Scalable and customizable benchmark problems for many-objective optimization

Solving many-objective problems (MaOPs) is still a significant challenge in the multi-objective optimization (MOO) field. One way to measure algorithm performance is through the use of benchmark functions (also called test functions or test suites), which are artificial problems with a well-defined mathematical formulation, known solutions and a variety of features and difficulties. In this paper we propose a parameterized generator of scalable and customizable benchmark problems for MaOPs. It is able to generate problems that reproduce features present in other benchmarks and also problems with some new features. We propose here the concept of generative benchmarking, in which one can generate an infinite number of MOO problems, by varying parameters that control specific features that the problem should have: scalability in the number of variables and objectives, bias, deceptiveness, multimodality, robust and non-robust solutions, shape of the Pareto front, and constraints. The proposed Generalized Position-Distance (GPD) tunable benchmark generator uses the position-distance paradigm, a basic approach to building test functions, used in other benchmarks such as Deb, Thiele, Laumanns and Zitzler (DTLZ), Walking Fish Group (WFG) and others. It includes scalable problems in any number of variables and objectives and it presents Pareto fronts with different characteristics. The resulting functions are easy to understand and visualize, easy to implement, fast to compute and their Pareto optimal solutions are known.This work has been supported by the Brazilian agencies (i) National Council for Scientific and Technological Development (CNPq); (ii) Coordination for the Improvement of Higher Education (CAPES) and (iii) Foundation for Research of the State of Minas Gerais (FAPEMIG, in Portuguese)

Advanced p-Metric Based Many-Objective Evolutionary Algorithm

Evolutionary many objective based optimization has been gaining a lot of attention from the evolutionary computation researchers and computational intelligence community. Many of the state-of-the-art multi-objective and many-objective optimization problems (MOPs, MaOPs) are inefficient in maintaining the convergence and diversity performances as the number of objectives increases in the modern-day real-world applications. This phenomenon is obvious indeed as Pareto-dominance based EAs employ non-dominated sorting which fails considerably in providing enough convergent pressure towards the Pareto front (PF). Researchers invested much more time and effort in addressing this issue by improving the scalability in MaOPs and they have come up with non-Pareto-dominance-based EAs such as decomposition-based, indicator-based and reference-based approaches. In addition to that, the algorithm has to account for the additional computational budget. This thesis proposes an advanced polar-metric (p-metric) based Many-objective EA (in short APMOEA) for tackling both MOPs and MaOPs. p-metric, a recently proposed performance based visualization metric, employs an array of uniformly, distributed direction vectors. In APMOEA, a two-phase selection scheme is employed which combines both non-dominated sorting and p-metric. Moreover, this thesis also proposes a modified P-metric methodology in order to adjust the direction vectors dynamically. In the experiments, we compare APMOEA with four state-of-the-art Many-objective EAs under, three performance indicators. According to the empirical results, APMOEA shows much improved performances on most of the test problems, involving both MOPs and MaOPs.Electrical Engineerin

Visualising Mutually Non-dominating Solution Sets in Many-objective Optimisation

Copyright © 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.As many-objective optimization algorithms mature, the problem owner is faced with visualizing and understanding a set of mutually nondominating solutions in a high dimensional space. We review existing methods and present new techniques to address this problem. We address a common problem with the well-known heatmap visualization, since the often arbitrary ordering of rows and columns renders the heatmap unclear, by using spectral seriation to rearrange the solutions and objectives and thus enhance the clarity of the heatmap. A multiobjective evolutionary optimizer is used to further enhance the simultaneous visualization of solutions in objective and parameter space. Two methods for visualizing multiobjective solutions in the plane are introduced. First, we use RadViz and exploit interpretations of barycentric coordinates for convex polygons and simplices to map a mutually nondominating set to the interior of a regular convex polygon in the plane, providing an intuitive representation of the solutions and objectives. Second, we introduce a new measure of the similarity of solutions—the dominance distance—which captures the order relations between solutions. This metric provides an embedding in Euclidean space, which is shown to yield coherent visualizations in two dimensions. The methods are illustrated on standard test problems and data from a benchmark many-objective problem

