Toward an estimation of nadir objective vector using a hybrid of evolutionary and local search approaches

A nadir objective vector is constructed from the worst Pareto-optimal objective values in a multiobjective optimization problem and is an important entity to compute because of its significance in estimating the range of objective values in the Pareto-optimal front and also in executing a number of interactive multiobjective optimization techniques. Along with the ideal objective vector, it is also needed for the purpose of normalizing different objectives, so as to facilitate a comparison and agglomeration of the objectives. However, the task of estimating the nadir objective vector necessitates information about the complete Pareto-optimal front and has been reported to be a difficult task, and importantly an unsolved and open research issue. In this paper, we propose certain modifications to an existing evolutionary multiobjective optimization procedure to focus its search toward the extreme objective values and combine it with a reference-point based local search approach to constitute a couple of hybrid procedures for a reliable estimation of the nadir objective vector. With up to 20-objective optimization test problems and on a three-objective engineering design optimization problem, one of the proposed procedures is found to be capable of finding the nadir objective vector reliably. The study clearly shows the significance of an evolutionary computing based search procedure in assisting to solve an age-old important task in the field of multiobjective optimization

A review of Nadir point estimation procedures using evolutionary approaches: a tale of dimensionality reduction

Estimation of the nadir objective vector is an important task, particularly for multi-objective optimization problems having more than two conflicting objectives. Along with the ideal point, nadir point can be used to normalize the objectives so that multi-objective optimization algorithms can be used more reliably. The knowledge of the nadir point is also a pre-requisite to many multiple criteria decision making methodologies.Moreover, nadir point is useful for an aid in interactive methodologies and visualization softwares catered for multi-objective optimization. However, the computation of exact nadir point formore than two objectives is not an easy matter, simply because nadir point demands the knowledge of extreme Paretooptimal solutions. In the past few years, researchers have proposed several nadir point estimation procedures using evolutionary optimization methodologies. In this paper, we review the past studies and reveal an interesting chronicle of events in this direction. To make the estimation procedure computationally faster and more accurate, the methodologies were refined one after the other by mainly focusing on increasingly lower dimensional subset of Pareto-optimal solutions. Simulation results on a number of numerical test problems demonstrate better efficacy of the approach which aims to find only the extreme Pareto-optimal points compared to its higher-dimensional counterparts

A hybrid integrated multi-objective optimization procedure for estimating nadir point

A nadir point is constructed by the worst objective values of the solutions of the entire Pareto-optimal set. Along with the ideal point, the nadir point provides the range of objective values within which all Pareto-optimal solutions must lie. Thus, a nadir point is an important point to researchers and practitioners interested in multi-objective optimization. Besides, if the nadir point can be computed relatively quickly, it can be used to normalize objectives in many multi-criterion decision making tasks. Importantly, estimating the nadir point is a challenging and unsolved computing problem in case of more than two objectives. In this paper, we revise a previously proposed serial application of an EMO and a local search method and suggest an integrated approach for finding the nadir point. A local search procedure based on the solution of a bi-level achievement scalarizing function is employed to extreme solutions in stabilized populations in an EMO procedure. Simulation results on a number of problems demonstrate the viability and working of the proposed procedure

New Insights to Approximate the Pareto Optimal Front in Evolutionary Multiobjective Optimization. An Application to Students’ Satisfaction

