NAUTILUS Navigator: Búsqueda Interactiva de Soluciones en Optimización Multiobjetivo sin Trade-offs

En este trabajo, se propone un método interactivo de ayuda a la decisión para resolver problemas de optimización multiobjetivo: NAUTILUS Navigator. En este método, el decisor explora libremente el espacio de objetivos hasta que encuentra la solución eficiente que mejor se ajusta a sus preferencias. El proceso de búsqueda consiste en navegar, en tiempo real, por el conjunto de soluciones hasta converger en la solución preferida, partiendo de una solución "mala"(en el sentido de que alcanza valores no deseables para las funciones objetivo). La información preferencial que proporciona el decisor consiste en valores de aspiración para cada función objetivo, así como cotas que no desearía sobrepasar.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

DESDEO : An Open Framework for Interactive Multiobjective Optimization

We introduce a framework for interactive multiobjective optimization methods called DESDEO released under an open source license. With the framework, we want to make interactive methods easily accessible to be applied in solving real-world problems. The framework follows an object-oriented software design paradigm, where functionalities have been divided to modular, self-contained components. The framework contains implementations of some interactive methods, but also components which can be utilized to implement more interactive methods and, thus, increase the applicability of the framework. To demonstrate how the framework can be used, we consider an example problem where the pollution of a river is controlled. To solve this problem with four objectives, we apply two interactive methods called NAUTILUS and NIMBUS and show how the method can be switched during the solution process.peerReviewe

Demonstrating the Applicability of PAINT to Computationally Expensive Real-life Multiobjective Optimization

We demonstrate the applicability of a new PAINT method to speed up iterations of interactive methods in multiobjective optimization. As our test case, we solve a computationally expensive non-linear, five-objective problem of designing and operating a wastewater treatment plant. The PAINT method interpolates between a given set of Pareto optimal outcomes and constructs a computationally inexpensive mixed integer linear surrogate problem for the original problem. We develop an IND-NIMBUS R PAINT module to combine the interactive NIMBUS method and the PAINT method and to find a preferred solution to the original problem. With the PAINT method, the solution process with the NIMBUS method take a comparatively short time even though the original problem is computationally expensive.nonPeerReviewe

Implementation aspects of interactive multiobjective optimization for modeling environments: The case of GAMS-NIMBUS

Abstract. Interactive multiobjective optimization methods have provided promising results in the literature but still their implementations are rare. Here we introduce a core structure of interactive methods to enable their convenient implementation. We also demonstrate how this core structure can be applied when implementing an interactive method using a modeling environment. Many modeling environments contain tools for single objective optimization but not for interactive multiobjective optimization. Furthermore, as a concrete example, we present GAMS-NIMBUS Tool which is an implementation of the classification-based NIMBUS method for the GAMS modeling environment. So far, interactive methods have not been available in the GAMS environment, but with the GAMS-NIMBUS Tool we open up the possibility of solving multiobjective optimization problems modeled in the GAMS modeling environment. Finally, we give some examples of the benefits of applying an interactive method by using the GAMS-NIMBUS Tool for solving multiobjective optimization problems modeled in the GAMS environment.peerReviewe

An Approach to the Automatic Comparison of Reference Point-Based Interactive Methods for Multiobjective Optimization

Solving multiobjective optimization problems means finding the best balance among multiple conflicting objectives. This needs preference information from a decision maker who is a domain expert. In interactive methods, the decision maker takes part in an iterative process to learn about the interdependencies and can adjust the preferences. We address the need to compare different interactive multiobjective optimization methods, which is essential when selecting the most suited method for solving a particular problem. We concentrate on a class of interactive methods where a decision maker expresses preference information as reference points, i.e., desirable objective function values. Comparison of interactive methods with human decision makers is not a straightforward process due to cost and reliability issues. The lack of suitable behavioral models hampers creating artificial decision makers for automatic experiments. Few approaches to automating testing have been proposed in the literature; however, none are widely used. As a result, empirical performance studies are scarce for this class of methods despite its popularity among researchers and practitioners.We have developed a new approach to replace a decision maker to automatically compare interactive methods based on reference points or similar preference information. Keeping in mind the lack of suitable human behavioral models, we concentrate on evaluating general performance characteristics. Such an evaluation can partly address the absence of any tests and is appropriate for screening methods before more rigorous testing. We have implemented our approach as a ready-to-use Python module and illustrated it with computational examples.peerReviewe

