UMOEA/D: A Multiobjective Evolutionary Algorithm for Uniform Pareto Objectives based on Decomposition

Multiobjective optimization (MOO) is prevalent in numerous applications, in which a Pareto front (PF) is constructed to display optima under various preferences. Previous methods commonly utilize the set of Pareto objectives (particles on the PF) to represent the entire PF. However, the empirical distribution of the Pareto objectives on the PF is rarely studied, which implicitly impedes the generation of diverse and representative Pareto objectives in previous methods. To bridge the gap, we suggest in this paper constructing \emph{uniformly distributed} Pareto objectives on the PF, so as to alleviate the limited diversity found in previous MOO approaches. We are the first to formally define the concept of ``uniformity" for an MOO problem. We optimize the maximal minimal distances on the Pareto front using a neural network, resulting in both asymptotically and non-asymptotically uniform Pareto objectives. Our proposed method is validated through experiments on real-world and synthetic problems, which demonstrates the efficacy in generating high-quality uniform Pareto objectives and the encouraging performance exceeding existing state-of-the-art methods. The detailed model implementation and the code are scheduled to be open-sourced upon publication

A Bayesian approach to constrained single- and multi-objective optimization

This article addresses the problem of derivative-free (single- or multi-objective) optimization subject to multiple inequality constraints. Both the objective and constraint functions are assumed to be smooth, non-linear and expensive to evaluate. As a consequence, the number of evaluations that can be used to carry out the optimization is very limited, as in complex industrial design optimization problems. The method we propose to overcome this difficulty has its roots in both the Bayesian and the multi-objective optimization literatures. More specifically, an extended domination rule is used to handle objectives and constraints in a unified way, and a corresponding expected hyper-volume improvement sampling criterion is proposed. This new criterion is naturally adapted to the search of a feasible point when none is available, and reduces to existing Bayesian sampling criteria---the classical Expected Improvement (EI) criterion and some of its constrained/multi-objective extensions---as soon as at least one feasible point is available. The calculation and optimization of the criterion are performed using Sequential Monte Carlo techniques. In particular, an algorithm similar to the subset simulation method, which is well known in the field of structural reliability, is used to estimate the criterion. The method, which we call BMOO (for Bayesian Multi-Objective Optimization), is compared to state-of-the-art algorithms for single- and multi-objective constrained optimization

Preventing premature convergence and proving the optimality in evolutionary algorithms

http://ea2013.inria.fr//proceedings.pdfInternational audienceEvolutionary Algorithms (EA) usually carry out an efficient exploration of the search-space, but get often trapped in local minima and do not prove the optimality of the solution. Interval-based techniques, on the other hand, yield a numerical proof of optimality of the solution. However, they may fail to converge within a reasonable time due to their inability to quickly compute a good approximation of the global minimum and their exponential complexity. The contribution of this paper is a hybrid algorithm called Charibde in which a particular EA, Differential Evolution, cooperates with a Branch and Bound algorithm endowed with interval propagation techniques. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate its efficiency on a benchmark of highly multimodal problems, for which we provide previously unknown global minima and certification of optimality

Preference-Based Evolutionary Many-Objective Optimization for Agile Satellite Mission Planning

With the development of aerospace technologies, the mission planning of agile earth observation satellites has to consider several objectives simultaneously, such as profit, observation task number, image quality, resource balance, and observation timeliness. In this paper, a five-objective mixed-integer optimization problem is formulated for agile satellite mission planning. Preference-based multi-objective evolutionary algorithms, i.e., T-MOEA/D-TCH, T-MOEA/D-PBI, and T-NSGA-III are applied to solve the problem. Problem-specific coding and decoding approaches are proposed based on heuristic rules. Experiments have shown the advantage of integrating preferences in many-objective satellite mission planning. A comparative study is conducted with other state-of-the-art preference-based methods (T-NSGA-II, T-RVEA, and MOEA/D-c). Results have demonstrated that the proposed T-MOEA/D-TCH has the best performance with regard to IGD and elapsed runtime. An interactive framework is also proposed for the decision maker to adjust preferences during the search. We have exemplified that a more satisfactory solution could be gained through the interactive approach.Algorithms and the Foundations of Software technolog

Multi-Fidelity Methods for Optimization: A Survey

Real-world black-box optimization often involves time-consuming or costly experiments and simulations. Multi-fidelity optimization (MFO) stands out as a cost-effective strategy that balances high-fidelity accuracy with computational efficiency through a hierarchical fidelity approach. This survey presents a systematic exploration of MFO, underpinned by a novel text mining framework based on a pre-trained language model. We delve deep into the foundational principles and methodologies of MFO, focusing on three core components -- multi-fidelity surrogate models, fidelity management strategies, and optimization techniques. Additionally, this survey highlights the diverse applications of MFO across several key domains, including machine learning, engineering design optimization, and scientific discovery, showcasing the adaptability and effectiveness of MFO in tackling complex computational challenges. Furthermore, we also envision several emerging challenges and prospects in the MFO landscape, spanning scalability, the composition of lower fidelities, and the integration of human-in-the-loop approaches at the algorithmic level. We also address critical issues related to benchmarking and the advancement of open science within the MFO community. Overall, this survey aims to catalyze further research and foster collaborations in MFO, setting the stage for future innovations and breakthroughs in the field.Comment: 47 pages, 9 figure

