Approximating Pareto frontier using a hybrid line search approach

This is the post-print version of the final paper published in Information Sciences. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2010 Elsevier B.V.The aggregation of objectives in multiple criteria programming is one of the simplest and widely used approach. But it is well known that this technique sometimes fail in different aspects for determining the Pareto frontier. This paper proposes a new approach for multicriteria optimization, which aggregates the objective functions and uses a line search method in order to locate an approximate efficient point. Once the first Pareto solution is obtained, a simplified version of the former one is used in the context of Pareto dominance to obtain a set of efficient points, which will assure a thorough distribution of solutions on the Pareto frontier. In the current form, the proposed technique is well suitable for problems having multiple objectives (it is not limited to bi-objective problems) and require the functions to be continuous twice differentiable. In order to assess the effectiveness of this approach, some experiments were performed and compared with two recent well known population-based metaheuristics namely ParEGO and NSGA II. When compared to ParEGO and NSGA II, the proposed approach not only assures a better convergence to the Pareto frontier but also illustrates a good distribution of solutions. From a computational point of view, both stages of the line search converge within a short time (average about 150 ms for the first stage and about 20 ms for the second stage). Apart from this, the proposed technique is very simple, easy to implement and use to solve multiobjective problems.CNCSIS IDEI 2412, Romani

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

Computer-Aided Multi-Objective Optimization in Small Molecule Discovery

Molecular discovery is a multi-objective optimization problem that requires identifying a molecule or set of molecules that balance multiple, often competing, properties. Multi-objective molecular design is commonly addressed by combining properties of interest into a single objective function using scalarization, which imposes assumptions about relative importance and uncovers little about the trade-offs between objectives. In contrast to scalarization, Pareto optimization does not require knowledge of relative importance and reveals the trade-offs between objectives. However, it introduces additional considerations in algorithm design. In this review, we describe pool-based and de novo generative approaches to multi-objective molecular discovery with a focus on Pareto optimization algorithms. We show how pool-based molecular discovery is a relatively direct extension of multi-objective Bayesian optimization and how the plethora of different generative models extend from single-objective to multi-objective optimization in similar ways using non-dominated sorting in the reward function (reinforcement learning) or to select molecules for retraining (distribution learning) or propagation (genetic algorithms). Finally, we discuss some remaining challenges and opportunities in the field, emphasizing the opportunity to adopt Bayesian optimization techniques into multi-objective de novo design

Small Approximate Pareto Sets with Quality Bounds

We present and empirically characterize a general, parallel, heuristic algorithm for computing small ε-Pareto sets. The algorithm can be used as part of a decision support tool for settings in which computing points in objective space is computationally expensive. We use the graph clearing problem, a formalization of indirect organ exchange markets, as a prototypical example setting. We characterize the performance of the algorithm through ε-Pareto set size, ε value provided, and parallel speedup achieved. Our results show that the algorithm\u27s combination of parallel speedup and small ε-Pareto sets is sufficient to be appealing in settings requiring manual review (i.e., those that have a human in the loop) and real-time solutions

Multi-Criteria Decision Making in Complex Decision Environments

In the future, many decisions will either be fully automated or supported by autonomous system. Consequently, it is of high importance that we understand how to integrate human preferences correctly. This dissertation dives into the research field of multi-criteria decision making and investigates the satellite image acquisition scheduling problem and the unmanned aerial vehicle routing problem to further the research on a priori preference integration frameworks. The work will aid in the transition towards autonomous decision making in complex decision environments. A discussion on the future of pairwise and setwise preference articulation methods is also undertaken. "Simply put, a direct consequence of the improved decision-making methods is,that bad decisions more clearly will stand out as what they are - bad decisions.

Data-Driven Process Optimization of Additive Manufacturing Systems

The goal of the present dissertation is to develop and apply novel and systematic data-driven optimization approaches that can efficiently optimize Additive Manufacturing (AM) systems with respect to targeted properties of final parts. The proposed approaches are capable of achieving sets of process parameters that result in the satisfactory level of part quality in an accelerated manner. First, an Accelerated Process Optimization (APO) methodology is developed to optimize an individual scalar property of parts. The APO leverages data from similar—but non-identical—prior studies to accelerate sequential experimentation for optimizing the AM system in the current study. Using Bayesian updating, the APO characterizes and updates the difference between prior and current experimental studies. The APO accounts for the differences in experimental conditions and utilizes prior data to facilitate the optimization procedure in the current study. The efficiency and robustness of the APO is tested against an extensive simulation studies and a real-world case study for optimizing relative density of stainless steel parts fabricated by a Selective Laser Melting (SLM) system. Then, we extend the idea behind the APO in order to handle multi-objective process optimization problems in which some of the characteristics of the AMabricated parts are uncorrelated. The proposed Multi-objective Process Optimization (m-APO) breaks down the master multi-objective optimization problem into a series of convex combinations of single-objective sub-problems. The m-APO maps and scales experimental data from previous sub-problems to guide remaining sub-problems that improve the solutions while reducing the number of experiments required. The robustness and efficiency of the m-APO is verified by conducting a series of challenging simulation studies and a real-world case study to minimize geometric inaccuracy of parts fabricated by a Fused Filament Fabrication () system. At the end, we apply the proposed m-APO to maximize the mechanical properties of AMabricated parts that show conflicting behavior in the optimal window, namely relative density and elongation-toailure. Numerical studies show that the m-APO can achieve the best trade-off among conflicting mechanical properties while significantly reducing the number of experimental runs compared with existing methods

Numerical and Evolutionary Optimization 2020

This book was established after the 8th International Workshop on Numerical and Evolutionary Optimization (NEO), representing a collection of papers on the intersection of the two research areas covered at this workshop: numerical optimization and evolutionary search techniques. While focusing on the design of fast and reliable methods lying across these two paradigms, the resulting techniques are strongly applicable to a broad class of real-world problems, such as pattern recognition, routing, energy, lines of production, prediction, and modeling, among others. This volume is intended to serve as a useful reference for mathematicians, engineers, and computer scientists to explore current issues and solutions emerging from these mathematical and computational methods and their applications

Understanding Complexity in Multiobjective Optimization

This report documents the program and outcomes of the Dagstuhl Seminar 15031 Understanding Complexity in Multiobjective Optimization. This seminar carried on the series of four previous Dagstuhl Seminars (04461, 06501, 09041 and 12041) that were focused on Multiobjective Optimization, and strengthening the links between the Evolutionary Multiobjective Optimization (EMO) and Multiple Criteria Decision Making (MCDM) communities. The purpose of the seminar was to bring together researchers from the two communities to take part in a wide-ranging discussion about the different sources and impacts of complexity in multiobjective optimization. The outcome was a clarified viewpoint of complexity in the various facets of multiobjective optimization, leading to several research initiatives with innovative approaches for coping with complexity