Multi self-adapting particle swarm optimization algorithm (MSAPSO).

The performance and stability of the Particle Swarm Optimization algorithm depends on parameters that are typically tuned manually or adapted based on knowledge from empirical parameter studies. Such parameter selection is ineffectual when faced with a broad range of problem types, which often hinders the adoption of PSO to real world problems. This dissertation develops a dynamic self-optimization approach for the respective parameters (inertia weight, social and cognition). The effects of self-adaption for the optimal balance between superior performance (convergence) and the robustness (divergence) of the algorithm with regard to both simple and complex benchmark functions is investigated. This work creates a swarm variant which is parameter-less, which means that it is virtually independent of the underlying examined problem type. As PSO variants always have the issue, that they can be stuck-in-local-optima, as second main topic the MSAPSO algorithm do have a highly flexible escape-lmin-strategy embedded, which works dimension-less. The MSAPSO algorithm outperforms other PSO variants and also other swarm inspired approaches such as Memetic Firefly algorithm with these two major algorithmic elements (parameter-less approach, dimension-less escape-lmin-strategy). The average performance increase in two dimensions is at least fifteen percent with regard to the compared swarm variants. In higher dimensions (≥ 250) the performance gain accumulates to about fifty percent in average. At the same time the error-proneness of MSAPSO is in average similar or even significant better when converging to the respective global optima’s

THEORETICAL PREDICTION AND STUDIES OF SELECTED NOVEL MATERIALS UNDER AMBIENT AND EXTREME CONDITIONS

The development of powerful computer algorithms that are specialized at exploring the energy landscape of chemical systems has revolutionized chemical physics and its derived disciplines. Such algorithms that ranges from random search to genetic algorithm are capable of uncovering a geometric configuration for a combination of chemical elements with minimum energy. The unbiased particle swarm-intelligence optimization algorithm extends the capabilities of the genetic algorithm by incorporating social intelligence through particle communication. Social communication during energy surface exploration improves the efficiency and convergence of the algorithm by preventing prediction of similar-energy structures. Particle swarm-intelligence optimization algorithm is capable of solving crystal structure problems and predicting novel crystal structures across dimensions ranging from 0D (clusters) to 3D bulk solids at specific pressure. In this study, the particle swarm-intelligence optimization algorithm was used to study and solve crystal structure problems relating to two classes of materials of industrial significance – high energy density materials and bimetallic nanoclusters. As a significant step towards solving the problem of finding a single-bonded allotrope of nitrogen, we discuss the prediction and characterization of this member of very important class of material – high energy density materials (HEDMs). A new allotrope of nitrogen formed solely by N−N single bonds is predicted to exist between 100 and 150 GPa using the metadynamics algorithm with a biased potential. The crystal structure is characterized by a distorted tetrahedral network consisting of fused N8, N10, and N12 rings. Stability of the structure is established by phonon and vibrational free energy calculations at zero and finite temperatures, respectively. The simulated x-ray diffraction pattern of the new phase is compared to the pattern of a recently synthesized nitrogen phase at the same P-T conditions and an excellent agreement is observed. This suggests the new phase is likely to form above the stability field of cubic gauche (cg) phase. The outstanding metastability of the new phase is attributed to the intrinsic stability of the sp3 bonding as well as the energetically favorable dihedral angles between N−N single bonds, in either gauche or trans conformation. The results of this work after the lab-synthesized cg phase will stimulate new research on metastable phases of nitrogen and their applications as environment-friendly HEDMs. Furthermore, in the second part of this thesis, bimetallic cluster growth is theoretically explored up to the bulk phase. Small clusters provide a unique medium between a single atom and the bulk crystal. Preliminary theoretical and experimental results show that the geometric structures and electronic properties of clusters often differ radically from those of the solid state. Here, a first-principles investigation to explore the growth mechanism of bimetallic clusters AlnAun (n=1-10) and AlAu crystal structures is carried out. It was found that the tetrahedral Al2Au2 cluster can serve as the building block to construct the subsequent nanomaterials as a function of the cluster size until the AlAu bulk. The results in this work provide a clear illustration of how structure evolve from a two-atom particle to multi-atom nanoclusters, and to 3D bulk element. Continued experimental and theoretical studies of these AlnAun clusters may lead to the discovery of how properties transform from a particle to the bulk phase which has important technological implications in electronics, engineering and catalysis