Applied (Meta)-Heuristic in Intelligent Systems

Engineering and business problems are becoming increasingly difficult to solve due to the new economics triggered by big data, artificial intelligence, and the internet of things. Exact algorithms and heuristics are insufficient for solving such large and unstructured problems; instead, metaheuristic algorithms have emerged as the prevailing methods. A generic metaheuristic framework guides the course of search trajectories beyond local optimality, thus overcoming the limitations of traditional computation methods. The application of modern metaheuristics ranges from unmanned aerial and ground surface vehicles, unmanned factories, resource-constrained production, and humanoids to green logistics, renewable energy, circular economy, agricultural technology, environmental protection, finance technology, and the entertainment industry. This Special Issue presents high-quality papers proposing modern metaheuristics in intelligent systems

Analytical cost metrics: days of future past

2019 Summer.Includes bibliographical references.Future exascale high-performance computing (HPC) systems are expected to be increasingly heterogeneous, consisting of several multi-core CPUs and a large number of accelerators, special-purpose hardware that will increase the computing power of the system in a very energy-efficient way. Specialized, energy-efficient accelerators are also an important component in many diverse systems beyond HPC: gaming machines, general purpose workstations, tablets, phones and other media devices. With Moore's law driving the evolution of hardware platforms towards exascale, the dominant performance metric (time efficiency) has now expanded to also incorporate power/energy efficiency. This work builds analytical cost models for cost metrics such as time, energy, memory access, and silicon area. These models are used to predict the performance of applications, for performance tuning, and chip design. The idea is to work with domain specific accelerators where analytical cost models can be accurately used for performance optimization. The performance optimization problems are formulated as mathematical optimization problems. This work explores the analytical cost modeling and mathematical optimization approach in a few ways. For stencil applications and GPU architectures, the analytical cost models are developed for execution time as well as energy. The models are used for performance tuning over existing architectures, and are coupled with silicon area models of GPU architectures to generate highly efficient architecture configurations. For matrix chain products, analytical closed form solutions for off-chip data movement are built and used to minimize the total data movement cost of a minimum op count tree

An Investigation of Search Behaviour in Search-Based Unit Test Generation

As software testing is a laborious and error-prone task, automation is desirable. Search-based unit test generation applies evolutionary search algorithms to generate software tests and, in the context of unit testing object-oriented software, Genetic Algorithms (GAs) are frequently employed to generate unit tests that maximise code coverage. Although GAs are effective at generating tests that achieve high code coverage, they are still far from being able to satisfy all test goals (e.g., covering all branches). While some general limitations are known, there is still a lack of understanding of the search behaviour during the optimization, making it difficult to identify the factors that make a search problem difficult. Therefore, this thesis aims to investigate the search behaviour when GAs are applied to generate object-oriented unit tests and, more specifically, identify the reasons why the search fails to achieve the desired test goals. This is achieved by investigating (1) the fitness landscape structure and the impact of its features on the generation of unit tests and (2) the influence of population diversity on generating potential unit tests. Based on the outcome of this investigation, the impact of test case reduction on the landscape features and population diversity is also investigated. Our results reveal that classical indicators for rugged fitness landscapes suggest well searchable problems in the case of unit test generation, but the fitness landscape for most problem instances is dominated by detrimental plateaus. However, increasing diversity does not have a beneficial effect on coverage in general, but it may improve coverage when diversity is promoted adaptively. In fact, increasing diversity has a negative impact on the individual length, which can also be mitigated with the adaptive diversity. Applying the test case reduction seems to be promising in improving the landscape structure and reducing the negative side effects of diversity on length, but have no considerable impact on the search performance

