Solving the Set Packing Problem via a Maximum Weighted Independent Set Heuristic

The set packing problem (SPP) is a significant NP-hard combinatorial optimization problem with extensive applications. In this paper, we encode the set packing problem as the maximum weighted independent set (MWIS) problem and solve the encoded problem with an efficient algorithm designed to the MWIS problem. We compare the independent set-based method with the state-of-the-art algorithms for the set packing problem on the 64 standard benchmark instances. The experimental results show that the independent set-based method is superior to the existing algorithms in terms of the quality of the solutions and running time obtained the solutions.

Download Full-text

A NOVEL GREEDY GENETIC ALGORITHM TO SOLVE COMBINATORIAL OPTIMIZATION PROBLEM

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprs-archives-xliv-4-w3-2020-117-2020 ◽

2020 ◽

Vol XLIV-4/W3-2020 ◽

pp. 117-120

Author(s):

M. A. Basmassi ◽

L. Benameur ◽

J. A. Chentoufi

Keyword(s):

Genetic Algorithm ◽

Combinatorial Optimization ◽

Optimization Problem ◽

Combinatorial Optimization Problem ◽

Sequential Algorithm ◽

Solution Quality ◽

Graph Coloring Problem ◽

Benchmark Instances ◽

Crossover And Mutation

Abstract. In this paper, a modified genetic algorithm based on greedy sequential algorithm is presented to solve combinatorial optimization problem. The algorithm proposed here is a hybrid of heuristic and computational intelligence algorithm where greedy sequential algorithm is used as operator inside genetic algorithm like crossover and mutation. The greedy sequential function is used to correct non realizable solution after crossover and mutation which contribute to increase the rate of convergence and upgrade the population by improving the quality of chromosomes toward the chromatic number. Experiments on a set of 6 well-known DIMACS benchmark instances of graph coloring problem to test this approach show that the proposed algorithm achieves competitive results in comparison with three states of art algorithms in terms of either success rate and solution quality.

Download Full-text

On Complexity of Optimal Recombination for Binary Representations of Solutions

Evolutionary Computation ◽

10.1162/evco.2008.16.1.127 ◽

2008 ◽

Vol 16 (1) ◽

pp. 127-147 ◽

Cited By ~ 13

Author(s):

Anton V. Eremeev

Keyword(s):

Optimization Problem ◽

Minimum Weight ◽

Packing Problem ◽

Set Covering ◽

Set Packing ◽

Set Partition ◽

Maximum Weight ◽

Linear Programming Problems ◽

Optimal Recombination ◽

Set Packing Problem

We consider the optimization problem of finding the best possible offspring as a result of a recombination operator in an evolutionary algorithm, given two parent solutions. The optimal recombination is studied in the case where a vector of binary variables is used as a solution encoding. By means of efficient reductions of the optimal recombination problems (ORPs) we show the polynomial solvability of the ORPs for the maximum weight set packing problem, the minimum weight set partition problem, and for linear Boolean programming problems with at most two variables per inequality, and some other problems. We also identify several NP-hard cases of optimal recombination: the Boolean linear programming problems with three variables per inequality, the knapsack, the set covering, the p-median, and some other problems.

Download Full-text

From Decimation to Local Search and Back: A New Approach to MaxSAT

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/80 ◽

2017 ◽

Cited By ~ 7

Author(s):

Shaowei Cai ◽

Chuan Luo ◽

Haochen Zhang

Keyword(s):

