An Information-Theoretic Analysis on the Interactions of Variables in Combinatorial Optimization Problems

2007 ◽  
Vol 15 (2) ◽  
pp. 169-198 ◽  
Author(s):  
Dong-Il Seo ◽  
Byung-Ro Moon
Keyword(s):  
Information Theory ◽  
Combinatorial Optimization ◽  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Experimental Results ◽  
Theoretic Analysis ◽  
Information Theoretic ◽  
Combinatorial Optimization Problems ◽  
Theoretical Results

In optimization problems, the contribution of a variable to fitness often depends on the states of other variables. This phenomenon is referred to as epistasis or linkage. In this paper, we show that a new theory of epistasis can be established on the basis of Shannon's information theory. From this, we derive a new epistasis measure called entropic epistasis and some theoretical results. We also provide experimental results verifying the measure and showing how it can be used for designing efficient evolutionary algorithms.

A Quantum-Inspired Evolutionary Algorithm with Elite Group Guided

2015 ◽  
Vol 738-739 ◽  
pp. 323-333 ◽  
Author(s):  
Sheng Xiang ◽  
Yi Gang He
Keyword(s):  
Combinatorial Optimization ◽  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Knapsack Problems ◽  
Elite Group ◽  
Combinatorial Optimization Problems ◽  
Np Complete ◽  
Number Of Individuals

To improve the performance of quantum-inspired evolutionary algorithms (QIEAs), a new kind of QIEAs——elite group guided QIEA (EQIEA) are proposed through introducing an elite group guidance updating approach to solve knapsack problems. In EQIEA, the elite group at each iteration is composed of a certain number of individuals with better fitness values in the current population; all the individuals in the elite group cooperate together to affect quantum-inspired gates to produce off spring. Knapsack problems, a class of well-known NP-complete combinatorial optimization problems, are used to conduct experiments. The choices of parameters in EQIEA are discussed in an empirical way. Extensive experiments show that the EQIEA outperform six variants of QIEAs recently reported in the literature in terms of the quality of solutions. This paper also analyzes the convergence of EQIEA and the six variants of QIEAs. Experimental results show that EQIEA has better convergence than the six variants of QIEAs.

An Improved Generalized Quantum-Inspired Evolutionary Algorithm for Multiple Knapsack Problem

2021 ◽  
pp. 22-50
Author(s):  
Sulabh Bansal ◽  
C. Patvardhan
Keyword(s):  
Combinatorial Optimization ◽  
Evolutionary Algorithms ◽  
Knapsack Problem ◽  
Optimization Problems ◽  
Problem Solution ◽  
Np Hard ◽  
Combinatorial Optimization Problems ◽  
Multiple Knapsack Problem ◽  
Multiple Knapsack ◽  
Decimal Numbers

This article describes how the 0/1 Multiple Knapsack Problem (MKP), a generalization of popular 0/1 Knapsack Problem, is NP-hard and harder than simple Knapsack Problem. Solution of MKP involves two levels of choice – one for selecting an item to be placed and the other for selecting the knapsack in which it is to be placed. Quantum Inspired Evolutionary Algorithms (QIEAs), a subclass of Evolutionary algorithms, have been shown to be effective in solving difficult problems particularly NP-hard combinatorial optimization problems. QIEAs provide a general framework which needs to be customized according to the requirements of a given problem to obtain good solutions in reasonable time. An existing QIEA for MKP (QIEA-MKP) is based on the representation where a Q-bit collapse into a binary number. But decimal numbers are required to identify the knapsack where an item is placed. The implementation based on such representation suffers from overhead of frequent conversion from binary numbers to decimal numbers and vice versa. The generalized QIEA (GQIEA) is based on a representation where a Q-bit can collapse into an integer and thus no inter conversion between binary and decimal is required. A set of carefully selected features have been incorporated in proposed GQIEA-MKP to obtain better solutions in lesser time. Comparison with QIEA-MKP shows that GQIEA-MKP outperforms it in providing better solutions in lesser time for large sized MKPs. The generalization proposed can be used with advantage in other Combinatorial Optimization problems with integer strings as solutions.

An Improved Generalized Quantum-Inspired Evolutionary Algorithm for Multiple Knapsack Problem

2018 ◽  
Vol 9 (1) ◽  
pp. 17-51
Author(s):  
Sulabh Bansal ◽  
C. Patvardhan
Keyword(s):  
Combinatorial Optimization ◽  
Evolutionary Algorithms ◽  
Knapsack Problem ◽  
Optimization Problems ◽  
Binary Number ◽  
Np Hard ◽  
Combinatorial Optimization Problems ◽  
Multiple Knapsack Problem ◽  
Multiple Knapsack ◽  
Decimal Numbers

This article describes how the 0/1 Multiple Knapsack Problem (MKP), a generalization of popular 0/1 Knapsack Problem, is NP-hard and harder than simple Knapsack Problem. Solution of MKP involves two levels of choice – one for selecting an item to be placed and the other for selecting the knapsack in which it is to be placed. Quantum Inspired Evolutionary Algorithms (QIEAs), a subclass of Evolutionary algorithms, have been shown to be effective in solving difficult problems particularly NP-hard combinatorial optimization problems. QIEAs provide a general framework which needs to be customized according to the requirements of a given problem to obtain good solutions in reasonable time. An existing QIEA for MKP (QIEA-MKP) is based on the representation where a Q-bit collapse into a binary number. But decimal numbers are required to identify the knapsack where an item is placed. The implementation based on such representation suffers from overhead of frequent conversion from binary numbers to decimal numbers and vice versa. The generalized QIEA (GQIEA) is based on a representation where a Q-bit can collapse into an integer and thus no inter conversion between binary and decimal is required. A set of carefully selected features have been incorporated in proposed GQIEA-MKP to obtain better solutions in lesser time. Comparison with QIEA-MKP shows that GQIEA-MKP outperforms it in providing better solutions in lesser time for large sized MKPs. The generalization proposed can be used with advantage in other Combinatorial Optimization problems with integer strings as solutions.

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