Computing the set of Epsilon-efficient solutions in multiobjective space mission design

In this work, we consider multiobjective space mission design problems. We will start from the need, from a practical point of view, to consider in addition to the (Pareto) optimal solutions also nearly optimal ones. In fact, extending the set of solutions for a given mission to those nearly optimal significantly increases the number of options for the decision maker and gives a measure of the size of the launch windows corresponding to each optimal solution, i.e., a measure of its robustness. Whereas the possible loss of such approximate solutions compared to optimal—and possibly even ‘better’—ones is dispensable. For this, we will examine several typical problems in space trajectory design—a biimpulsive transfer from the Earth to the asteroid Apophis and two low-thrust multigravity assist transfers—and demonstrate the possible benefit of the novel approach. Further, we will present a multiobjective evolutionary algorithm which is designed for this purpose

On the detection of nearly optimal solutions in the context of single-objective space mission design problems

When making decisions, having multiple options available for a possible realization of the same project can be advantageous. One way to increase the number of interesting choices is to consider, in addition to the optimal solution x*, also nearly optimal or approximate solutions; these alternative solutions differ from x* and can be in different regions – in the design space – but fulfil certain proximity to its function value f(x*). The scope of this article is the efficient computation and discretization of the set E of e–approximate solutions for scalar optimization problems. To accomplish this task, two strategies to archive and update the data of the search procedure will be suggested and investigated. To make emphasis on data storage efficiency, a way to manage significant and insignificant parameters is also presented. Further on, differential evolution will be used together with the new archivers for the computation of E. Finally, the behaviour of the archiver, as well as the efficiency of the resulting search procedure, will be demonstrated on some academic functions as well as on three models related to space mission design

Approximate solutions in space mission design

In this paper, we address multi-objective space mission design problems. From a practical point of view, it is often the case that,during the preliminary phase of the design of a space mission, the solutions that are actually considered are not 'optimal' (in the Pareto sense)but belong to the basin of attraction of optimal ones (i.e. they are nearly optimal). This choice is motivated either by additional requirements that the decision maker has to take into account or, more often, by robustness considerations. For this, we suggest a novel MOEA which is a modification of the well-known NSGA-II algorithm equipped with a recently proposed archiving strategy which aims at storing the set of approximate solutions of a given MOP. Using this algorithm we will examine some space trajectory design problems and demonstrate the benefit of the novel approach

About Designing an Observer Pattern-Based Architecture for a Multi-objective Metaheuristic Optimization Framework

Multi-objective optimization with metaheuristics is an active and popular research field which is supported by the availability of software frameworks providing algorithms, benchmark problems, quality indicators and other related components. Most of these tools follow a monolithic architecture that frequently leads to a lack of flexibility when a user intends to add new features to the included algorithms. In this paper, we explore a different approach by designing a component-based architecture for a multi-objective optimization framework based on the observer pattern. In this architecture, most of the algorithmic components are observable entities that naturally allows to register a number of observers. This way, a metaheuristic is composed of a set of observable and observer elements, which can be easily extended without requiring to modify the algorithm. We have developed a prototype of this architecture and implemented the NSGA-II evolutionary algorithm on top of it as a case study. Our analysis confirms the improvement of flexibility using this architecture, pointing out the requirements it imposes and how performance is affected when adopting it.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Dynamic Multi-Objective Optimization With jMetal and Spark: a Case Study

Technologies for Big Data and Data Science are receiving increasing research interest nowadays. This paper introduces the prototyping architecture of a tool aimed to solve Big Data Optimization problems. Our tool combines the jMetal framework for multi-objective optimization with Apache Spark, a technology that is gaining momentum. In particular, we make use of the streaming facilities of Spark to feed an optimization problem with data from different sources. We demonstrate the use of our tool by solving a dynamic bi-objective instance of the Traveling Salesman Problem (TSP) based on near real-time traffic data from New York City, which is updated several times per minute. Our experiment shows that both jMetal and Spark can be integrated providing a software platform to deal with dynamic multi-optimization problems.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Two enhancements for improving the convergence speed of a robust multi-objective coevolutionary algorithm.

We describe two enhancements that significantly improve the rapid convergence behavior of DECM02 - a previously proposed robust coevolutionary algorithm that integrates three different multi-objective space exploration paradigms: differential evolution, two-tier Pareto-based selection for survival and decomposition-based evolutionary guidance. The first enhancement is a refined active search adaptation mechanism that relies on run-time sub-population performance indicators to estimate the convergence stage and dynamically adjust and steer certain parts of the coevolutionary process in order to improve its overall efficiency. The second enhancement consists in a directional intensification operator that is applied in the early part of the run during the decomposition-based search phases. This operator creates new random local linear individuals based on the recent historically successful solution candidates of a given directional decomposition vector. As the two efficiency-related enhancements are complementary, our results show that the resulting coevolutionary algorithm is a highly competitive improvement of the baseline strategy when considering a comprehensive test set aggregated from 25 (standard) benchmark multi-objective optimization problems

A MOPSO Algorithm Based Exclusively on Pareto Dominance Concepts

Copyright © 2005 Springer Verlag. The final publication is available at link.springer.com3rd International Conference, EMO 2005, Guanajuato, Mexico, March 9-11, 2005. ProceedingsBook title: Evolutionary Multi-Criterion OptimizationIn extending the Particle Swarm Optimisation methodology to multi-objective problems it is unclear how global guides for particles should be selected. Previous work has relied on metric information in objective space, although this is at variance with the notion of dominance which is used to assess the quality of solutions. Here we propose methods based exclusively on dominance for selecting guides from a non-dominated archive. The methods are evaluated on standard test problems and we find that probabilistic selection favouring archival particles that dominate few particles provides good convergence towards and coverage of the Pareto front. We demonstrate that the scheme is robust to changes in objective scaling. We propose and evaluate methods for confining particles to the feasible region, and find that allowing particles to explore regions close to the constraint boundaries is important to ensure convergence to the Pareto front

Evolving temporal fuzzy association rules from quantitative data with a multi-objective evolutionary algorithm

A novel method for mining association rules that are both quantitative and temporal using a multi-objective evolutionary algorithm is presented. This method successfully identifies numerous temporal association rules that occur more frequently in areas of a dataset with specific quantitative values represented with fuzzy sets. The novelty of this research lies in exploring the composition of quantitative and temporal fuzzy association rules and the approach of using a hybridisation of a multi-objective evolutionary algorithm with fuzzy sets. Results show the ability of a multi-objective evolutionary algorithm (NSGA-II) to evolve multiple target itemsets that have been augmented into synthetic datasets

Knowledge discovery for friction stir welding via data driven approaches: Part 2 – multiobjective modelling using fuzzy rule based systems

In this final part of this extensive study, a new systematic data-driven fuzzy modelling approach has been developed, taking into account both the modelling accuracy and its interpretability (transparency) as attributes. For the first time, a data-driven modelling framework has been proposed designed and implemented in order to model the intricate FSW behaviours relating to AA5083 aluminium alloy, consisting of the grain size, mechanical properties, as well as internal process properties. As a result, ‘Pareto-optimal’ predictive models have been successfully elicited which, through validations on real data for the aluminium alloy AA5083, have been shown to be accurate, transparent and generic despite the conservative number of data points used for model training and testing. Compared with analytically based methods, the proposed data-driven modelling approach provides a more effective way to construct prediction models for FSW when there is an apparent lack of fundamental process knowledge