Combinatorial Optimization ◽

Local Search ◽

Optimization Problem ◽

State Of The Art ◽

Search Algorithm ◽

Combinatorial Optimization Problem ◽

Np Hard ◽

Local Search Algorithm ◽

Maximum Satisfiability ◽

New Approach

Maximum Satisfiability (MaxSAT) is an important NP-hard combinatorial optimization problem with many applications and MaxSAT solving has attracted much interest. This work proposes a new incomplete approach to MaxSAT. We propose a novel decimation algorithm for MaxSAT, and then combine it with a local search algorithm. Our approach works by interleaving between the decimation algorithm and the local search algorithm, with useful information passed between them. Experiments show that our solver DeciLS achieves state of the art performance on all unweighted benchmarks from the MaxSAT Evaluation 2016. Moreover, compared to SAT-based MaxSAT solvers which dominate industrial benchmarks for years, it performs better on industrial benchmarks and significantly better on application formulas from SAT Competition. We also extend this approach to (Weighted) Partial MaxSAT, and the resulting solvers significantly improve local search solvers on crafted and industrial benchmarks, and are complementary (better on WPMS crafted benchmarks) to SAT-based solvers.

Download Full-text

Rectangular Bin-Packing Problem: a computational evaluation of 4 heuristics algorithms

U Porto Journal of Engineering ◽

10.24840/2183-6493_001.001_0005 ◽

2017 ◽

Vol 1 (1) ◽

pp. 35-49 ◽

Cited By ~ 2

Author(s):

Duarte Nuno Gonçalves Ferreira

Keyword(s):

Genetic Algorithm ◽

Optimization Problem ◽

Bin Packing ◽

Packing Problem ◽

Combinatorial Optimization Problem ◽

Two Dimensional ◽

Computational Evaluation ◽

Bin Packing Problem ◽

Benchmark Instances ◽

Minimum Number

The Rectangular Bin-packing Problem, also known as The Two-dimensional Bin-packing Problem (2DBPP), is a well-known combinatorial optimization problem which is the problem of orthogonally packing a given set of rectangles into a minimum number of two-dimensional rectangular bins. In this article we benchmark four heuristics: constructive, based on a First Fit Decreasing strategy, local search using a greedy packing First-Fit algorithm, Simulated Annealing with multiple cooling values and Genetic Algorithm. All implementations are written in Python, run using the Pypy environment and the new multiprocessing module. All implementations were tested using the Berkey and Wang and Martelo and Vigo Benchmark Instances.

Download Full-text

An Easy Way to Build Parallel State-of-the-art Combinatorial Optimization Problem Solvers: A Computational Study on Solving Steiner Tree Problems and Mixed Integer Semidefinite Programs by using ug[SCIP-,]-Libraries

2019 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW) ◽

10.1109/ipdpsw.2019.00095 ◽

2019 ◽

Author(s):

Yuji Shinano ◽

Daniel Rehfeldt ◽

Tristan Gally

Keyword(s):

Combinatorial Optimization ◽

Steiner Tree ◽

Optimization Problem ◽

State Of The Art ◽

Computational Study ◽

Combinatorial Optimization Problem ◽

Mixed Integer ◽

Semidefinite Programs ◽

Steiner Tree Problems ◽

Problem Solvers

Download Full-text

Combinatorial clustering and Its Application to 3D Polygonal Traffic Sign Reconstruction From Multiple Images

ISPRS Annals of Photogrammetry Remote Sensing and Spatial Information Sciences ◽

10.5194/isprsannals-ii-3-165-2014 ◽

2014 ◽

Vol II-3 ◽

pp. 165-172 ◽

Cited By ~ 1

Author(s):

B. Vallet ◽

B. Soheilian ◽

M. Brédif

Keyword(s):

Combinatorial Optimization ◽

3D Reconstruction ◽

Optimization Problem ◽

Combinatorial Optimization Problem ◽

Traffic Sign ◽

Multiple Images ◽

3D Objects ◽

Geometric Quality ◽

The Individual

The 3D reconstruction of similar 3D objects detected in 2D faces a major issue when it comes to grouping the 2D detections into clusters to be used to reconstruct the individual 3D objects. Simple clustering heuristics fail as soon as similar objects are close. This paper formulates a framework to use the geometric quality of the reconstruction as a hint to do a proper clustering. We present a methodology to solve the resulting combinatorial optimization problem with some simplifications and approximations in order to make it tractable. The proposed method is applied to the reconstruction of 3D traffic signs from their 2D detections to demonstrate its capacity to solve ambiguities.

Download Full-text