Ant Colony Optimization for Mixed-Variable Optimization Problems 论文
摘要
In this paper, we introduce ACO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MV</sub> : an ant colony optimization (ACO) algorithm that extends the ACO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> algorithm for continuous optimization to tackle mixed-variable optimization problems. In ACO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MV</sub> , 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MV</sub> includes three solution generation mechanisms: a continuous optimization mechanism (ACO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> ), a continuous relaxation mechanism (ACO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MV</sub> -o) for ordinal variables, and a categorical optimization mechanism (ACO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MV</sub> -c) for categorical variables. Together, these mechanisms allow ACO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MV</sub> 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MV</sub> 's parameters. The tuned ACO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MV</sub> 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MV</sub> on mixed-variable optimization problems.