Group aggregation of pairwise comparisons using multi-objective optimization

AbstractIn group decision making, multiple decision makers (DMs) aim to reach a consensus ranking of alternatives in a decision problem. The differing expertise, experience and, potentially conflicting, interests of the DMs will result in the need for some form of conciliation to achieve consensus. Pairwise comparisons are commonly used to elicit values of preference of a DM. The aggregation of the preferences of multiple DMs must additionally consider potential conflict between DMs and how these conflicts may result in a need for compromise to reach group consensus.We present an approach to aggregating the preferences of multiple DMs, utilizing multi-objective optimization, to derive and highlight underlying conflict between the DMs when seeking to achieve consensus. Extracting knowledge of conflict facilitates both traceability and transparency of the trade-offs involved when reaching a group consensus.Further, the approach incorporates inconsistency reduction during the aggregation process to seek to diminish adverse effects upon decision outcomes. The approach can determine a single final solution based on either global compromise information or through utilizing weights of importance of the DMs.Within multi-criteria decision making, we present a case study within the Analytical Hierarchy Process from which we derive a richer final ranking of the decision alternatives

Rough set and rule-based multicriteria decision aiding

The aim of multicriteria decision aiding is to give the decision maker a recommendation concerning a set of objects evaluated from multiple points of view called criteria. Since a rational decision maker acts with respect to his/her value system, in order to recommend the most-preferred decision, one must identify decision maker's preferences. In this paper, we focus on preference discovery from data concerning some past decisions of the decision maker. We consider the preference model in the form of a set of "if..., then..." decision rules discovered from the data by inductive learning. To structure the data prior to induction of rules, we use the Dominance-based Rough Set Approach (DRSA). DRSA is a methodology for reasoning about data, which handles ordinal evaluations of objects on considered criteria and monotonic relationships between these evaluations and the decision. We review applications of DRSA to a large variety of multicriteria decision problems

Multi-objective constrained Bayesian optimization for structural design

The planning and design of buildings and civil engineering concrete structures constitutes a complex problem subject to constraints, for instance, limit state constraints from design codes, evaluated by expensive computations such as finite element (FE) simulations. Traditionally, the focus has been on minimizing costs exclusively, while the current trend calls for good trade-offs of multiple criteria such as sustainability, buildability, and performance, which can typically be computed cheaply from the design parameters. Multi-objective methods can provide more relevant design strategies to find such trade-offs. However, the potential of multi-objective optimization methods remains unexploited in structural concrete design practice, as the expensiveness of structural design problems severely limits the scope of applicable algorithms. Bayesian optimization has emerged as an efficient approach to optimizing expensive functions, but it has not been, to the best of our knowledge, applied to constrained multi-objective optimization of structural concrete design problems. In this work, we develop a Bayesian optimization framework explicitly exploiting the features inherent to structural design problems, that is, expensive constraints and cheap objectives. The framework is evaluated on a generic case of structural design of a reinforced concrete (RC) beam, taking into account sustainability, buildability, and performance objectives, and is benchmarked against the well-known Non-dominated Sorting Genetic Algorithm II (NSGA-II) and a random search procedure. The results show that the Bayesian algorithm performs considerably better in terms of rate-of-improvement, final solution quality, and variance across repeated runs, which suggests it is well-suited for multi-objective constrained optimization problems in structural design

PriEsT: an interactive decision support tool to estimate priorities from pairwise comparison judgments

Pairwise comparison (PC) is a well-established method to assist decision makers (DMs) in estimating their preferences. This paper considers the rationale, design, and evaluation of an open-source priority estimation tool, PriEsT, which has been developed to offer new features related to the PC method. PriEsT is able to assist DMs in interactively identifying and revising their judgments based on different consistency measures and graphical aids. When inconsistency cannot be improved due to practical limitations, PriEsT offers a wide range of Pareto-optimal solutions based on multiobjective optimization, unlike other tools that offer only a single solution. DMs have the flexibility to select any of these nondominated solutions according to their requirements. The features of PriEsT have been demonstrated and evaluated through its application to a real-world case study: the selection of the most appropriate telecom infrastructure for rural areas. This case study using PriEsT has highlighted the presence of intransitive judgments in the acquired data, and the correction of these judgments has led to a different ranking of the available alternatives

An Empirical Study of Meta- and Hyper-Heuristic Search for Multi-Objective Release Planning

