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

A game theoretic perspective on Bayesian multi-objective optimization

This chapter addresses the question of how to efficiently solve many-objective optimization problems in a computationally demanding black-box simulation context. We shall motivate the question by applications in machine learning and engineering, and discuss specific harsh challenges in using classical Pareto approaches when the number of objectives is four or more. Then, we review solutions combining approaches from Bayesian optimization, e.g., with Gaussian processes, and concepts from game theory like Nash equilibria, Kalai-Smorodinsky solutions and detail extensions like Nash-Kalai-Smorodinsky solutions. We finally introduce the corresponding algorithms and provide some illustrating results

Preference-based evolutionary algorithm for airport surface operations

In addition to time efficiency, minimisation of fuel consumption and related emissions has started to be considered by research on optimisation of airport surface operations as more airports face severe congestion and tightening environmental regulations. Objectives are related to economic cost which can be used as preferences to search for a region of cost efficient and Pareto optimal solutions. A multi-objective evolutionary optimisation framework with preferences is proposed in this paper to solve a complex optimisation problem integrating runway scheduling and airport ground movement problem. The evolutionary search algorithm uses modified crowding distance in the replacement procedure to take into account cost of delay and fuel price. Furthermore, uncertainty inherent in prices is reflected by expressing preferences as an interval. Preference information is used to control the extent of region of interest, which has a beneficial effect on algorithm performance. As a result, the search algorithm can achieve faster convergence and potentially better solutions. A filtering procedure is further proposed to select an evenly distributed subset of Pareto optimal solutions in order to reduce its size and help the decision maker. The computational results with data from major international hub airports show the efficiency of the proposed approach

Investigating Normalization in Preference-based Evolutionary Multi-objective Optimization Using a Reference Point

Normalization of objectives plays a crucial role in evolutionary multi-objective optimization (EMO) to handle objective functions with different scales, which can be found in real-world problems. Although the effect of normalization methods on the performance of EMO algorithms has been investigated in the literature, that of preference-based EMO (PBEMO) algorithms is poorly understood. Since PBEMO aims to approximate a region of interest, its population generally does not cover the Pareto front in the objective space. This property may make normalization of objectives in PBEMO difficult. This paper investigates the effectiveness of three normalization methods in three representative PBEMO algorithms. We present a bounded archive-based method for approximating the nadir point. First, we demonstrate that the normalization methods in PBEMO perform significantly worse than that in conventional EMO in terms of approximating the ideal point, nadir point, and range of the PF. Then, we show that PBEMO requires normalization of objectives on problems with differently scaled objectives. Our results show that there is no clear "best normalization method" in PBEMO, but an external archive-based method performs relatively well

Otimização multiobjetivo com estimação de distribuição guiada por tomada de decisão multicritério

