : Volume 17, Issue 3, September 2002
Applied Mathematics-A Journal of Chinese Universities : Volume 17, Issue 2, June 2002
A degree sequence method for the cutwidth problem of graphs
Existence of three-solutions for second-order differential equations with nonlinear boundary value conditions
Periodic solutions of third-order functional differential equations with variable coefficients
Inverse computation of optical-absorption coefficient in inhomogeneous material with varied thermal conductivity
A remark on the quasi-harmonic spheres
A nonlinear degenerate parabolic equation with non-local source
Ordered analytic representation of pdes by hamiltonian canonical system
Global asymptotic stability for a nonlinear delay difference equation
Convergence rate estimate of ishikawa iterative sequence for strictly pseudocontractive mappings
Weakly algebraic reflexivity and strongly algebraic reflexivity
Some results on lag increments of principal value of brownian local time
A class of nonmonotone conjugate gradient methods for nonconvex functions
C $^{ n }$-continuous B-type spline curves with its localization interpolation and approximation
Two approaches to improving the consistency of complementary judgement matrix
An optimal fuzzy approximator
Semi-definite relaxation algorithm of multiple knapsack problem
Applied Mathematics-A Journal of Chinese Universities : Volume 17, Issue 1, March 2002
Applied Mathematics-A Journal of Chinese Universities : Volume 16
Applied Mathematics-A Journal of Chinese Universities : Volume 15
Applied Mathematics-A Journal of Chinese Universities : Volume 14
Applied Mathematics-A Journal of Chinese Universities : Volume 13
Applied Mathematics-A Journal of Chinese Universities : Volume 12

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Semi-definite relaxation algorithm of multiple knapsack problem

Content Provider Springer Nature Link
Author Chen, Feng Yao, Enyu
Copyright Year 1993
Abstract The multiple knapsack problem denoted by MKP (B,S,m,n) can be defined as follows. A set B of n items and a set S of m knapsacks are given such that each item j has a profit p $_{ j }$ and weight w $_{ j }$, and each knapsack i has a capacity C $_{ i }$. The goal is to find a subset of items of maximum profit such that they have a feasible packing in the knapsacks. MKP (B,S,m,n) is strongly NP-Complete and no polynomial-time approximation algorithm can have an approximation ratio better than 0.5. In the last ten years, semi-definite programming has been empolyed to solve some combinatorial problems successfully. This paper firstly presents a semi-definite relaxation algorithm (MKPS) for MKP (B,S,m,n). It is proved that MKPS have a approximation ratio better than 0.5 for a subclass of MKP (B,S,m,n) with n⩽100, m⩽5 and $$\frac{{max_{j = 1}^n \left\{ {w_j } \right\}}}{{min_{i = 1}^m \left\{ {C_i } \right\}}} \leqslant \frac{2}{3}$$ .
Starting Page 241
Ending Page 250
Page Count 10
File Format PDF
ISSN 10051031
Journal Applied Mathematics-A Journal of Chinese Universities
Volume Number 17
Issue Number 2
e-ISSN 19930445
Language English
Publisher Editorial Committee of Applied Mathematics
Publisher Date 1993-01-01
Publisher Place Hangzhou
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword multiple knapsack problem semi-definite relaxation approximation algorithm combinatorial optimization Mathematics Applications of Mathematics
Content Type Text
Resource Type Article
Subject Applied Mathematics
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