Preference incorporation in MOEA/D using an outranking approach with imprecise model parameters

Multi-objective Optimization Evolutionary Algorithms (MOEAs) face numerous challenges when they are used to solve Many-objective Optimization Problems (MaOPs). Decomposition-based strategies, such as MOEA/D, divide an MaOP into multiple single-optimization sub-problems, achieving better diversity and a better approximation of the Pareto front, and dealing with some of the challenges of MaOPs. However, these approaches still require one to solve a multi-criteria selection problem that will allow a Decision-Maker (DM) to choose the final solution. Incorporating preferences may provide results that are closer to the region of interest of a DM. Most of the proposals to integrate preferences in decomposition-based MOEAs prefer progressive articulation over the “a priori” incorporation of preferences. Progressive articulation methods can hardly work without comparable and transitive preferences, and they can significantly increase the cognitive effort required of a DM. On the other hand, the “a priori” strategies do not demand transitive judgements from the DM but require a direct parameter elicitation that usually is subject to imprecision. Outranking approaches have properties that allow them to suitably handle non-transitive preferences, veto conditions, and incomparability, which are typical characteristics of many real DMs. This paper explores how to incorporate DM preferences into MOEA/D using the “a priori” incorporation of preferences, based on interval outranking relations, to handle imprecision when preference parameters are elicited. Several experiments make it possible to analyze the proposal's performance on benchmark problems and to compare the results with the classic MOEA/D without preference incorporation and with a recent, state-of-the-art preference-based decomposition algorithm. In many instances, our results are closer to the Region of Interest, particularly when the number of objectives increases

Integration of Preferences in Decomposition Multiobjective Optimization

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.© 2018 IEEE. Rather than a whole Pareto-optimal front, which demands too many points (especially in a high-dimensional space), the decision maker (DM) may only be interested in a partial region, called the region of interest (ROI). In this case, solutions outside this region can be noisy to the decision-making procedure. Even worse, there is no guarantee that we can find the preferred solutions when tackling problems with complicated properties or many objectives. In this paper, we develop a systematic way to incorporate the DM's preference information into the decomposition-based evolutionary multiobjective optimization methods. Generally speaking, our basic idea is a nonuniform mapping scheme by which the originally evenly distributed reference points on a canonical simplex can be mapped to new positions close to the aspiration-level vector supplied by the DM. By this means, we are able to steer the search process toward the ROI either directly or interactively and also handle many objectives. Meanwhile, solutions lying on the boundary can be approximated as well given the DM's requirements. Furthermore, the extent of the ROI is intuitively understandable and controllable in a closed form. Extensive experiments on a variety of benchmark problems with 2 to 10 objectives, fully demonstrate the effectiveness of our proposed method for approximating the preferred solutions in the ROI.Royal Society (Government)Ministry of Science and Technology of ChinaScience and Technology Innovation Committee Foundation of ShenzhenShenzhen Peacock PlanEngineering and Physical Sciences Research Council (EPSRC)Engineering and Physical Sciences Research Council (EPSRC

Evolutionary optimization using equitable fuzzy sorting genetic algorithm (EFSGA)

https://ieeexplore.ieee.org/document/8598717This paper presents a fuzzy dominance-based analytical sorting method as an advancement to the existing multi-objective evolutionary algorithms (MOEA). Evolutionary algorithms (EAs), on account of their sorting schemes, may not establish clear discrimination amongst solutions while solving many-objective optimization problems. Moreover, these algorithms are also criticized for issues such as uncertain termination criterion and difficulty in selecting a final solution from the set of Pareto optimal solutions for practical purposes. An alternate approach, referred here as equitable fuzzy sorting genetic algorithm (EFSGA), is proposed in this paper to address these vital issues. Objective functions are defined as fuzzy objectives and competing solutions are provided an overall activation score (OAS) based on their respective fuzzy objective values. Subsequently, OAS is used to assign an explicit fuzzy dominance ranking to these solutions for improved sorting process. Benchmark optimization problems, used as case studies, are optimized using proposed algorithm with three other prevailing methods. Performance indices are obtained to evaluate various aspects of the proposed algorithm and present a comparison with existing methods. It is shown that the EFSGA exhibits strong discrimination ability and provides unambiguous termination criterion. The proposed approach can also help user in selecting final solution from the set of Pareto optimal solutions