Orientadores: Fernando José Von Zuben, Guilherme Palermo CoelhoDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Considerando as meta-heurísticas estado-da-arte para otimização multiobjetivo (MOO, do inglês Multi-Objective Optimization), como NSGA-II, NSGA-III, SPEA2 e SMS-EMOA, apenas um critério de preferência por vez é levado em conta para classificar soluções ao longo do processo de busca. Neste trabalho, alguns dos critérios de seleção adotados por esses algoritmos estado-da-arte, incluindo classe de não-dominância e contribuição para a métrica de hipervolume, são utilizados em conjunto por uma técnica de tomada de decisão multicritério (MCDM, do inglês Multi-Criteria Decision Making), mais especificamente o algoritmo TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution), responsável por ordenar todas as soluções candidatas. O algoritmo TOPSIS permite o uso de abordagens baseadas em múltiplas preferências, ao invés de apenas uma como na maioria das técnicas híbridas de MOO e MCDM. Cada preferência é tratada como um critério com uma importância relativa determinada pelo tomador de decisão. Novas soluções candidatas são então amostradas por meio de um modelo de distribuição, neste caso uma mistura de Gaussianas, obtido a partir da lista ordenada de soluções candidatas produzida pelo TOPSIS. Essencialmente, um operador de roleta é utilizado para selecionar um par de soluções candidatas de acordo com o seu mérito relativo, adequadamente determinado pelo TOPSIS, e então uma novo par de soluções candidatas é gerado a partir de perturbações Gaussianas centradas nas correspondentes soluções candidatas escolhidas. O desvio padrão das funções Gaussianas é definido em função da distância das soluções no espaço de decisão. Também foram utilizados operadores para auxiliar a busca a atingir regiões potencialmente promissoras do espaço de busca que ainda não foram mapeadas pelo modelo de distribuição. Embora houvesse outras opções, optou-se por seguir a estrutura do algoritmo NSGA-II, também adotada no algoritmo NSGA-III, como base para o método aqui proposto, denominado MOMCEDA (Multi-Objective Multi-Criteria Estimation of Distribution Algorithm). Assim, os aspectos distintos da proposta, quando comparada com o NSGA-II e o NSGA-III, são a forma como a população de soluções candidatas é ordenada e a estratégia adotada para gerar novos indivíduos. Os resultados nos problemas de teste ZDT mostram claramente que nosso método é superior aos algoritmos NSGA- II e NSGA-III, e é competitivo com outras meta-heurísticas bem estabelecidas na literatura de otimização multiobjetivo, levando em conta as métricas de convergência, hipervolume e a medida IGDAbstract: Considering the state-of-the-art meta-heuristics for multi-objective optimization (MOO), such as NSGA-II, NSGA-III, SPEA2 and SMS-EMOA, only one preference criterion at a time is considered to properly rank candidate solutions along the search process. Here, some of the preference criteria adopted by those state-of-the-art algorithms, including non-dominance level and contribution to the hypervolume, are taken together as inputs to a multi-criteria decision making (MCDM) strategy, more specifically the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), responsible for sorting all candidate solutions. The TOPSIS algorithm allows the use of multiple preference based approaches, rather than focusing on a particular one like in most hybrid algorithms composed of MOO and MCDM techniques. Here, each preference is treated as a criterion with a relative relevance to the decision maker (DM). New candidate solutions are then generated using a distribution model, in our case a Gaussian mixture model, derived from the sorted list of candidate solutions produced by TOPSIS. Essentially, a roulette wheel is used to choose a pair of the current candidate solutions according to the relative quality, suitably determined by TOPSIS, and after that a new pair of candidate solutions is generated as Gaussian perturbations centered at the corresponding parent solutions. The standard deviation of the Gaussian functions is defined in terms of the parents distance in the decision space. We also adopt refreshing operators, aiming at reaching potentially promising regions of the search space not yet mapped by the distribution model. Though other choices could have been made, we decided to follow the structural conception of the NSGA-II algorithm, also adopted in the NSGA-III algorithm, as basis for our proposal, denoted by MOMCEDA (Multi-Objective Multi-Criteria Estimation of Distribution Algorithm). Therefore, the distinctive aspects, when compared to NSGA-II and NSGA-III, are the way the current population of candidate solutions is ranked and the strategy adopted to generate new individuals. The results on ZDT benchmarks show that our method is clearly superior to NSGA-II and NSGA-III, and is competitive with other wellestablished meta-heuristics for multi-objective optimization from the literature, considering convergence to the Pareto front, hypervolume and IGD as performance metricsMestradoEngenharia de ComputaçãoMestre em Engenharia Elétrica2016/21031-0FAPESPCAPE

Preference-based evolutionary algorithm for airport surface operations

In addition to time efficiency, minimisation of fuel consumption and related emissions has started to be considered by research on optimisation of airport surface operations as more airports face severe congestion and tightening environmental regulations. Objectives are related to economic cost which can be used as preferences to search for a region of cost efficient and Pareto optimal solutions. A multi-objective evolutionary optimisation framework with preferences is proposed in this paper to solve a complex optimisation problem integrating runway scheduling and airport ground movement problem. The evolutionary search algorithm uses modified crowding distance in the replacement procedure to take into account cost of delay and fuel price. Furthermore, uncertainty inherent in prices is reflected by expressing preferences as an interval. Preference information is used to control the extent of region of interest, which has a beneficial effect on algorithm performance. As a result, the search algorithm can achieve faster convergence and potentially better solutions. A filtering procedure is further proposed to select an evenly distributed subset of Pareto optimal solutions in order to reduce its size and help the decision maker. The computational results with data from major international hub airports show the efficiency of the proposed approach.This work is supported in part by the Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/H004424/1, EP/N029496/1 and EP/N029496/2

Multiobjective Planning and Design of Distributed Stormwater Harvesting and Treatment Systems through Optimization and Visual Analytics

