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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 142194, 7 pages
Research Article

Using the ACS Approach to Solve Continuous Mathematical Problems in Engineering

1Department of Computer Science and Engineering, National Sun Yat-sen University, 70 Lienhai Road, Kaohsiung 80424, Taiwan
2Department of Computer Science and Information Engineering, National University of Kaohsiung, 700 Kaohsiung University Road, Kaohsiung 81148, Taiwan

Received 15 February 2014; Revised 16 May 2014; Accepted 6 June 2014; Published 24 June 2014

Academic Editor: Jianquan Lu

Copyright © 2014 Min-Thai Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.