A Parameterized Complexity Analysis of Bi-level Optimisation with Evolutionary Algorithms

Bi-level optimisation problems have gained increasing interest in the field of combinatorial optimisation in recent years. With this paper, we start the runtime analysis of evolutionary algorithms for bi-level optimisation problems. We examine two NP-hard problems, the generalised minimum spanning tree problem (GMST), and the generalised travelling salesman problem (GTSP) in the context of parameterised complexity. For the generalised minimum spanning tree problem, we analyse the two approaches presented by Hu and Raidl (2012) with respect to the number of clusters that distinguish each other by the chosen representation of possible solutions. Our results show that a (1+1) EA working with the spanning nodes representation is not a fixed-parameter evolutionary algorithm for the problem, whereas the global structure representation enables to solve the problem in fixed-parameter time. We present hard instances for each approach and show that the two approaches are highly complementary by proving that they solve each other's hard instances very efficiently. For the generalised travelling salesman problem, we analyse the problem with respect to the number of clusters in the problem instance. Our results show that a (1+1) EA working with the global structure representation is a fixed-parameter evolutionary algorithm for the problem

Multiobjective optimization of electromagnetic structures based on self-organizing migration

Práce se zabývá popisem nového stochastického vícekriteriálního optimalizačního algoritmu MOSOMA (Multiobjective Self-Organizing Migrating Algorithm). Je zde ukázáno, že algoritmus je schopen řešit nejrůznější typy optimalizačních úloh (s jakýmkoli počtem kritérií, s i bez omezujících podmínek, se spojitým i diskrétním stavovým prostorem). Výsledky algoritmu jsou srovnány s dalšími běžně používanými metodami pro vícekriteriální optimalizaci na velké sadě testovacích úloh. Uvedli jsme novou techniku pro výpočet metriky rozprostření (spread) založené na hledání minimální kostry grafu (Minimum Spanning Tree) pro problémy mající více než dvě kritéria. Doporučené hodnoty pro parametry řídící běh algoritmu byly určeny na základě výsledků jejich citlivostní analýzy. Algoritmus MOSOMA je dále úspěšně použit pro řešení různých návrhových úloh z oblasti elektromagnetismu (návrh Yagi-Uda antény a dielektrických filtrů, adaptivní řízení vyzařovaného svazku v časové oblasti…).This thesis describes a novel stochastic multi-objective optimization algorithm called MOSOMA (Multi-Objective Self-Organizing Migrating Algorithm). It is shown that MOSOMA is able to solve various types of multi-objective optimization problems (with any number of objectives, unconstrained or constrained problems, with continuous or discrete decision space). The efficiency of MOSOMA is compared with other commonly used optimization techniques on a large suite of test problems. The new procedure based on finding of minimum spanning tree for computing the spread metric for problems with more than two objectives is proposed. Recommended values of parameters controlling the run of MOSOMA are derived according to their sensitivity analysis. The ability of MOSOMA to solve real-life problems from electromagnetics is shown in a few examples (Yagi-Uda and dielectric filters design, adaptive beam forming in time domain…).

Constructing computer virus phylogenies

There has been much recent algorithmic work on the problem of reconstructing the evolutionary history of biological species. Computer virus specialists are interested in finding the evolutionary history of computer viruses - a virus is often written using code fragments from one or more other viruses, which are its immediate ancestors. A phylogeny for a collection of computer viruses is a directed acyclic graph whose nodes are the viruses and whose edges map ancestors to descendants and satisfy the property that each code fragment is "invented" only once. To provide a simple explanation for the data, we consider the problem of constructing such a phylogeny with a minimum number of edges. In general this optimization problem is NP-complete; some associated approximation problems are also hard, but others are easy. When tree solutions exist, they can be constructed and randomly sampled in polynomial time

Multi-Objective Self-Organizing Migrating Algorithm: Sensitivity on Controlling Parameters