Stormwater harvesting (SWH) is an important water sensitive urban design (WSUD) approach that provides an alternate water source and/or improves runoff quality through stormwater best management practice technologies (BMPs). Through integrated SWH system design at the development scale practitioners must account for trade-offs between cost, harvested volume, and water quality improvement performance which are usually dependent on design decisions for the type, size, and spatial distribution of BMPs. In catchment management planning, additional objectives such as catchment vegetation improvement and public recreation benefit need to be maximized for a catchment region within a limited budget. As such, planning and design of SWH systems with distributed BMPs is a complex problem that requires optimal allocation of limited resources to maximize multiple benefits. In this thesis, two innovative formal optimization approaches are presented for formulating and identifying optimal solutions to problems requiring distributed BMPs. Firstly, a multiobjective optimization framework is presented and applied to a case study for the conceptual design of integrated systems of BMPs for stormwater harvesting. The aim of this work is to develop a conceptual design modelling framework that handles the optimal placement of stormwater harvesting (SWH) infrastructure within an urban development. The framework produces preliminary SWH system designs representing optimal trade-offs between cost, water harvesting, and water quality improvement measures. Secondly, a many (>3) -objective optimization framework is presented and applied to a case study for catchment planning requiring the selection of a portfolio of distributed BMP projects. The framework produces portfolios that are optimal with respect to four objectives, and enables exploration of the many-objective trade-off surface using interactive visual analytics. In addition, a multi-stakeholder method is presented, which enables catchment managers and local government authorities to identify solutions that represent a compromise between 16 objectives and eight optimization problem representations using interactive visual analytics to encourage a negotiated solution. This thesis contains one paper accepted in the Journal of Water Resources Planning and Management (Paper 1), and one paper submitted (Paper 2), and one paper to be submitted (Paper 3) to peer-reviewed journals in the field of water resources management.Thesis (Ph.D.) -- University of Adelaide, School of Civil, Environmental & Mining Engineering, 201

Modelling and aerodynamic design of optimisation of the twin-boom aegis UAV.

The aircraft industry gives considerable attention to computational optimisation tools in order to enhance the design process and product quality in terms of efficiency and performance, respectively. In reality, most real-world applications contain many complicating factors and constraints that affect system behaviour. Consequently, finding optimal solutions, or even only those viable for a given design problem, in an economical computational time is a difficult task, even with the availability of superfast computers. Thus, it is important to optimise the use of available computational resources. This research project presents a method for using stochastic multi-objective optimisation approaches combined with Artificial Intelligence and Interactive Design techniques to support the decision-making process. The improved ability of the developed methods to accelerate the search while retaining all the useful information in the design space was the main area of work. Both the efficiency and reliability of the proposed methodology have been demonstrated through the aerodynamic design of the Aegis-UAV. Initially, the optimisation platform Nimrod/O was deployed to enable the designer to manipulate and better understand different design scenarios. This happened before any commitment to a specific design architecture to allow for a wider exploration of the design space before a decision was made for a more detailed study of the problem. This had the potential to improve the quality of the product and reduce the design cycle time. The optimisation was performed using the Multi-Objective Tabu Search (MOTS) algorithm, chosen for its suitability for this type of complex aerodynamic design problem. Prior to the optimisation process, a parametric study was performed using the Sweep Method (SM) to explore the design space and identify design limitations. Analysis and investigation of the SM results were used to help determine the formulation of the design problem. SM was chosen because it has been proven to be reliable, effective, and able to provide a large amount of structured information about the design problem to the decision maker (DM) at this stage. Next, since most decisions of a DM in practical applications concern regions of the Pareto front, an interactive optimisation framework was proposed where the DM was involved with the optimisation process in real time. The framework used the Multi-Objective Particle Swarm Optimisation (MOPSO) algorithm for its suitability to this type of design problem. The results obtained confirmed the ability of the DM to use its preferences effectively, to steer the search to the Region of Interest (ROI) without degrading the aerodynamic performance of the optimised configurations. Even using only half the evaluations, the DM was able to obtain results similar to, or better than those obtained by the non-interactive use of MOTS and MOPSO. Furthermore, it was possible for the DM to stop the search at any iteration, which is not possible in non-interactive approaches even though the solutions do not converge or may be infeasible. Finally an Artificial Neural Network (ANN) was introduced to guide the MOPSO algorithm in deciding whether the trial solution was worthy of full evaluation, or not. The results obtained showed the success of the ANN in recognising non-valid particles. Consequently, the solver avoided wasting computational efforts on non-worthwhile particles. The optimisation process provides particles that are more valid for almost the same computational time. Demonstrating the algorithm’s effectiveness was done by comparing results of the ANN-MOPSO solutions with those obtained by the other approaches for the same design problems. In conclusion, future avenues of research have been identified and presented in the final chapter of the thesis.PhD in Aerospac