Agent assisted interactive algorithm for computationally demanding multiobjective optimization problems

We generalize the applicability of interactive methods for solving computationally demanding, that is, time-consuming, multiobjective optimization problems. For this purpose we propose a new agent assisted interactive algorithm. It employs a computationally inexpensive surrogate problem and four different agents that intelligently update the surrogate based on the preferences specified by a decision maker. In this way, we decrease the waiting times imposed on the decision maker during the interactive solution process and at the same time decrease the amount of preference information expected from the decision maker. The agent assisted algorithm is not specific to any interactive method or surrogate problem. As an example we implement our algorithm for the interactive NIMBUS method and the PAINT method for constructing the surrogate. This implementation was applied to support a real decision maker in solving a two-stage separation problem.peerReviewe

Towards Automatic Testing of Reference Point Based Interactive Methods

In order to understand strengths and weaknesses of optimization algorithms, it is important to have access to different types of test problems, well defined performance indicators and analysis tools. Such tools are widely available for testing evolutionary multiobjective optimization algorithms. To our knowledge, there do not exist tools for analyzing the performance of interactive multiobjective optimization methods based on the reference point approach to communicating preference information. The main barrier to such tools is the involvement of human decision makers into interactive solution processes, which makes the performance of interactive methods dependent on the performance of humans using them. In this research, we aim towards a testing framework where the human decision maker is replaced with an artificial one and which allows to repetitively test interactive methods in a controlled environment.peerReviewe

Comparing reference point based interactive multiobjective optimization methods without a human decision maker

Interactive multiobjective optimization methods have proven promising in solving optimization problems with conflicting objectives since they iteratively incorporate preference information of a decision maker in the search for the most preferred solution. To find the appropriate interactive method for various needs involves analysis of the strengths and weaknesses. However, extensive analysis with human decision makers may be too costly and for that reason, we propose an artificial decision maker to compare a class of popular interactive multiobjective optimization methods, i.e., reference point based methods. Without involving any human decision makers, the artificial decision maker works automatically to interact with different methods to be compared and evaluate the final results. It makes a difference between a learning phase and a decision phase, that is, learns about the problem based on information acquired to identify a region of interest and refines solutions in that region to find a final solution, respectively. We adopt different types of utility functions to evaluation solutions, present corresponding performance indicators and propose two examples of artificial decision makers. A series of experiments on benchmark test problems and a water resources planning problem is conducted to demonstrate how the proposed artificial decision makers can be used to compare reference point based methods.peerReviewe

Flexible Data Driven Inventory Management with Interactive Multiobjective Lot Size Optimization

We study data-driven decision support and formalise a path from data to decision making. We focus on lot sizing in inventory management with stochastic demand and propose an interactive multi-objective optimisation approach. We forecast demand with a Bayesian model, which is based on sales data. After identifying relevant objectives relying on the demand model, we formulate an optimisation problem to determine lot sizes for multiple future time periods. Our approach combines different interactive multi-objective optimisation methods for finding the best balance among the objectives. For that, a decision maker with substance knowledge directs the solution process with one’s preference information to find the most preferred solution with acceptable trade-offs. As a proof of concept, to demonstrate the benefits of the approach, we utilise real-world data from a production company and compare the optimised lot sizes to decisions made without support. With our approach, the decision maker obtained very satisfactory solutions.peerReviewe