Los resultados de la segunda parte demuestran el buen comportamiento de la combinación de técnicas econométricas y multiobjetivo, especialmente cuando utilizamos algoritmos evolutivos, para la resolución de problemas socio-económicos con la finalidad de encontrar la compensación (trade-offs) entre los objetivos estudiados y así poder sugerir mejoras, en este caso, en economía de la educación.La tesis presentada se basa en el desarrollo de nuevos algoritmos evolutivos para resolver problemas de optimización multiobjetivo, especialmente problemas con más de tres funciones objetivos, y en la modelización y resolución de un problema de economía de la educación. Dicha tesis está realizada en la modalidad de compendio de artículos y se compone de tres de los mismos. Los dos primeros relacionados con el desarrollo de un nuevo algoritmo evolutivo. En ellos, partiendo del algoritmo Global Weighting Achievement Scalarizing Fucntion Genetic Algorithm (GWASF-GA) (Saborido, Ruiz, and Luque, 2017), se plantea y desarrolla un nuevo algoritmo centrado en la adaptación de los vectores de pesos durante el proceso de ejecución, que ofrece muy buenos resultados en comparación con algoritmos muy conocidos y muy contrastados dentro del campo de los algoritmos evolutivos. El tercer artículo se centra en la modelización y resolución de un problema multiobjetivo obtenido a partir del análisis econométrico de datos referidos al rendimiento académico y satisfacción de los estudiantes andaluces con diferentes aspectos del proceso enseñanza-aprendizaje en los colegios de secundaria. Con los resultados obtenidos y teniendo en cuenta los algoritmos considerados, aunque los frentes óptimos de Pareto aproximados por A-GWASF-GA no sean los mejores en todos los casos (especialmente para los problemas con tres funciones objetivo), podemos asegurar que el nuevo algoritmo algoritmo evolutivo aquí propuesto (A-GWASF-GA) muestra resultados muy prometedores en problemas con más de tres funciones objetivo. De esta forma, A-GWASF-GA se autodefine como un algoritmo para trabajar con problemas manyobjective (con más de tres objetivos)

Towards a framework to combine multiobjective optimization and econometrics and an application in economics of education

Acknowledgements. This work was supported by the Spanish Ministry of Science and Innovation (project PID2020-115429GB-I00), by the Andalusian Regional Ministry of Economy, Knowledge, Business and University (PAI group SEJ-532 and project UMA18-FEDERJA-024, also supported by FEDER funding), and by the University of Malaga (project B1-2020 18). Sandra Gonzalez-Gallardo is recipient of a research contract within “Ayudas para la Recualificación del Sistema Universitario Español, Modalidad Margarita Salas”, financiado por la Unión Europea – NextGenerationEU.In this paper, we propose a theoretical framework that combines econometric and multiobjective programming methodologies to help researchers to identify and achieve optimal solutions to socio-economic and management problems. Sometimes, it is important to analyse which combination of values of the explanatory variables -in an econometric model- would imply the simultaneous achievement of the best values of the response variables. In such situations, if certain degree of conflict is observed among the response variables, we propose to formulate a multiobjective optimization problem based on the conclusions obtained from a regression analysis. Subsequently, the application of multiobjective optimization techniques allows gaining a better insight about the conflicting relation between the response variables, and how a balanced “optimal” situation among them could be achieved. This piece of information can be hardly extracted just by econometric techniques. An application in the field of economics of education, related to the analysis of the students’ well-being as a way to improve their academic performance, demonstrates the potential of our proposal.Spanish Ministry of Science and Innovation (project PID2020-115429GB-I00)Andalusian Regional Ministry of Economy, Knowledge, Business and University (PAI group SEJ-532 and project UMA18-FEDERJA-024, also supported by FEDER funding)University of Malaga (project B1-2020 18)“Ayudas para la Recualificación del Sistema Universitario Español, Modalidad Margarita Salas”, financiado por la Unión Europea – NextGenerationE

An Interactive Multi-Criteria Decision Model for Reservoir Management: The Shellmouth Reservoir Case

Reservoir management is inherently multi-criterial, since any release decision involves implicit trade-offs between various conflicting objectives. The release decision reflects concerns such as flood protection, hydroelectric power generation, dilution of downstream wastewater and heat effluents, downstream municipal, agricultural and industrial water supply, environmental standards and recreational needs. This paper presents a framework for analysing trade-offs between several decision criteria, and includes the management of heated effluents from downstream thermoelectric power generation in an optimisation model for reservoir management. The model is formulated and analysed in an interactive multi-criteria decision making (MCDM) modelling framework. Rather than providing specific target levels or ad hoc constants in a Goal Programming framework, as proposed elsewhere, our multi-criteria framework suggests a systematic way of evaluating trade-offs by progressive preference assessment. The MCDM model, based on a Tchebycheff metric and a contracted cone approach, is learning-oriented and permits a natural exploration of the decision space while maintaining non-dominated decisions. A detailed case study of the Shellmouth Reservoir in Manitoba, Canada, serves as an illustration of the model

Decision support systems for solving discrete multicriteria decision making problems

