A Kaizen Programming algorithm for multi-output regression based on a heterogeneous island model
Abstract: This article proposes an algorithm to construct multi-output symbolic regression models in a single execution. The algorithm extends the single-output Kaizen programming (KP) to a multi-output KP. KP is a hybrid evolutionary algorithm used to solve symbolic regression problems, without making any prior assumptions on the structure of the models. The extension to multi-output KP is made through an island model (MOKP\(_\mathrm{{IM}}\)). The idea behind MOKP\(_\mathrm{{IM}}\) is to find common terms among the outputs by balancing the solution obtained by each island working independently on a different output, with their cooperation due to the periodic exchange of migrants. In a previous effort, we followed a different approach for extending KP to multi-output scenarios based on using a multi-output linear regression in the linear regression step of the algorithm (MOKP\(_\mathrm{{MLR}}\)). A comparative analysis of the performance of MOKP\(_\mathrm{{IM}}\) with the classical single-output KP, our previous multi-output approach for KP, a multi-output Gaussian Process, and a multi-output decision tree regressor was conducted. The evaluation of algorithms used four different schemes of term sharing; five classical benchmark functions and a chemical process case study were considered for each scheme. The numerical results show that MOKP\(_\mathrm{{IM}}\) is the best-performing algorithm regarding both the independent analysis of each output and the global analysis of all the outputs together. The proposed algorithm MOKP\(_\mathrm{{IM}}\) outperformed the other multi-output symbolic regression methods tested in this work. It also obtained competitive results with state-of-the-art methods when the outputs were considered independently.
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