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 Bayesian approach to find Pareto optima in multiobjective programming problems using Sequential Monte Carlo algorithms

In this paper we consider a new approach to multicriteria decision making problems. Such problems are, usually, cast into a Pareto framework where the objective functions are aggregated into a single one using certain weights. The problem is embedded into a statistical framework by adopting a posterior distribution for both the decision variables and the Pareto weights. This embedding dates back to [25] but in this work we operationalize the concept further. We propose a Metropolis-Hastings and a Sequential Monte Carlo (SMC) to trace out the entire Pareto frontier and / or find the global optimum of the problem. We apply the new techniques to a multicriteria portfolio decision making problem proposed in [37] and to a test problem proposed by [27]. The good performance of new techniques suggests that SMC and other algorithms, like the classical Metropolis-Hastings algorithm, can be used profitably in the context of multicriteria decision making problems to trace out the Pareto frontier and / or find a global optimum. Most importantly SMC can be considered as an off-the-shelf technique to solve arbitrary multicriteria decision making problems routinely and efficiently

Solving the waste collection problem from a multiobjective perspective: New methodologies and case studies

Fecha de lectura Tesis Doctoral: 19 de marzo de 2018.Economía Aplicada ( Matemáticas) Resumen tesis: El tratamiento de residuos es un tema de estudio por parte de las administraciones locales a nivel mundial. Distintos factores han de tenerse en cuenta para realizar un servicio eficiente. En este trabajo se desarrolla una herramienta para analizar y resolver el problema de la recogida de residuos sólidos en Málaga. Tras un análisis exhaustivo de los datos, se aborda el problema real como un problema de rutas multiobjetivo con capacidad limitada. Para los problemas multiobjetivo, no suele existir una única solución óptima, sino un conjunto de soluciones eficientes de Pareto. Las características del problema hacen inviable su resolución de forma exacta, por lo que se aplican distintas estrategias metaheurísticas para obtener una buena aproximación. En particular, se combinan las técnicas de GRASP, Path Relinking y Variable Neighborhood Search, que son adaptadas a la perspectiva multicriterio. Se trata de una aproximación en dos fases: una primera aproximación de la frontera eficiente se genera mediante un GRASP multiobjetivo. Tres son los métodos propuestos para la primera aproximación, dos de ellos derivados de la publicación de Martí et al. (2015) y el último se apoya en la función escalarizada de logro de Wierzbicki (Wierzbicki, 1980) para distintas combinaciones de pesos. A continuación, esta aproximación es mejorada con una versión de Path Relinking o Variable Neighborhood Search, con un punto de referencia diseñado para problemas multiobjetivo. Una vez generada la aproximación de la frontera eficiente, el proceso de obtención de la solución que más se adecúa a las preferencias de los gestores se basa en el desarrollo de un método interactivo sin trade – off, derivado de la filosofía NAUTILUS (Miettinen et al. 2010). Para evitar gastos de cómputo extensos, esta metodología se apoya en una pre - computación de los elementos de la frontera eficiente

Multiobjective Optimization in Health Care Management. A metaheuristic and simulation approach.

This paper describes a methodology which combines elements of statistics, probability, mathematical programming, simulation, multiobjective optimization and metaheuristics, to analyze management problems in a health care context. We apply this approach to a staffing problem in a primary care center, taking into account both cost and service quality criteria. We illustrate our approach with a case study

Advances and applications in high-dimensional heuristic optimization

“Applicable to most real-world decision scenarios, multiobjective optimization is an area of multicriteria decision-making that seeks to simultaneously optimize two or more conflicting objectives. In contrast to single-objective scenarios, nontrivial multiobjective optimization problems are characterized by a set of Pareto optimal solutions wherein no solution unanimously optimizes all objectives. Evolutionary algorithms have emerged as a standard approach to determine a set of these Pareto optimal solutions, from which a decision-maker can select a vetted alternative. While easy to implement and having demonstrated great efficacy, these evolutionary approaches have been criticized for their runtime complexity when dealing with many alternatives or a high number of objectives, effectively limiting the range of scenarios to which they may be applied. This research introduces mechanisms to improve the runtime complexity of many multiobjective evolutionary algorithms, achieving state-of-the-art performance, as compared to many prominent methods from the literature. Further, the investigations here presented demonstrate the capability of multiobjective evolutionary algorithms in a complex, large-scale optimization scenario. Showcasing the approach’s ability to intelligently generate well-performing solutions to a meaningful optimization problem. These investigations advance the concept of multiobjective evolutionary algorithms by addressing a key limitation and demonstrating their efficacy in a challenging real-world scenario. Through enhanced computational efficiency and exhibited specialized application, the utility of this powerful heuristic strategy is made more robust and evident”--Abstract, page iv

OPTIMIZATION OF RAILWAY TRANSPORTATION HAZMATS AND REGULAR COMMODITIES

Transportation of dangerous goods has been receiving more attention in the realm of academic and scientific research during the last few decades as countries have been increasingly becoming industrialized throughout the world, thereby making Hazmats an integral part of our life style. However, the number of scholarly articles in this field is not as many as those of other areas in SCM. Considering the low-probability-and-high-consequence (LPHC) essence of transportation of Hazmats, on the one hand, and immense volume of shipments accounting for more than hundred tons in North America and Europe, on the other, we can safely state that the number of scholarly articles and dissertations have not been proportional to the significance of the subject of interest. On this ground, we conducted our research to contribute towards further developing the domain of Hazmats transportation, and sustainable supply chain management (SSCM), in general terms. Transportation of Hazmats, from logistical standpoint, may include all modes of transport via air, marine, road and rail, as well as intermodal transportation systems. Although road shipment is predominant in most of the literature, railway transportation of Hazmats has proven to be a potentially significant means of transporting dangerous goods with respect to both economies of scale and risk of transportation; these factors, have not just given rise to more thoroughly investigation of intermodal transportation of Hazmats using road and rail networks, but has encouraged the competition between rail and road companies which may indeed have some inherent advantages compared to the other medium due to their infrastructural and technological backgrounds. Truck shipment has ostensibly proven to be providing more flexibility; trains, per contra, provide more reliability in terms of transport risk for conveying Hazmats in bulks. In this thesis, in consonance with the aforementioned motivation, we provide an introduction into the hazardous commodities shipment through rail network in the first chapter of the thesis. Providing relevant statistics on the volume of Hazmat goods, number of accidents, rate of incidents, and rate of fatalities and injuries due to the incidents involving Hazmats, will shed light onto the significance of the topic under study. As well, we review the most pertinent articles while putting more emphasis on the state-of-the-art papers, in chapter two. Following the discussion in chapter 3 and looking at the problem from carrier company’s perspective, a mixed integer quadratically constraint problem (MIQCP) is developed which seeks for the minimization of transportation cost under a set of constraints including those associating with Hazmats. Due to the complexity of the problem, the risk function has been piecewise linearized using a set of auxiliary variables, thereby resulting in an MIP problem. Further, considering the interests of both carrier companies and regulatory agencies, which are minimization of cost and risk, respectively, a multiobjective MINLP model is developed, which has been reduced to an MILP through piecewise linearization of the risk term in the objective function. For both single-objective and multiobjective formulations, model variants with bifurcated and nonbifurcated flows have been presented. Then, in chapter 4, we carry out experiments considering two main cases where the first case presents smaller instances of the problem and the second case focuses on a larger instance of the problem. Eventually, in chapter five, we conclude the dissertation with a summary of the overall discussion as well as presenting some comments on avenues of future work