Conception des réseaux maillés sans fil à multiples-radios multiples-canaux

Généralement, les problèmes de conception de réseaux consistent à sélectionner les arcs et les sommets d’un graphe G de sorte que la fonction coût est optimisée et l’ensemble de contraintes impliquant les liens et les sommets dans G sont respectées. Une modification dans le critère d’optimisation et/ou dans l’ensemble de contraintes mène à une nouvelle représentation d’un problème différent. Dans cette thèse, nous nous intéressons au problème de conception d’infrastructure de réseaux maillés sans fil (WMN- Wireless Mesh Network en Anglais) où nous montrons que la conception de tels réseaux se transforme d’un problème d’optimisation standard (la fonction coût est optimisée) à un problème d’optimisation à plusieurs objectifs, pour tenir en compte de nombreux aspects, souvent contradictoires, mais néanmoins incontournables dans la réalité. Cette thèse, composée de trois volets, propose de nouveaux modèles et algorithmes pour la conception de WMNs où rien n’est connu à l’ avance. Le premiervolet est consacré à l’optimisation simultanée de deux objectifs équitablement importants : le coût et la performance du réseau en termes de débit. Trois modèles bi-objectifs qui se différent principalement par l’approche utilisée pour maximiser la performance du réseau sont proposés, résolus et comparés. Le deuxième volet traite le problème de placement de passerelles vu son impact sur la performance et l’extensibilité du réseau. La notion de contraintes de sauts (hop constraints) est introduite dans la conception du réseau pour limiter le délai de transmission. Un nouvel algorithme basé sur une approche de groupage est proposé afin de trouver les positions stratégiques des passerelles qui favorisent l’extensibilité du réseau et augmentent sa performance sans augmenter considérablement le coût total de son installation. Le dernier volet adresse le problème de fiabilité du réseau dans la présence de pannes simples. Prévoir l’installation des composants redondants lors de la phase de conception peut garantir des communications fiables, mais au détriment du coût et de la performance du réseau. Un nouvel algorithme, basé sur l’approche théorique de décomposition en oreilles afin d’installer le minimum nombre de routeurs additionnels pour tolérer les pannes simples, est développé. Afin de résoudre les modèles proposés pour des réseaux de taille réelle, un algorithme évolutionnaire (méta-heuristique), inspiré de la nature, est développé. Finalement, les méthodes et modèles proposés on été évalués par des simulations empiriques et d’événements discrets.Generally, network design problems consist of selecting links and vertices of a graph G so that a cost function is optimized and all constraints involving links and the vertices in G are met. A change in the criterion of optimization and/or the set of constraints leads to a new representation of a different problem. In this thesis, we consider the problem of designing infrastructure Wireless Mesh Networks (WMNs) where we show that the design of such networks becomes an optimization problem with multiple objectives instead of a standard optimization problem (a cost function is optimized) to take into account many aspects, often contradictory, but nevertheless essential in the reality. This thesis, composed of three parts, introduces new models and algorithms for designing WMNs from scratch. The first part is devoted to the simultaneous optimization of two equally important objectives: cost and network performance in terms of throughput. Three bi-objective models which differ mainly by the approach used to maximize network performance are proposed, solved and compared. The second part deals with the problem of gateways placement, given its impact on network performance and scalability. The concept of hop constraints is introduced into the network design to reduce the transmission delay. A novel algorithm based on a clustering approach is also proposed to find the strategic positions of gateways that support network scalability and increase its performance without significantly increasing the cost of installation. The final section addresses the problem of reliability in the presence of single failures. Allowing the installation of redundant components in the design phase can ensure reliable communications, but at the expense of cost and network performance. A new algorithm is developed based on the theoretical approach of "ear decomposition" to install the minimum number of additional routers to tolerate single failures. In order to solve the proposed models for real-size networks, an evolutionary algorithm (meta-heuristics), inspired from nature, is developed. Finally, the proposed models and methods have been evaluated through empirical and discrete events based simulations

Crashworthiness analysis and design optimization of hybrid energy absorption devices: application to aircraft structures

