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Most real world engineering design problems, such as cross-country water mains, include combinations of continuous, discrete, and binary value decision variables. Very often, the binary decision variables associate with the presence and/or absence of some nominated alternatives or project’s components. This study extends an existing continuous Ant Colony Optimization (ACO) algorithm to simultaneously handle mixed-variable problems. The approach provides simultaneous solution to a binary value problem with both discrete and continuous variables to locate and size design components of the proposed system. This paper shows how the existing continuous ACO algorithm may be revised to cope with mixed-variable search spaces with binary variables. Performance of the proposed version of the ACO is tested on a set of mathematical benchmark problems followed by a highly nonlinear forced water main optimization problem. Comparing with few other optimization algorithms, the proposed optimization method demonstrates satisfactory performance in locating good near optimal solutions.

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Ant colony optimization algorithms (ACOs) have been basically introduced to discrete variable problems and applied to different research domains in several engineering fields. Meanwhile, abundant studies have been already involved to adapt different ant models to continuous search spaces. Assessments indicate competitive performance of ACOs on discrete or continuous domains. Therefore, as potent optimization algorithms, it is encouraging to involve ant models to mixed-variable domains which simultaneously tackle discrete and continuous variables. This paper introduces four ant-based methods to solve mixed-variable problems. Each method is based upon superlative ant algorithms in discrete and/or continuous domains. Proposed methods’ performances are then tested on a set of three mathematical functions and also a water main design problem in engineering field, which are elaborately subject to linear and non-linear constraints. All proposed methods perform rather satisfactorily on considered problems and it is suggested to further extend the application of methods to other engineering studies.