A variety of meta-heuristic search algorithms have been introduced for optimising software release planning. However, there has been no comprehensive empirical study of different search algorithms across multiple different real-world datasets. In this article, we present an empirical study of global, local, and hybrid meta- and hyper-heuristic search-based algorithms on 10 real-world datasets. We find that the hyper-heuristics are particularly effective. For example, the hyper-heuristic genetic algorithm significantly outperformed the other six approaches (and with high effect size) for solution quality 85% of the time, and was also faster than all others 70% of the time. Furthermore, correlation analysis reveals that it scales well as the number of requirements increases

Risk based multi-objective security control and congestion management

Deterministic security criterion has served power system operation, congestion management quite well in last decades. It is simple to be implemented in a security control model, for example, security constrained optimal power flow (SCOPF). However, since event likelihood and violation information are not addressed, it does not provide quantitative security understanding, and so results in system inadequate awareness. Therefore, even if computation capability and information techniques have been greatly improved and widely applied in the operation support tool, operators are still not able to get rid of the security threat, especially in the market competitive environment.;Probability approach has shown its strong ability for planning purpose, and recently gets attention in operation area. Since power system security assessment needs to analyze consequence of all credible events, risk defined as multiplication of event probability and severity is well suited to give an indication to quantify the system security level, and congestion level as well. Since risk addresses extra information, its application for making BETTER online operation decision becomes an attractive research topic.;This dissertation focus on system online risk calculation, risk based multi-objective optimization model development, risk based security control design, and risk based congestion management. A regression model is proposed to predict contingency probability using weather and geography information for online risk calculation. Risk based multi-objective optimization (RBMO) model is presented, considering conflict objectives: risks and cost. Two types of method, classical methods and evolutionary algorithms, are implemented to solve RBMO problem, respectively. A risk based decision making architecture for security control is designed based on the Pareto-optimal solution understanding, visualization tool and high level information analysis. Risk based congestion management provides a market lever to uniformly expand a security VOLUME , where greater volume means more risk. Meanwhile, risk based LMP signal contracts ALL dimensions of this VOLUME in proper weights (state probabilities) at a time.;Two test systems, 6-bus and IEEE RTS 96, are used to test developed algorithms. The simulation results show that incorporating risk into security control and congestion management will evolve our understanding of security level, improve control and market efficiency, and support operator to maneuver system in an effective fashion

Machine learning-driven approach for large scale decision making with the analytic hierarchy process

The Analytic Hierarchy Process (AHP) multicriteria method can be cognitively demanding for large-scale decision problems due to the requirement for the decision maker to make pairwise evaluations of all alternatives. To address this issue, this paper presents an interactive method that uses online learning to provide scalability for AHP. The proposed method involves a machine learning algorithm that learns the decision maker’s preferences through evaluations of small subsets of solutions, and guides the search for the optimal solution. The methodology was tested on four optimization problems with different surfaces to validate the results. We conducted a one factor at a time experimentation of each hyperparameter implemented, such as the number of alternatives to query the decision maker, the learner method, and the strategies for solution selection and recommendation. The results demonstrate that the model is able to learn the utility function that characterizes the decision maker in approximately 15 iterations with only a few comparisons, resulting in significant time and cognitive effort savings. The initial subset of solutions can be chosen randomly or from a cluster. The subsequent ones are recommended during the iterative process, with the best selection strategy depending on the problem type. Recommendation based solely on the smallest Euclidean or Cosine distances reveals better results on linear problems. The proposed methodology can also easily incorporate new parameters and multicriteria methods based on pairwise comparisons.This research was funded by National Funds through the FCT—Portuguese Foundation for Science and Technology, References UIDB/05256/2020 and UIDP/05256/2020

Numerical and Evolutionary Optimization 2020

This book was established after the 8th International Workshop on Numerical and Evolutionary Optimization (NEO), representing a collection of papers on the intersection of the two research areas covered at this workshop: numerical optimization and evolutionary search techniques. While focusing on the design of fast and reliable methods lying across these two paradigms, the resulting techniques are strongly applicable to a broad class of real-world problems, such as pattern recognition, routing, energy, lines of production, prediction, and modeling, among others. This volume is intended to serve as a useful reference for mathematicians, engineers, and computer scientists to explore current issues and solutions emerging from these mathematical and computational methods and their applications