Progressive Preference Articulation for Decision Making in Multi-Objective Optimisation Problems

This paper proposes a novel algorithm for addressing multi-objective optimisation problems, by employing a progressive preference articu- lation approach to decision making. This enables the interactive incorporation of problem knowledge and decision maker preferences during the optimisation process. A novel progressive preference articulation mechanism, derived from a statistical technique, is herein proposed and implemented within a multi-objective framework based on evolution strategy search and hypervolume indicator selection. The proposed algo- rithm is named the Weighted Z-score Covariance Matrix Adaptation Pareto Archived Evolution Strategy with Hypervolume-sorted Adaptive Grid Algorithm (WZ-HAGA). WZ-HAGA is based on a framework that makes use of evolution strategy logic with covariance matrix adaptation to perturb the solutions, and a hypervolume indicator driven algorithm to select successful solutions for the subsequent generation. In order to guide the search towards interesting regions, a preference articulation procedure composed of four phases and based on the weighted z-score approach is employed. The latter procedure cascades into the hypervolume driven algorithm to perform the selection of the solutions at each generation. Numerical results against five modern algorithms representing the state-of-the-art in multi-objective optimisation demonstrate that the pro- posed WZ-HAGA outperforms its competitors in terms of both the hypervolume indicator and pertinence to the regions of interest

Evolutionary Many-objective Optimization of Hybrid Electric Vehicle Control: From General Optimization to Preference Articulation

Many real-world optimization problems have more than three objectives, which has triggered increasing research interest in developing efficient and effective evolutionary algorithms for solving many-objective optimization problems. However, most many-objective evolutionary algorithms have only been evaluated on benchmark test functions and few applied to real-world optimization problems. To move a step forward, this paper presents a case study of solving a many-objective hybrid electric vehicle controller design problem using three state-of-the-art algorithms, namely, a decomposition based evolutionary algorithm (MOEA/D), a non-dominated sorting based genetic algorithm (NSGA-III), and a reference vector guided evolutionary algorithm (RVEA). We start with a typical setting aiming at approximating the Pareto front without introducing any user preferences. Based on the analyses of the approximated Pareto front, we introduce a preference articulation method and embed it in the three evolutionary algorithms for identifying solutions that the decision-maker prefers. Our experimental results demonstrate that by incorporating user preferences into many-objective evolutionary algorithms, we are not only able to gain deep insight into the trade-off relationships between the objectives, but also to achieve high-quality solutions reflecting the decision-maker’s preferences. In addition, our experimental results indicate that each of the three algorithms examined in this work has its unique advantages that can be exploited when applied to the optimization of real-world problems

User preference extraction using dynamic query sliders in conjunction with UPS-EMO algorithm

One drawback of evolutionary multiobjective optimization algorithms (EMOA) has traditionally been high computational cost to create an approximation of the Pareto front: number of required objective function evaluations usually grows high. On the other hand, for the decision maker (DM) it may be difficult to select one of the many produced solutions as the final one, especially in the case of more than two objectives. To overcome the above mentioned drawbacks number of EMOA's incorporating the decision makers preference information have been proposed. In this case, it is possible to save objective function evaluations by generating only the part of the front the DM is interested in, thus also narrowing down the pool of possible selections for the final solution. Unfortunately, most of the current EMO approaches utilizing preferences are not very intuitive to use, i.e. they may require tweaking of unintuitive parameters, and it is not always clear what kind of results one can get with given set of parameters. In this study we propose a new approach to visually inspect produced solutions, and to extract preference information from the DM to further guide the search. Our approach is based on intuitive use of dynamic query sliders, which serve as a means to extract preference information and are part of the graphical user interface implemented for the efficient UPS-EMO algorithm

An ACO-based Hyper-heuristic for Sequencing Many-objective Evolutionary Algorithms that Consider Different Ways to Incorporate the DM's Preferences

Many-objective optimization is an area of interest common to researchers, professionals, and practitioners because of its real-world implications. Preference incorporation into Multi-Objective Evolutionary Algorithms (MOEAs) is one of the current approaches to treat Many-Objective Optimization Problems (MaOPs). Some recent studies have focused on the advantages of embedding preference models based on interval outranking into MOEAs; several models have been proposed to achieve it. Since there are many factors influencing the choice of the best outranking model, there is no clear notion of which is the best model to incorporate the preferences of the decision maker into a particular problem. This paper proposes a hyper-heuristic algorithm—named HyperACO—that searches for the best combination of several interval outranking models embedded into MOEAs to solve MaOPs. HyperACO is able not only to select the most appropriate model but also to combine the already existing models to solve a specific MaOP correctly. The results obtained on the DTLZ and WFG test suites corroborate that HyperACO can hybridize MOEAs with a combined preference model that is suitable to the problem being solved. Performance comparisons with other state-of-the-art MOEAs and tests for statistical significance validate this conclusion

Multi-Criteria Performance Evaluation and Control in Power and Energy Systems

The role of intuition and human preferences are often overlooked in autonomous control of power and energy systems. However, the growing operational diversity of many systems such as microgrids, electric/hybrid-electric vehicles and maritime vessels has created a need for more flexible control and optimization methods. In order to develop such flexible control methods, the role of human decision makers and their desired performance metrics must be studied in power and energy systems. This dissertation investigates the concept of multi-criteria decision making as a gateway to integrate human decision makers and their opinions into complex mathematical control laws. There are two major steps this research takes to algorithmically integrate human preferences into control environments: MetaMetric (MM) performance benchmark: considering the interrelations of mathematical and psychological convergence, and the potential conflict of opinion between the control designer and end-user, a novel holistic performance benchmark, denoted as MM, is developed to evaluate control performance in real-time. MM uses sensor measurements and implicit human opinions to construct a unique criterion that benchmarks the system\u27s performance characteristics. MM decision support system (DSS): the concept of MM is incorporated into multi-objective evolutionary optimization algorithms as their DSS. The DSS\u27s role is to guide and sort the optimization decisions such that they reflect the best outcome desired by the human decision-maker and mathematical considerations. A diverse set of case studies including a ship power system, a terrestrial power system, and a vehicular traction system are used to validate the approaches proposed in this work. Additionally, the MM DSS is designed in a modular way such that it is not specific to any underlying evolutionary optimization algorithm

Physical programming for preference driven evolutionary multi-objective optimization

Preference articulation in multi-objective optimization could be used to improve the pertinency of solutions in an approximated Pareto front. That is, computing the most interesting solutions from the designer's point of view in order to facilitate the Pareto front analysis and the selection of a design alternative. This articulation can be achieved in an a priori, progressive, or a posteriori manner. If it is used within an a priori frame, it could focus the optimization process toward the most promising areas of the Pareto front, saving computational resources and assuring a useful Pareto front approximation for the designer. In this work, a physical programming approach embedded in an evolutionary multi-objective optimization is presented as a tool for preference inclusion. The results presented and the algorithm developed validate the proposal as a potential tool for engineering design by means of evolutionary multi-objective optimization.This work was partially supported by the FPI-2010/19 grant and the PAID-2011/2732 project from the Universitat Polittccnica de Valencia and the projects TIN2011-28082 and ENE2011-25900 from the Spanish Ministry of Economy and Competitiveness.Reynoso Meza, G.; Sanchís Saez, J.; Blasco Ferragud, FX.; Garcia Nieto, S. (2014). Physical programming for preference driven evolutionary multi-objective optimization. Applied Soft Computing. 24:341-362. https://doi.org/10.1016/j.asoc.2014.07.009S3413622

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

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