BAG-DSM: A Method for Generating Alternatives for Hierarchical Multi-Attribute Decision Models Using Bayesian Optimization

Funding Information: Funding: This work was partially funded by the Slovenian Research Agency (ARRS) under research core funding Knowledge Technologies No. P2-0103 (B), and by the Slovenian Ministry of Education, Science and Sport (funding agreement No. C3330-17-529020). Publisher Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. Multi-attribute decision analysis is an approach to decision support in which decision alternatives are evaluated by multi-criteria models. An advanced feature of decision support models is the possibility to search for new alternatives that satisfy certain conditions. This task is important for practical decision support; however, the related work on generating alternatives for qualitative multi-attribute decision models is quite scarce. In this paper, we introduce Bayesian Alternative Generator for Decision Support Models (BAG-DSM), a method to address the problem of generating alternatives. More specifically, given a multi-attribute hierarchical model and an alternative representing the initial state, the goal is to generate alternatives that demand the least change in the provided alternative to obtain a desirable outcome. The brute force approach has exponential time complexity and has prohibitively long execution times, even for moderately sized models. BAGDSM avoids these problems by using a Bayesian optimization approach adapted to qualitative DEX models. BAG-DSM was extensively evaluated and compared to a baseline method on 43 different DEX decision models with varying complexity, e.g., different depth and attribute importance. The comparison was performed with respect to: the time to obtain the first appropriate alternative, the number of generated alternatives, and the number of attribute changes required to reach the generated alternatives. BAG-DSM outperforms the baseline in all of the experiments by a large margin. Additionally, the evaluation confirms BAG-DSM’s suitability for the task, i.e., on average, it generates at least one appropriate alternative within two seconds. The relation between the depth of the multi-attribute hierarchical models—a parameter that increases the search space exponentially— and the time to obtaining the first appropriate alternative was linear and not exponential, by which BAG-DSM’s scalability is empirically confirmed.