Inverse Problems and Data Assimilation

These notes are designed with the aim of providing a clear and concise introduction to the subjects of Inverse Problems and Data Assimilation, and their inter-relations, together with citations to some relevant literature in this area. The first half of the notes is dedicated to studying the Bayesian framework for inverse problems. Techniques such as importance sampling and Markov Chain Monte Carlo (MCMC) methods are introduced; these methods have the desirable property that in the limit of an infinite number of samples they reproduce the full posterior distribution. Since it is often computationally intensive to implement these methods, especially in high dimensional problems, approximate techniques such as approximating the posterior by a Dirac or a Gaussian distribution are discussed. The second half of the notes cover data assimilation. This refers to a particular class of inverse problems in which the unknown parameter is the initial condition of a dynamical system, and in the stochastic dynamics case the subsequent states of the system, and the data comprises partial and noisy observations of that (possibly stochastic) dynamical system. We will also demonstrate that methods developed in data assimilation may be employed to study generic inverse problems, by introducing an artificial time to generate a sequence of probability measures interpolating from the prior to the posterior

A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications

Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1995. It is now one of the most commonly used optimization techniques. This survey presented a comprehensive investigation of PSO. On one hand, we provided advances with PSO, including its modifications (including quantum-behaved PSO, bare-bones PSO, chaotic PSO, and fuzzy PSO), population topology (as fully connected, von Neumann, ring, star, random, etc.), hybridization (with genetic algorithm, simulated annealing, Tabu search, artificial immune system, ant colony algorithm, artificial bee colony, differential evolution, harmonic search, and biogeography-based optimization), extensions (to multiobjective, constrained, discrete, and binary optimization), theoretical analysis (parameter selection and tuning, and convergence analysis), and parallel implementation (in multicore, multiprocessor, GPU, and cloud computing forms). On the other hand, we offered a survey on applications of PSO to the following eight fields: electrical and electronic engineering, automation control systems, communication theory, operations research, mechanical engineering, fuel and energy, medicine, chemistry, and biology. It is hoped that this survey would be beneficial for the researchers studying PSO algorithms

Sparse Stabilization and Control of Alignment Models

From a mathematical point of view self-organization can be described as patterns to which certain dynamical systems modeling social dynamics tend spontaneously to be attracted. In this paper we explore situations beyond self-organization, in particular how to externally control such dynamical systems in order to eventually enforce pattern formation also in those situations where this wished phenomenon does not result from spontaneous convergence. Our focus is on dynamical systems of Cucker-Smale type, modeling consensus emergence, and we question the existence of stabilization and optimal control strategies which require the minimal amount of external intervention for nevertheless inducing consensus in a group of interacting agents. We provide a variational criterion to explicitly design feedback controls that are componentwise sparse, i.e. with at most one nonzero component at every instant of time. Controls sharing this sparsity feature are very realistic and convenient for practical issues. Moreover, the maximally sparse ones are instantaneously optimal in terms of the decay rate of a suitably designed Lyapunov functional, measuring the distance from consensus. As a consequence we provide a mathematical justification to the general principle according to which "sparse is better" in the sense that a policy maker, who is not allowed to predict future developments, should always consider more favorable to intervene with stronger action on the fewest possible instantaneous optimal leaders rather than trying to control more agents with minor strength in order to achieve group consensus. We then establish local and global sparse controllability properties to consensus and, finally, we analyze the sparsity of solutions of the finite time optimal control problem where the minimization criterion is a combination of the distance from consensus and of the l1-norm of the control.Comment: 33 pages, 5 figure

Swarm gradient dynamics for global optimization: the density case

Using jointly geometric and stochastic reformulations of nonconvex problems and exploiting a Monge-Kantorovich gradient system formulation with vanishing forces, we formally extend the simulated annealing method to a wide class of global optimization methods. Due to an inbuilt combination of a gradient-like strategy and particles interactions, we call them swarm gradient dynamics. As in the original paper of Holley-Kusuoka-Stroock, the key to the existence of a schedule ensuring convergence to a global minimizeris a functional inequality. One of our central theoretical contributions is the proof of such an inequality for one-dimensional compact manifolds. We conjecture the inequality to be true in a much wider setting. We also describe a general method allowing for global optimization and evidencing the crucial role of functional inequalities à la Łojasiewicz