Interactive Multiobjective Optimization: A Review of the State-of-the-Art

Interactive multiobjective optimization (IMO) aims at finding the most preferred solution of a decision maker with the guidance of his/her preferences which are provided progressively. During the process, the decision maker can adjust his/her preferences and explore only interested regions of the search space. In recent decades, IMO has gradually become a common interest of two distinct communities, namely, the multiple criteria decision making (MCDM) and the evolutionary multiobjective optimization (EMO). The IMO methods developed by the MCDM community usually use the mathematical programming methodology to search for a single preferred Pareto optimal solution, while those which are rooted in EMO often employ evolutionary algorithms to generate a representative set of solutions in the decision maker's preferred region. This paper aims to give a review of IMO research from both MCDM and EMO perspectives. Taking into account four classification criteria including the interaction pattern, preference information, preference model, and search engine (i.e., optimization algorithm), a taxonomy is established to identify important IMO factors and differentiate various IMO methods. According to the taxonomy, state-of-the-art IMO methods are categorized and reviewed and the design ideas behind them are summarized. A collection of important issues, e.g., the burdens, cognitive biases and preference inconsistency of decision makers, and the performance measures and metrics for evaluating IMO methods, are highlighted and discussed. Several promising directions worthy of future research are also presented.