Estimation of distribution algorithms using Gaussian Bayesian networks to solve industrial optimization problems constrained by environment variables

• Published in: Journal of combinatorial optimization 2022-09, Vol.44 (2), p.1077-1098
• Main Authors: Soloviev, Vicente P., Larrañaga, Pedro, Bielza, Concha
• Format: Article
• Language: English
• Subjects: Algorithms; Bayesian analysis; Combinatorics; Convex and Discrete Geometry; Cost function; Iterative methods; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Normal distribution; Operations Research/Decision Theory; Optimization; Real variables; Theory of Computation
• ISSN: 1382-6905; 1573-2886
• DOI: 10.1007/s10878-022-00879-6

Many real-world optimization problems involve two different subsets of variables: decision variables, and those variables which are not present in the cost function but constrain the solutions, and thus, must be considered during optimization. Thus, dependencies between and within both subsets of variables must be considered. In this paper, an estimation of distribution algorithm (EDA) is implemented to solve this type of complex optimization problems. A Gaussian Bayesian network is used to build an abstraction model of the search space in each iteration to identify patterns among the variables. As the algorithm is initialized from data, we introduce a new hyper-parameter to control the influence of the initial data in the decisions made during the EDA execution. The results show that our algorithm improves the cost function more than the expert knowledge does.