In this paper, we investigate the sensitivity of a novel Multi-Objective Self-Organizing Migrating Algorithm (MOSOMA) on setting its control parameters. Usually, efficiency and accuracy of searching for a solution depends on the settings of a used stochastic algorithm, because multi-objective optimization problems are highly non-linear. In the paper, the sensitivity analysis is performed exploiting a large number of benchmark problems having different properties (the number of optimized parameters, the shape of a Pareto front, etc.). The quality of solutions revealed by MOSOMA is evaluated in terms of a generational distance, a spread and a hyper-volume error. Recommendations for proper settings of the algorithm are derived: These recommendations should help a user to set the algorithm for any multi-objective task without prior knowledge about the solved problem

Preface: Swarm Intelligence, Focus on Ant and Particle Swarm Optimization

In the era globalisation the emerging technologies are governing engineering industries to a multifaceted state. The escalating complexity has demanded researchers to find the possible ways of easing the solution of the problems. This has motivated the researchers to grasp ideas from the nature and implant it in the engineering sciences. This way of thinking led to emergence of many biologically inspired algorithms that have proven to be efficient in handling the computationally complex problems with competence such as Genetic Algorithm (GA), Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), etc. Motivated by the capability of the biologically inspired algorithms the present book on ""Swarm Intelligence: Focus on Ant and Particle Swarm Optimization"" aims to present recent developments and applications concerning optimization with swarm intelligence techniques. The papers selected for this book comprise a cross-section of topics that reflect a variety of perspectives and disciplinary backgrounds. In addition to the introduction of new concepts of swarm intelligence, this book also presented some selected representative case studies covering power plant maintenance scheduling; geotechnical engineering; design and machining tolerances; layout problems; manufacturing process plan; job-shop scheduling; structural design; environmental dispatching problems; wireless communication; water distribution systems; multi-plant supply chain; fault diagnosis of airplane engines; and process scheduling. I believe these 27 chapters presented in this book adequately reflect these topics

Multi-objective optimal design of obstacle-avoiding two-dimensional Steiner trees with application to ascent assembly engineering.

We present an effective optimization strategy that is capable of discovering high-quality cost-optimal solution for two-dimensional (2D) path network layouts (i.e., groups of obstacle-avoiding Euclidean Steiner trees) that, among other applications, can serve as templates for complete ascent assembly structures (CAA-structures). The main innovative aspect of our approach is that our aim is not restricted to simply synthesizing optimal assembly designs with regard to a given goal, but we also strive to discover the best trade-offs between geometric and domain-dependent optimal designs. As such, the proposed approach is centred on a variably constrained multi-objective formulation of the optimal design task and on an efficient co-evolutionary solver. The results we obtained on both artificial problems and realistic design scenarios based on an industrial test case empirically support the value of our contribution to the fields of optimal obstacle-avoiding path generation in particular and design automation in general

Inference of Ancestral Recombination Graphs through Topological Data Analysis

The recent explosion of genomic data has underscored the need for interpretable and comprehensive analyses that can capture complex phylogenetic relationships within and across species. Recombination, reassortment and horizontal gene transfer constitute examples of pervasive biological phenomena that cannot be captured by tree-like representations. Starting from hundreds of genomes, we are interested in the reconstruction of potential evolutionary histories leading to the observed data. Ancestral recombination graphs represent potential histories that explicitly accommodate recombination and mutation events across orthologous genomes. However, they are computationally costly to reconstruct, usually being infeasible for more than few tens of genomes. Recently, Topological Data Analysis (TDA) methods have been proposed as robust and scalable methods that can capture the genetic scale and frequency of recombination. We build upon previous TDA developments for detecting and quantifying recombination, and present a novel framework that can be applied to hundreds of genomes and can be interpreted in terms of minimal histories of mutation and recombination events, quantifying the scales and identifying the genomic locations of recombinations. We implement this framework in a software package, called TARGet, and apply it to several examples, including small migration between different populations, human recombination, and horizontal evolution in finches inhabiting the Gal\'apagos Islands.Comment: 33 pages, 12 figures. The accompanying software, instructions and example files used in the manuscript can be obtained from https://github.com/RabadanLab/TARGe