Includes bibliography.The aim of this study was the design and implementation of an interactive decision support system, assisting a single decision maker in reaching a satisfactory decision when faced by a multicriteria decision making problem. There are clearly two components involved in designing such a system, namely the concept of decision support systems (DSS) and the area of multicriteria decision making (MCDM). The multicriteria decision making environment as well as the definitions of the multicriteria decision making concepts used, are discussed in chapter 1. Chapter 2 gives a brief historical review on MCDM, highlighting the origins of some of the more well-known methods for solving MCDM problems. A detailed discussion of interactive decision making is also given. Chapter 3 is concerned with the DSS concept, including a historical review thereof, a framework for the design of a DSS, various development approaches as well as the components constituting a decision support system. In chapter 4, the possibility of integrating the two concepts, MCDM and DSS, are discussed. A detailed discussion of various methodologies for solving MCDM problems is given in chapter 5. Specific attention is given to identifying the methodologies to be implemented in the DSS. Chapter 6 can be seen as a theoretical description of the system developed, while Chapter 7 is concerned with the evaluation procedures used for testing the system. A final summary and concluding remarks are given in Chapter 8

Developing A Group Decision Support System (gdss) For Decision Making Under Uncertainty

Multi-Criteria Decision Making (MCDM) problems are often associated with tradeoffs between performances of the available alternative solutions under decision making criteria. These problems become more complex when performances are associated with uncertainty. This study proposes a stochastic MCDM procedure that can handle uncertainty in MCDM problems. The proposed method coverts a stochastic MCDM problem into many deterministic ones through a Monte-Carlo (MC) selection. Each deterministic problem is then solved using a range of MCDM methods and the ranking order of the alternatives is established for each deterministic MCDM. The final ranking of the alternatives can be determined based on winning probabilities and ranking distribution of the alternatives. Ranking probability distributions can help the decision-maker understand the risk associated with the overall ranking of the options. Therefore, the final selection of the best alternative can be affected by the risk tolerance of the decisionmakers. A Group Decision Support System (GDSS) is developed here with a user-friendly interface to facilitate the application of the proposed MC-MCDM approach in real-world multiparticipant decision making for an average user. The GDSS uses a range of decision making methods to increase the robustness of the decision analysis outputs and to help understand the sensitivity of the results to level of cooperation among the decision-makers. The decision analysis methods included in the GDSS are: 1) conventional MCDM methods (Maximin, Lexicographic, TOPSIS, SAW and Dominance), appropriate when there is a high cooperation level among the decision-makers; 2) social choice rules or voting methods (Condorcet Choice, Borda scoring, Plurality, Anti-Plurality, Median Voting, Hare System of voting, Majoritarian iii Compromise ,and Condorcet Practical), appropriate for cases with medium cooperation level among the decision-makers; and 3) Fallback Bargaining methods (Unanimity, Q-Approval and Fallback Bargaining with Impasse), appropriate for cases with non-cooperative decision-makers. To underline the utility of the proposed method and the developed GDSS in providing valuable insights into real-world hydro-environmental group decision making, the GDSS is applied to a benchmark example, namely the California‘s Sacramento-San Joaquin Delta decision making problem. The implications of GDSS‘ outputs (winning probabilities and ranking distributions) are discussed. Findings are compared with those of previous studies, which used other methods to solve this problem, to highlight the sensitivity of the results to the choice of decision analysis methods and/or different cooperation levels among the decision-maker

A Hybrid Integrated Multi-Objective Optimization Procedure for Estimating Nadir Point

Abstract. A nadir point is constructed by the worst objective values of the solutions of the entire Pareto-optimal set. Along with the ideal point, the nadir point provides the range of objective values within which all Pareto-optimal solutions must lie. Thus, a nadir point is an important point to researchers and practitioners interested in multi-objective optimization. Besides, if the nadir point can be computed relatively quickly, it can be used to normalize objectives in many multi-criterion decision making tasks. Importantly, estimating the nadir point is a challenging and unsolved computing problem in case of more than two objectives. In this paper, we revise a previously proposed serial application of an EMO and a local search method and suggest an integrated approach for finding the nadir point. A local search procedure based on the solution of a bi-level achievement scalarizing function is employed to extreme solutions in stabilized populations in an EMO procedure. Simulation results on a number of problems demonstrate the viability and working of the proposed procedure