Programa Oficial de Doutoramento en Enxeñaría Civil . 5011V01[Abstract]Amid the main research lines for the enhancement of aircraft and automotive designs, structural optimization and crashworthiness studies are at their pinnacle. Means of transport need to be robust and safe, albeit efficiency and lightness cannot be neglected. While active safety systems have avoided innumerable accidents, passive crashworthiness systems need to protect passengers when they do occur. In the event of a crash, modern structures are designed to collapse progressively, dissipating high amounts of kinetic energy and protecting the passengers against abrupt decelerations. Within this broad field of study, the aim of this thesis is that of bettering traditional crash structures by designing and optimizing thin-walled hybrid energy absorbers, and ultimately proving reduced occupant injury levels during representative impact scenarios. The collapsible energy absorbers studied throughout this research originated by combining square metallic tubes with inner cores made from glass-fiber reinforced polymer (GFRP) and foam structures. Honeycombs are studied in depth, showing their outstanding behavior as load bearing structures and identifying the effects of modifying their cell’s shape. Another composite structure investigated was that of an intertwined four-plate star core, slightly less stiff than honeycombs but promising crushing behavior. Foam extrusions are also used as standalone reinforcements and as filling of the inner core’s voids, always enhancing the energy absorption capabilities of specimens. Specimens are characterized according to different crashworthiness metrics, including their energy absorption value, peak force undergone during its collapse and the mass of the components. Moreover, each initial design is subjected to optimization techniques to achieve the utmost from the aforementioned metrics. For that, finite element simulations of axial dynamic loading are parametrized as to obtain variable core heights, material thicknesses and modifiable honeycomb’s cell size and shape. These are later coupled with sampling and metamodeling algorithms, constructing a surrogate model which performs accordingly with the simulation during any fluctuation in the design variables. Later on, the metamodels are single- and multi-objectively optimized with genetic algorithms, yielding various sets of designs that excel in one or more of the selected responses. As a second goals of this work, the previous energy absorber design and the methodology used are to be applied in a significant impact scenario of a passenger vehicle. A drop-test numerical simulation from a Boeing 737-200 fuselage section is developed and correlated with extensive experimental data, later analyzing the crushing behavior of isolated components and their energy absorption trends. The effect of adding hollow thin-walled tubes as vertical struts is studied, expecting a great enhancement of the conventional design response. Surrogate-based optimization methodologies are also applied to this simulation, monitoring various crashworthiness biometrics and the specimen’s mass. Results show that on a coupon basis, the usage of inner reinforcements can modify the tube’s collapse patterns and increase its specific energy absorption values by up to 30 %, mainly caused by the interaction between the core and the confining structure. Moreover, reducing the core’s height has also shown improved responses, offsetting the triggering loads of each component and yielding peak force values 33 % lower. Topographic optimization of honeycomb cells has revealed that the highest specific energy absorption values for dynamic loads are not achieved with a regular cell but with a pseudo-rectangular one. The usage of foam as cell-filling has also proved superb, increasing energy absorption by another 28 % with minor hindering on the specimen’s mass. As for the validation of the full size aircraft drop-test simulation, numerical and graphical results closely match those of the experimental procedure. It was found that removing the auxiliary fuel tank from the original section increased occupant injury levels due to high structural deformation and low energy absorption by the main structures. In a later phase, hybrid energy absorbers are added to the fuselage section with an empty cargo area, and a new surrogate model is built with 600 full-scale drop test simulation. The surrogate is then single- and multi-objectively optimized, reducing acceleration peak values by 50 % and injury levels from severe to moderate at different occupant locations

Applied Metaheuristic Computing

For decades, Applied Metaheuristic Computing (AMC) has been a prevailing optimization technique for tackling perplexing engineering and business problems, such as scheduling, routing, ordering, bin packing, assignment, facility layout planning, among others. This is partly because the classic exact methods are constrained with prior assumptions, and partly due to the heuristics being problem-dependent and lacking generalization. AMC, on the contrary, guides the course of low-level heuristics to search beyond the local optimality, which impairs the capability of traditional computation methods. This topic series has collected quality papers proposing cutting-edge methodology and innovative applications which drive the advances of AMC