Decision Trees+Evolutionary Algorithm for Predict then Optimize Kevin Lagos Universidad Técnica Federico Santa María Valparaíso, Chile Andrés Navarro Universidad Técnica Federico Santa María Valparaíso, Chile Felipe Dumont Universidad Técnica Federico Santa María Valparaíso, Chile María Cristina Riff Universidad Técnica Federico Santa María Valparaíso, Chile maria-cristina.riff@inf.utfsm.cl ABSTRACT We present a collaboration between decision trees and an evolution- ary algorithm inspired by Smart "Predict then Optimize" framework. In this work, we analyze the requirements for designing an evolu- tionary algorithm to solve complex combinatorial problem which can change over the time. We study the effect of changing the parameters of the objective function and how we can adapt the evolutionary algorithm to efficiently tackle new conditions of the problem. To predict the parameters of the objective function we use a decision tree. We evaluate our collaborative schema using instances for the shortest path problem and compare it with re- cently published work that uses complete techniques, obtaining encouraging results. KEYWORDS evolutionary algorithms, combinatorial optimization, dynamic op- timization ACM Reference Format: Kevin Lagos, Andrés Navarro, Felipe Dumont, and María Cristina Riff. 2023. Decision Trees+Evolutionary Algorithm for Predict then Optimize. In . ACM, New York, NY, USA, 4 pages. https://doi.org/10.1145/3583133.3590683 1 INTRODUCTION In this paper, we explore the integration of Smart "Predict then Optimize" (SPO) framework [2] with evolutionary algorithms for solving optimization problems that change over time. The predict- then-optimize paradigm has been widely used in analytical practices to handle the complexity of both tasks. However, SPO proposes a new framework that measures the sub-optimality of the results obtained with the predicted parameters instead of minimizing the prediction error. We use SPOT [3], an implementation of SPO that uses decision trees for the prediction step. Our research question is whether it is possible to reduce the decision error of a complete approach by using an evolutionary algorithm in the SPOT framework. To answer this question, we solve instances of the shortest path problem and evaluate and compare our approach. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the owner/author(s). GECCO ’23 Companion, July 15–19, 2023, Lisbon, Portugal © 2023 Copyright held by the owner/author(s). ACM ISBN 979-8-4007-0120-7/23/07. https://doi.org/10.1145/3583133.3590683 The contributions of this paper are: (1) a study of the SPO frame- work using decision trees in combination with an evolutionary algorithm, and (2) guidelines for designing evolutionary algorithms that can handle problems that change over time, reducing the need for re-tuning and re-designing the algorithm. Our research aims to identify the requirements for designing evolutionary algorithms that can react to problems that change over time, and to extend the analysis of the SPO technique by using an incomplete approach for the optimization task, specifically an evolutionary algorithm in collaboration with decision trees for the prediction task. 2 RELATED WORK In [2], the SPO Framework is proposed, which takes into account the optimization task during prediction of unknown parameters. Linear optimization models and a new loss function, SPO loss, are discussed, with a surrogate loss function, SPO+ loss, proposed to overcome non-differentiability issues. The framework is tested on the Shortest Path Problem and Portfolio Optimization, and applied to the Last-mile Delivery Problem in [1]. In [3], decision trees are trained using the SPO loss function, with experiments conducted on the Shortest Path Problem. 3 SMART PREDICT THEN OPTIMIZE Smart Predict then Optimize (SPO) has been proposed by Elmach- toub and Grigas in [2]. This framework has been designed for linear optimization models with unknown parameters on a convex fea- sible region. They applied it to solve the shortest path problem, where the goal is to reduce costs, the constraints are related to the network flow and the context concerns time of the day, holidays, speed limit, traffic, strike, etc. Roughly speaking the problem to solve is an optimization combinatorial problem with unknown edge costs. In this case usually there are available historical data that can be used to estimate the edge costs. Some features that can be useful to take into account for this problem could be the day, time of the day, available routes, flow direction, etc. For instance, in particular, in our city some routes change direction according to the time of the day. The generic problem to solve is: min  ∈ ( | )   (1) where  ∈ R  are the decision variables,  | ∈ R  is the problem data describing the linear objective function where  | are the costs for a context  and  ⊆ R  corresponds to the feasible region. SPO has two steps: the first one to predict and the second one to 731