Parametric Optimization: Applications in Systems Design

The aim of this research is to introduce the notion of parametric optimization (PO) as a useful approach for solving systems design challenges. In this research, we define PO as the process of finding the optimal solution as a function of one or more parameters. Parameters are variables that affect the optimal solution but, unlike the decision variables, are not directly controlled by the designer. The principal contributions of this research are (1) a novel formulation of the PO problem relevant to systems design, (2) a strategy for empirically assessing the performance of parametric search algorithms, (3) the development and evaluation of novel algorithms for PO, and (4) a demonstration of the use of PO for two real-world systems design challenges. The real-world demonstrations, include the design of (i) a multi-ratio vehicle transmission, and (ii) a Liquid Metal Magnetohydrodynamic Pump. A practical challenge of applying the notion PO to systems design is that existing methods are limited to problems where the models are accessible algebraic equations and single objectives. However, many challenges in systems design involve inaccessible models or are too complicated to be manipulated algebraically and have multiple objectives. If PO is to be used widely in systems design, there is a need for search methods that can approximate the solution to a general PO problem. As a step toward this goal, a strategy for performance assessment is developed. The use of the mean Hausdorff distance is proposed as a measure of solution quality for the PO problem. The mean Hausdorff distance has desirable properties from a mathematical and decision theoretic basis. Using the proposed performance assessment strategy, two algorithms for parametric optimization are evaluated, (a) p-NSGAII which is a straightforward extension of existing methods to the case with parameters, and (b) P3GA an algorithm intended to exploit the parametric structure of the problem. The results of the study indicate that a considered approach, P3GA, to the PO problem results in considerable computational advantage

Scalarized Preferences in Multi-objective Optimization

Multikriterielle Optimierungsprobleme verfügen über keine Lösung, die optimal in jeder Zielfunktion ist. Die Schwierigkeit solcher Probleme liegt darin eine Kompromisslösung zu finden, die den Präferenzen des Entscheiders genügen, der den Kompromiss implementiert. Skalarisierung – die Abbildung des Vektors der Zielfunktionswerte auf eine reelle Zahl – identifiziert eine einzige Lösung als globales Präferenzenoptimum um diese Probleme zu lösen. Allerdings generieren Skalarisierungsmethoden keine zusätzlichen Informationen über andere Kompromisslösungen, die die Präferenzen des Entscheiders bezüglich des globalen Optimums verändern könnten. Um dieses Problem anzugehen stellt diese Dissertation eine theoretische und algorithmische Analyse skalarisierter Präferenzen bereit. Die theoretische Analyse besteht aus der Entwicklung eines Ordnungsrahmens, der Präferenzen als Problemtransformationen charakterisiert, die präferierte Untermengen der Paretofront definieren. Skalarisierung wird als Transformation der Zielmenge in diesem Ordnungsrahmen dargestellt. Des Weiteren werden Axiome vorgeschlagen, die wünschenswerte Eigenschaften von Skalarisierungsfunktionen darstellen. Es wird gezeigt unter welchen Bedingungen existierende Skalarisierungsfunktionen diese Axiome erfüllen. Die algorithmische Analyse kennzeichnet Präferenzen anhand des Resultats, das ein Optimierungsalgorithmus generiert. Zwei neue Paradigmen werden innerhalb dieser Analyse identifiziert. Für beide Paradigmen werden Algorithmen entworfen, die skalarisierte Präferenzeninformationen verwenden: Präferenzen-verzerrte Paretofrontapproximationen verteilen Punkte über die gesamte Paretofront, fokussieren aber mehr Punkte in Regionen mit besseren Skalarisierungswerten; multimodale Präferenzenoptima sind Punkte, die lokale Skalarisierungsoptima im Zielraum darstellen. Ein Drei-Stufen-Algorith\-mus wird entwickelt, der lokale Skalarisierungsoptima approximiert und verschiedene Methoden werden für die unterschiedlichen Stufen evaluiert. Zwei Realweltprobleme werden vorgestellt, die die Nützlichkeit der beiden Algorithmen illustrieren. Das erste Problem besteht darin Fahrpläne für ein Blockheizkraftwerk zu finden, die die erzeugte Elektrizität und Wärme maximieren und den Kraftstoffverbrauch minimiert. Präferenzen-verzerrte Approximationen generieren mehr Energie-effiziente Lösungen, unter denen der Entscheider seine favorisierte Lösung auswählen kann, indem er die Konflikte zwischen den drei Zielen abwägt. Das zweite Problem beschäftigt sich mit der Erstellung von Fahrplänen für Geräte in einem Wohngebäude, so dass Energiekosten, Kohlenstoffdioxidemissionen und thermisches Unbehagen minimiert werden. Es wird gezeigt, dass lokale Skalarisierungsoptima Fahrpläne darstellen, die eine gute Balance zwischen den drei Zielen bieten. Die Analyse und die Experimente, die in dieser Arbeit vorgestellt werden, ermöglichen es Entscheidern bessere Entscheidungen zu treffen indem Methoden angewendet werden, die mehr Optionen generieren, die mit den Präferenzen der Entscheider übereinstimmen

Evolutionary Dynamic Multi-Objective Optimisation : A survey

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