# Decision-Maker's Preference-Driven Dynamic Multi-Objective Optimization  
[Computer Science Division, Stellenbosch University, Stellenbosch University, Stellenbosch 7600, South Africa Department of Computer Science, University of Pretoria, Hatfield 0002, South Africa Department of Computer Science, University of Pretoria, Hatfield 0002, South Africa School of ICT, Griffith University, Southport 4215, Australia  
optimization problems (MOPs) [9; 19; 20; 21; 22; 23; 24; 25; 26; 27]. Most of these studies used a priori, interactive, and a posteriori approaches. It is noteworthy to state that to the best of the authors' knowledge, a priori and interactive preference incorporation methods have not been applied to DMOPs. Posteriori could have been applied when real-world problems were solved and a set of solutions were provided to the real-world DM.  
Introducing DM preferences, however, leads to a reformulation of DMOPs as constrained problems, which are then solved by dynamic multi-objective optimization algorithms (DMOAs) using a variation of a penalty function [28; 29; 30; 31; 32]. The constraints imparted on DMOPs as a result of DM preferences are defined in the objective space; thereby, the constraints partition the objective space into feasible and infeasible regions.  
The contributions of this study are  
* A preference incorporation method adapted for DMOPs that is partly a priori and partly interactive and enables a DM to specify their preferences. The a priori incorporation of DM preferences occurs through a procedure, named bootstrap. The interactive incorporation of preferences is employed whenever a change occurs in the dynamic environment such that the DM preference set may be significantly affected.
* A bounding box approach (refer to Equation (2) in Section 2) to specify a DM's preferences in the dynamic multi-objective optimization (DMOO) search process. The proposed bounding box, unlike the proposal in [33], is employed in the context of DMOPs, thus making it the first of its kind.
* New approaches that can drive a DMOA's search constrained by the DM's preferences, as well as a comparative analysis of the constraint managing approaches incorporated into a DMOA. The proposed constraint managing approaches are fundamentally different from one another in terms of how they penalize solutions that violate a DM's preferences.
* New performance measures that measure how well a found solution adheres to the preferences of a DM. In this article, a solution will henceforth be referred to as a decision.  
The base DMOA used in this study is a hybrid form of differential evolution (DE) [34], combining non-dominated sorting [35] with vector-evaluation schemes for selecting target vectors and the vectors that survive to the next generation during the optimization process, since it has been shown to perform well in solving DMOPs [36]. The proposed constraint managing approaches are incorporated in the same DMOA (the hybrid DE) to ensure a fair comparison of their performance. Their performance is measured using current (traditional) DMOO measures [1; 37; 38] and the new measures proposed in this article. It should be noted, however, that the constraint managing approaches and the preferences incorporation approaches can be incorporated into any DMOA.  
The rest of the article is organized as follows: Section 2 presents background concepts and theories required to understand the rest of the article. The experimental setup, including the algorithmic setup, benchmark functions, performance measures, and statistical analysis employed in the study are discussed in Section 3. Section 4 presents and discusses the results of the experiments. Finally, conclusions are presented in Section 5 based on the results obtained from the experiments.