Interactive Decomposition Multi-Objective Optimization via Progressively Learned Value Functions

Decomposition has become an increasingly popular technique for evolutionary multi-objective optimization (EMO). A decomposition-based EMO algorithm is usually designed to approximate a whole Pareto-optimal front (PF). However, in practice, the decision maker (DM) might only be interested in her/his region of interest (ROI), i.e., a part of the PF. Solutions outside that might be useless or even noisy to the decision-making procedure. Furthermore, there is no guarantee to find the preferred solutions when tackling many-objective problems. This paper develops an interactive framework for the decomposition-based EMO algorithm to lead a DM to the preferred solutions of her/his choice. It consists of three modules, i.e., consultation, preference elicitation and optimization. Specifically, after every several generations, the DM is asked to score a few candidate solutions in a consultation session. Thereafter, an approximated value function, which models the DM's preference information, is progressively learned from the DM's behavior. In the preference elicitation session, the preference information learned in the consultation module is translated into the form that can be used in a decomposition-based EMO algorithm, i.e., a set of reference points that are biased toward to the ROI. The optimization module, which can be any decomposition-based EMO algorithm in principle, utilizes the biased reference points to direct its search process. Extensive experiments on benchmark problems with three to ten objectives fully demonstrate the effectiveness of our proposed method for finding the DM's preferred solutions.Comment: 25 pages, 18 figures, 3 table

A bi-objective genetic algorithm approach to risk mitigation in project scheduling

A problem of risk mitigation in project scheduling is formulated as a bi-objective optimization problem, where the expected makespan and the expected total cost are both to be minimized. The expected total cost is the sum of four cost components: overhead cost, activity execution cost, cost of reducing risks and penalty cost for tardiness. Risks for activities are predefined. For each risk at an activity, various levels are defined, which correspond to the results of different preventive measures. Only those risks with a probable impact on the duration of the related activity are considered here. Impacts of risks are not only accounted for through the expected makespan but are also translated into cost and thus have an impact on the expected total cost. An MIP model and a heuristic solution approach based on genetic algorithms (GAs) is proposed. The experiments conducted indicate that GAs provide a fast and effective solution approach to the problem. For smaller problems, the results obtained by the GA are very good. For larger problems, there is room for improvement

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

Research on Preference Polyhedron Model Based Evolutionary Multiobjective Optimization Method for Multilink Transmission Mechanism Conceptual Design

To make the optimal design of the multilink transmission mechanism applied in mechanical press, the intelligent optimization techniques are explored in this paper. A preference polyhedron model and new domination relationships evaluation methodology are proposed for the purpose of reaching balance among kinematic performance, dynamic performance, and other performances of the multilink transmission mechanism during the conceptual design phase. Based on the traditional evaluation index of single target of multicriteria design optimization, the robust metrics of the mechanism system and preference metrics of decision-maker are taken into consideration in this preference polyhedron model and reflected by geometrical characteristic of the model. At last, two optimized multilink transmission mechanisms are designed based on the proposed preference polyhedron model with different evolutionary algorithms, and the result verifies the validity of the proposed optimization method

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

A model for the decision-maker preferences in a polymer extrusion process

The NN-DM is a method developed to find a mathematical model that represents the Decision-Maker (DM) by employing an artificial neural network (NN) in situations in which the preferences can be represented by a utility function. This paper presents further developments to the NN-DM method to find a model in a polymer extrusion process. The form of the DM's interaction, the domain assignment, the ranking process, and the performance assessment are adapted to a real context of a multi-objective optimization problem followed by a design decision. The DM is then requested to fill a matrix expressing his preferences considering pairwise comparisons expressing ordinal relations only. Two multi-objective optimization problems are tested, each one with three estimates of different Pareto-optimal fronts. The adapted NN-DM method is able to provide a model which sorts the available solutions from the best to the worst according to the DM's preferences.info:eu-repo/semantics/publishedVersio

RIGA: A Regret-Based Interactive Genetic Algorithm

In this paper, we propose an interactive genetic algorithm for solving multi-objective combinatorial optimization problems under preference imprecision. More precisely, we consider problems where the decision maker's preferences over solutions can be represented by a parameterized aggregation function (e.g., a weighted sum, an OWA operator, a Choquet integral), and we assume that the parameters are initially not known by the recommendation system. In order to quickly make a good recommendation, we combine elicitation and search in the following way: 1) we use regret-based elicitation techniques to reduce the parameter space in a efficient way, 2) genetic operators are applied on parameter instances (instead of solutions) to better explore the parameter space, and 3) we generate promising solutions (population) using existing solving methods designed for the problem with known preferences. Our algorithm, called RIGA, can be applied to any multi-objective combinatorial optimization problem provided that the aggregation function is linear in its parameters and that a (near-)optimal solution can be efficiently determined for the problem with known preferences. We also study its theoretical performances: RIGA can be implemented in such way that it runs in polynomial time while asking no more than a polynomial number of queries. The method is tested on the multi-objective knapsack and traveling salesman problems. For several performance indicators (computation times, gap to optimality and number of queries), RIGA obtains better results than state-of-the-art algorithms