An Interactive Evolutionary Multiobjective Optimization Method Based on Progressively Approximated Value Functions

Abstract

This paper suggests a preference based methodology, which incorporates an evolutionary multiobjective optimization algorithm to lead a decision-maker to the most preferred solution of her or his choice. The progress towards the most preferred solution is made by accepting preference based information progressively from the decision maker after every few generations of an evolutionary multiobjective optimization algorithm. This preference information is used to model a strictly increasing value function, which is used for the subsequent iterations of the EMO algorithm. In addition to the development of the value function which satisfies DM's preference information, the proposed progressively interactive EMO (PI-EMO) approach utilizes the constructed value function in directing EMO algorithm's search to more preferred solutions. This is accomplished using a preference-based domination principle and utilizing a preference based termination criterion. Results on two to five-objective optimization problems using the progressively interactive NSGA-II approach shows the simplicity of the proposed approach and its future promise. A parametric study involving the algorithm's parameters reveals interesting insights of parameter interactions and indicates useful parameter values. A number of extensions to this study are also suggested.

Tester interactivity makes a difference in search-based software testing: A controlled experiment

“…The fitness function itself can be subject to change, including user preference as a factor in computing fitness [13,14], having elegance as a key factor in software design [15], or readjusting the fitness function to ensure that user preferred candidates receive a higher fitness score [16].…”

Interactive Evolutionary Multiple Objective Optimization for Group Decision Incorporating Value-based Preference Disaggregation Methods

“…These are used to derive the most discriminant additive linear value function, which serves to rank individuals in the evolutionary algorithm. Differently, in Deb et al (2010) one constructs a polynomial value function based on the DM's (partial) ranking of a small subset of solutions. Such function is employed to identify the most desirable solutions in the population and to reject a large subset of these which are non-relevant for the DM.…”

“…Hence, indirect preference questions have been proposed for lowering the elicitation effort (Kadziński and Tervonen 2013). In this regard, in some existing MOO studies, the DM is expected to provide a partial ranking for a limited subset of solutions (Deb et al 2010), to pick the best and the worst solutions from such subset (Korhonen et al 1984), or, more generally, to supply some pairwise comparisons (see Branke et al 2015;Phelps and Köksalan 2003). Such indirect preference information is claimed to be understandable, natural, and advantageous in terms of admitting the DM to see the connection between provided preferences and resulting recommendation .…”

Many-Objective Portfolio Optimization of Interdependent Projects with ‘a priori’ Incorporation of Decision-Maker Preferences

“…2.Those in which the DM makes pair-wise comparisons on a subset of the current population, in order to rank the sample's solutions (e.g. [41,42,43,44,45,46]). 3.Those in which pair-wise comparisons between pairs of objective functions are performed in order to rank the set of objective functions (e.g.…”