The True Destination of EGO is Multi-local Optimization

Efficient global optimization is a popular algorithm for the optimization of expensive multimodal black-box functions. One important reason for its popularity is its theoretical foundation of global convergence. However, as the budgets in expensive optimization are very small, the asymptotic properties only play a minor role and the algorithm sometimes comes off badly in experimental comparisons. Many alternative variants have therefore been proposed over the years. In this work, we show experimentally that the algorithm instead has its strength in a setting where multiple optima are to be identified

One PLOT to Show Them All: Visualization of Efficient Sets in Multi-Objective Landscapes

Visualization techniques for the decision space of continuous multi-objective optimization problems (MOPs) are rather scarce in research. For long, all techniques focused on global optimality and even for the few available landscape visualizations, e.g., cost landscapes, globality is the main criterion. In contrast, the recently proposed gradient field heatmaps (GFHs) emphasize the location and attraction basins of local efficient sets, but ignore the relation of sets in terms of solution quality. In this paper, we propose a new and hybrid visualization technique, which combines the advantages of both approaches in order to represent local and global optimality together within a single visualization. Therefore, we build on the GFH approach but apply a new technique for approximating the location of locally efficient points and using the divergence of the multi-objective gradient vector field as a robust second-order condition. Then, the relative dominance relationship of the determined locally efficient points is used to visualize the complete landscape of the MOP. Augmented by information on the basins of attraction, this Plot of Landscapes with Optimal Trade-offs (PLOT) becomes one of the most informative multi-objective landscape visualization techniques available.Comment: This version has been accepted for publication at the 16th International Conference on Parallel Problem Solving from Nature (PPSN XVI

Recognizing Sets in Evolutionary Multiobjective Optimization, Journal of Telecommunications and Information Technology, 2012, nr 1

Among Evolutionary Multiobjective Optimization Algorithms (EMOA) there are many which find only Paretooptimal solutions. These may not be enough in case of multimodal problems and non-connected Pareto fronts, where more information about the shape of the landscape is required. We propose a Multiobjective Clustered Evolutionary Strategy (MCES) which combines a hierarchic genetic algorithm consisting of multiple populations with EMOA rank selection. In the next stage, the genetic sample is clustered to recognize regions with high density of individuals. These regions are occupied by solutions from the neighborhood of the Pareto set. We discuss genetic algorithms with heuristic and the concept of well-tuning which allows for theoretical verification of the presented strategy. Numerical results begin with one example of clustering in a single-objective benchmark problem. Afterwards, we give an illustration of the EMOA rank selection in a simple two-criteria minimization problem and provide results of the simulation of MCES for multimodal, multi-connected example. The strategy copes with multimodal problems without losing local solutions and gives better insight into the shape of the evolutionary landscape. What is more, the stability of solutions in MCES may be analyzed analytically

Using Covariance Matrix Adaptation Evolutionary Strategy to boost the search accuracy in hierarchic memetic computations

Many global optimization problems arising naturally in science and engineering exhibit some form of intrinsic ill-posedness, such as multimodality and insensitivity. Severe ill-posedness precludes the use of standard regularization techniques and necessitates more specialized approaches, usually comprised of two separate stages - global phase, that determines the problem's modality and provides rough approximations of the solutions, and a local phase, which re fines these approximations. In this work, we attempt to improve one of the most efficient currently known approaches - Hierarchic Memetic Strategy (HMS) - by incorporating the Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) into its local phase. CMA-ES is a stochastic optimization algorithm that in some sense mimics the behavior of population-based evolutionary algorithms without explicitly evolving the population. This way, it avoids, to an extent, the associated cost of multiple evaluations of the objective function. We compare the performance of the HMS on relatively simple multimodal benchmark problems and on an engineering problem. To do so, we consider two con gurations: the CMA-ES and the standard SEA (Simple Evolutionary Algorithm). The results demonstrate that the HMS with CMA-ES in the local phase requires less objective function evaluations to provide the same accuracy, making this approach more efficient than the standard SEA

State switching in multi-stable systems: control and optimisation.

This thesis studies state-switching in multistable systems, so that they can switch from inefficient operating states to a more efficient one, in order to achieve performance enhancement in real-life engineering systems. Multistable systems have more than one stable state under a set of parameters and the process of switching from an undesired state to a desired state is achieved by the proposed PD-like controller. It exploits the difference of the displacement and velocity between the undesired and the desired stable conditions for feedback in state switching. Three test systems are used for investigating the performance of this PD-like controller, namely: the Duffing oscillator, which is a typical smooth multistable system; the non-smooth soft-impact oscillator; and the soft-impact oscillator with a drift. A randomised triangular subdivision algorithm is proposed to reconstruct the basins of attraction of the target multistable systems, in order to identify the desired state for switching. Due to the limited capacity of physical actuators, behaviours of the constrained PD-like controller are investigated using extensive simulation on the test systems. Moreover, optimisation of the controller (based on multiple performance objectives) can further improve system performance. Two performance objectives - maximum peak of control input and switching duration - are adopted in optimising the proposed PD-like controller. The first objective is minimised in order to avoid output limit and reduce energy consumption in the actuator, while the second objective is minimised in order to shorten the time required for state switching. These two performance objectives are considered independently in performance optimisation, using particle swarm optimisation (PSO). Since these two objectives are in conflict with each other, both objectives are minimised simultaneously in multiobjective optimisation of the performance of the PD-like controller using Non-Dominated Sorting Genetic Algorithms-II (NSGA-II). A trade-off in performance enhancement is achieved through selecting control parameters from the Pareto optimal set

Gene Regulatory Networks: Modeling, Intervention and Context

abstract: Biological systems are complex in many dimensions as endless transportation and communication networks all function simultaneously. Our ability to intervene within both healthy and diseased systems is tied directly to our ability to understand and model core functionality. The progress in increasingly accurate and thorough high-throughput measurement technologies has provided a deluge of data from which we may attempt to infer a representation of the true genetic regulatory system. A gene regulatory network model, if accurate enough, may allow us to perform hypothesis testing in the form of computational experiments. Of great importance to modeling accuracy is the acknowledgment of biological contexts within the models -- i.e. recognizing the heterogeneous nature of the true biological system and the data it generates. This marriage of engineering, mathematics and computer science with systems biology creates a cycle of progress between computer simulation and lab experimentation, rapidly translating interventions and treatments for patients from the bench to the bedside. This dissertation will first discuss the landscape for modeling the biological system, explore the identification of targets for intervention in Boolean network models of biological interactions, and explore context specificity both in new graphical depictions of models embodying context-specific genomic regulation and in novel analysis approaches designed to reveal embedded contextual information. Overall, the dissertation will explore a spectrum of biological modeling with a goal towards therapeutic intervention, with both formal and informal notions of biological context, in such a way that will enable future work to have an even greater impact in terms of direct patient benefit on an individualized level.Dissertation/ThesisPh.D. Computer Science 201

Peeking beyond peaks: challenges and research potentials of continuous multimodal multi-objective optimization

Computer Systems, Imagery and Medi

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