Using the ACS Approach to Solve Continuous Mathematical Problems in Engineering

Ant colony system (ACS) has been widely applied for solving discrete domain problems in recent years. In particular, they are efficient and effective in finding nearly optimal solutions to discrete search spaces. Because of the restriction of ant-based algorithms, when the solution space of a proble...

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Bibliographic Details
Published in:Mathematical problems in engineering 2014-01, Vol.2014 (2014), p.1-7
Main Authors: Wu, Min-Thai, Lee, Chung-Nan, Hong, Tzung Pei
Format: Article
Language:English
Subjects:
Algorithms
Binary codes
Computer science
Continuity (mathematics)
Domains
Experiments
Functions (mathematics)
Heuristic
Integer programming
Mathematical analysis
Mathematical functions
Mathematical problems
Operators (mathematics)
Optimization
Pheromones
Problem solving
Real variables
Searching
Solution space
Transition rules
Variables
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Summary:Ant colony system (ACS) has been widely applied for solving discrete domain problems in recent years. In particular, they are efficient and effective in finding nearly optimal solutions to discrete search spaces. Because of the restriction of ant-based algorithms, when the solution space of a problem to be solved is continuous, it is not so appropriate to use the original ACS to solve it. However, engineering mathematics in the real applications are always applied in the continuous domain. This paper thus proposes an extended ACS approach based on binary-coding to provide a standard process for solving problems with continuous variables. It first encodes solution space for continuous domain into a discrete binary-coding space (searching map), and a modified ACS can be applied to find the solution. Each selected edge in a complete path represents a part of a candidate solution. Different from the previous ant-based algorithms for continuous domain, the proposed binary coding ACS (BCACS) could retain the original operators and keep the benefits and characteristics of the traditional ACS. Besides, the proposed approach is easy to implement and could be applied in different kinds of problems in addition to mathematical problems. Several constrained functions are also evaluated to demonstrate the performance of the proposed algorithm.
ISSN:1024-123X
1563-5147
DOI:10.1155/2014/142194