scholarly journals Breeding diverse packings for the knapsack problem by means of diversity-tailored evolutionary algorithms

2021 ◽  
Author(s):  
Jakob Bossek ◽  
Aneta Neumann ◽  
Frank Neumann
Keyword(s):  
Evolutionary Algorithms ◽  
Knapsack Problem

Empirical Analysis of Locality, Heritability and Heuristic Bias in Evolutionary Algorithms: A Case Study for the Multidimensional Knapsack Problem

2005 ◽  
Vol 13 (4) ◽  
pp. 441-475 ◽  
Author(s):  
Günther R. Raidl ◽  
Jens Gottlieb
Keyword(s):  
Evolutionary Algorithms ◽  
Knapsack Problem ◽  
Multidimensional Knapsack Problem ◽  
Multidimensional Knapsack ◽  
Local Improvement ◽  
Hands On ◽  
Variation Operators ◽  
Insight Into ◽  
Shed Light

Our main aim is to provide guidelines and practical help for the design of appropriate representations and operators for evolutionary algorithms (EAs). For this purpose, we propose techniques to obtain a better understanding of various effects in the interplay of the representation and the operators. We study six different representations and associated variation operators in the context of a steady-state evolutionary algorithm for the multidimensional knapsack problem. Four of them are indirect decoder-based techniques, and two are direct encodings combined with different initialization, repair, and local improvement strategies. The complex decoders and the local improvement and repair strategies make it practically impossible to completely analyze such EAs in a fully theoretical way. After comparing the general performance of the chosen EA variants for the multidimensional knapsack problem on two benchmark suites, we present a hands-on approach for empirically analyzing important aspects of initialization, mutation, and crossover in an isolated fashion. Static, inexpensive measurements based on randomly created solutions are performed in order to quantify and visualize specific properties with respect to heuristic bias, locality, and heritability. These tests shed light onto the complex behavior of such EAs and point out reasons for good or bad performance. In addition, the proposed measures are also examined during actual EA runs, which gives further insight into dynamic aspects of evolutionary search and verifies the validity of the isolated static measurements. All measurements are described in a general way, allowing for an easy adaption to other representations and problems.

scholarly journals Comparison between Single and Multi-Objective Evolutionary Algorithms to Solve the Knapsack Problem and the Travelling Salesman Problem

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2018
Author(s):  
Mohammed Mahrach ◽  
Gara Miranda ◽  
Coromoto León ◽  
Eduardo Segredo
Keyword(s):  
Evolutionary Algorithms ◽  
Knapsack Problem ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Problem Formulation ◽  
Travelling Salesman ◽  
Multi Objective ◽  
Main Components ◽  
Pareto Fronts ◽  
Single Objective

One of the main components of most modern Multi-Objective Evolutionary Algorithms (MOEAs) is to maintain a proper diversity within a population in order to avoid the premature convergence problem. Due to this implicit feature that most MOEAs share, their application for Single-Objective Optimization (SO) might be helpful, and provides a promising field of research. Some common approaches to this topic are based on adding extra—and generally artificial—objectives to the problem formulation. However, when applying MOEAs to implicit Multi-Objective Optimization Problems (MOPs), it is not common to analyze how effective said approaches are in relation to optimizing each objective separately. In this paper, we present a comparative study between MOEAs and Single-Objective Evolutionary Algorithms (SOEAs) when optimizing every objective in a MOP, considering here the bi-objective case. For the study, we focus on two well-known and widely studied optimization problems: the Knapsack Problem (KNP) and the Travelling Salesman Problem (TSP). The experimental study considers three MOEAs and two SOEAs. Each SOEA is applied independently for each optimization objective, such that the optimized values obtained for each objective can be compared to the multi-objective solutions achieved by the MOEAs. MOEAs, however, allow optimizing two objectives at once, since the resulting Pareto fronts can be used to analyze the endpoints, i.e., the point optimizing objective 1 and the point optimizing objective 2. The experimental results show that, although MOEAs have to deal with several objectives simultaneously, they can compete with SOEAs, especially when dealing with strongly correlated or large instances.

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.

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