Ant Colony Optimization and Multiple Knapsack Problem

2007 ◽  
pp. 498-509 ◽  
Author(s):  
S. Fidanova
Keyword(s):  
Combinatorial Optimization ◽  
Ant Colony Optimization ◽  
Knapsack Problem ◽  
Optimization Problem ◽  
Combinatorial Optimization Problem ◽  
Ant Colony ◽  
Multiple Knapsack Problem ◽  
Constraint Problem ◽  
Multiple Knapsack ◽  
Ant Colony Optimization Algorithms

The ant colony optimization algorithms and their applications on the multiple knapsack problem (MKP) are introduced. The MKP is a hard combinatorial optimization problem with wide application. Problems from different industrial fields can be interpreted as a knapsack problem including financial and other management. The MKP is represented by a graph, and solutions are represented by paths through the graph. Two pheromone models are compared: pheromone on nodes and pheromone on arcs of the graph. The MKP is a constraint problem which provides possibilities to use varied heuristic information. The purpose of the chapter is to compare a variety of heuristic and pheromone models and different variants of ACO algorithms on MKP.

scholarly journals ANALYSIS AND SYNTHESIS OF ENHANCED ANT COLONY OPTIMIZATION WITH THE TRADITIONAL ANT COLONY OPTIMIZATION TO SOLVE TRAVELLING SALES PERSON PROBLEM

2011 ◽  
Vol 1 (1) ◽  
pp. 88-92
Author(s):  
Pallavi Arora ◽  
Harjeet Kaur ◽  
Prateek Agrawal
Keyword(s):  
Combinatorial Optimization ◽  
Ant Colony Optimization ◽  
Optimization Problem ◽  
Traditional Approach ◽  
Combinatorial Optimization Problem ◽  
Ant Colony ◽  
Ant Colony Optimization Algorithm ◽  
Analysis And Synthesis ◽  
Heuristic Technique ◽  
Travelling Salesperson Problem

Ant Colony optimization is a heuristic technique which has been applied to a number of combinatorial optimization problem and is based on the foraging behavior of the ants. Travelling Salesperson problem is a combinatorial optimization problem which requires that each city should be visited once. In this research paper we use the K means clustering technique and Enhanced Ant Colony Optimization algorithm to solve the TSP problem. We show a comparison of the traditional approach with the proposed approach. The simulated results show that the proposed algorithm is better compared to the traditional approach.

A Review and Comparison of Genetic Algorithms for the 0-1 Multidimensional Knapsack Problem

2015 ◽  
Vol 6 (2) ◽  
pp. 21-31 ◽  
Author(s):  
Bernhard Lienland ◽  
Li Zeng
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Combinatorial Optimization ◽  
Knapsack Problem ◽  
Optimization Problem ◽  
Real Life ◽  
Combinatorial Optimization Problem ◽  
Multidimensional Knapsack Problem ◽  
Multidimensional Knapsack ◽  
Problem Types

The 0-1 multidimensional knapsack problem (MKP) is a well-known combinatorial optimization problem with several real-life applications, for example, in project selection. Genetic algorithms (GA) are effective heuristics for solving the 0-1 MKP. Multiple individual GAs with specific characteristics have been proposed in literature. However, so far, these approaches have only been partially compared in multiple studies with unequal conditions. Therefore, to identify the “best” genetic algorithm, this article reviews and compares 11 existing GAs. The authors' tests provide detailed information on the GAs themselves as well as their performance. The authors validated fitness values and required computation times in varying problem types and environments. Results demonstrate the superiority of one GA.

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.

A Rank Based ACO Approach for Optimal Resource Allocation and Scheduling in FMS Modeled with Labelled Petri Net

2021 ◽  
Author(s):  
Amira Jablaoui ◽  
Hichem Kmimech ◽  
Layth Sliman ◽  
Lotfi Nabli
Keyword(s):  
Resource Allocation ◽  
Combinatorial Optimization ◽  
Ant Colony Optimization ◽  
Petri Net ◽  
Flexible Manufacturing ◽  
Optimization Problem ◽  
Flexible Manufacturing System ◽  
Combinatorial Optimization Problem ◽  
Optimal Resource Allocation ◽  
Optimal Resource

In this article, we study the NP-Hard combinatorial optimization problem of the minimum initial marking (MIM) computation in labeled Petri net (L-PN) while considering a sequence of labels to minimize the resource consumption in a flexible manufacturing system (FMS), and we propose an approach based on the ant colony optimization (ACO) precisely the extension Rank-based ACO to optimal resource allocation and scheduling in FMS. The ACO meta-heuristic is inspired by the behavior of ants in foraging based on pheromones deposit. The numerical results show that the proposed algorithm obtained much better results than previous studies.

Optimization of Torch Movements of Welding and Cutting Using Ant Colony Method

2009 ◽  
Vol 25 (03) ◽  
pp. 136-141
Author(s):  
Yasuhisa Okumoto
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Heuristic Method ◽  
Computation Time ◽  
Optimization Method ◽  
Combinatorial Optimization Problem ◽  
Ant Colony ◽  
Hull Structure ◽  
Optimum Path ◽  
The Traveling Salesman Problem

Though many methods are applied to solve the combinatorial optimization problem, there are many cases in which the solution cannot be solved in practical computation time, even if the computer becomes more advanced. Recently the "ant colony optimization method (ACO)" has been proposed as one of the meta-heuristic method. This research tried the ACO in ship production field. Firstly, the ACO was applied and verified for the traveling salesman problem (TSP) to obtain the shortest path in many cities, as a representative combinatorial optimization problem. Next, based on the result, the ACO was applied to the problem in search of the optimum torch movement of a welding robot for the assembly of ship hull structure, and of a NC plasma cutting machine of steel plate. As a result, it was confirmed that the ACO is effective to solve the optimum path of machines.

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