Ant Colony Optimization for Mixed-Variable Optimization Problems

In this paper, we introduce ACO_MV: an ant colony optimization (ACO) algorithm that extends the ACO_R algorithm for continuous optimization to tackle mixed-variable optimization problems. In ACO_MV, the decision variables of an optimization problem can be explicitly declared as continuous, ordinal, or categorical, which allows the algorithm to treat them adequately. ACO_MV includes three solution generation mechanisms: a continuous optimization mechanism (ACO_R), a continuous relaxation mechanism (ACO_MV-o) for ordinal variables, and a categorical optimization mechanism (ACO_MV-c) for categorical variables. Together, these mechanisms allow ACO_MV to tackle mixed-variable optimization problems. We also define a novel procedure to generate artificial, mixed-variable benchmark functions, and we use it to automatically tune ACO_MV´s parameters. The tuned ACO_MV is tested on various real-world continuous and mixed-variable engineering optimization problems. Comparisons with results from the literature demonstrate the effectiveness and robustness of ACO_MV on mixed-variable optimization problems.