\chapter*{ABSTRACT}

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Multi-objective optimization is actually required to solve many real-world design or decision making problems, however, most of the time engineers do consider single objective and try to freeze less relevant parameters.

An antenna acts as an interface between free-space radiations and transmitter or receiver. Yagi-Uda antenna introduced in 1926 by H. Yagi and S.Uda acts as a directional antenna consisting of a driven element (a dipole or folded dipole) and additional parasitic elements (called reflector and directors). The reflector element is slightly longer than the driven dipole, whereas the directors can be more than one in numbers whose lengths decrease in the direction of radiation. Yagi-Uda antenna is one of the most popular antenna designs in VHF and UHF due to its constructional ease and high gain, typically greater than 10 dB.

Yagi-Uda antenna is, however, difficult to design as physical design parameters such as element lengths, spacings between adjacent elements, and diameter bear complex and non-linear relationships for gain, impedance and Side Lobe Level (SLL), etc. This antenna design problem, further, complicates as (i) the number of antenna elements are increased so as to achieve higher directional gain or (ii) number of objectives (gain, impedance, etc.,) are increased to meet real world requirements. Therefore, multi-objective optimization of the antenna has always been a catchy problem for researchers. Although, a lot of work is done in this domain, still scope of improvement is visible with modern heuristic of Swarm Intelligence.

This thesis is intended to propose Non-dominated Sorting Biogeography Based Optimization (NSBBO) and investigate for multi-objective optimization of six-element Yagi-Uda antenna designs to achieve two objectives, viz. gain and impedance, simultaneously. However, designing a Yagi-Uda antenna involves determination of wire-lengths and their spacing which is highly complex and non-linear problem. If gain is intended to increase then imaginary part in impedance becomes significantly large.

The convergence performance of different variants of BBO algorithms reported, till date, are investigated in this thesis, along with Non-dominated Sorting (NS) approach for multi-objective optimization of Yagi-Uda antenna design parameters. NS Particle Swarm Optimization is also investigated for fair and comparative performance study.

BBO is one of the most recent population based stochastic optimization technique inspired from the science of biogeography, i.e.,
the study of distribution of biological species, over space and time. Similar to many other Evolutionary Algorithms (EAs), to
evolve optimal solution to any problem, BBO involves two inherent activities, i.e., (i) \textit{exploitation} of available solution
features (species) is made to happen using process of migration among various potential solutions (habitats), (ii) \textit{exploration}
of new solution features occur due to mutation operator. As BBO has shown impressive performance over other EAs for single objective
optimization, therefore, is proposed and considered here for multi-objective optimization.

PSO is another population based EA that is inspired from the flight patterns of bird flocks, which was mainly governed by three
major concerns: (i) \textit{collision avoidance}, (ii) \textit{velocity matching} and (iii) \textit{flock centering}. In nature,
birds exhibit flocking/swarm behavior for maximizing protection from predator, gaining-food from a large effective search-space
and finding mates for themselves. PSO uses a population of potential solutions called particles that are flown through the
search-space with adaptable velocities. Each particle has memory and, therefore, is capable of remembering the ever visited best
position in the search-space. The position corresponding to the past best fitness is known as \textit{pbest} and the overall best
amongst all particles in the population is called global best or \textit{gbest}.

Since the introduction of BBO, in 2008, various BBO variants have been reported by many researchers intended towards improved
convergence performance. Most significant three BBO variants, viz., (a) \textit{Blended migration}, (b) \textit{Immigration Refusal}
and (c) \textit{Enhanced Biogeography-Based Optimization} (EBBO), are considered here for comparative performances for
multi-objective optimization. Similarly, variants of PSO involves (a) Gloabl Best \textit{(gbest)} PSO, (b) Local Best
\textit{(lbest)} PSO. All these variants have been experimented for gain-impedance
optimization of six-wire Yagi-Uda antenna design for multiple times, in this thesis, under identical conditions.

During simulations, the antenna designs are evolved 10 times for gain-impedance optimization with non-dominated sorting.
Averages of all 10 Monte-Carlo evolutionary runs are presented for fair convergence investigation of stochastic natured BBO
and PSO algorithms. C++ programming platform is used for coding of NSBBO and NSPSO algorithms, whereas, Method of Moments (MoM)
based Numerical Electromagnetic Code (NEC2) freeware is used for evaluation of antenna designs for gain and impedance.
During gain-impedance optimization of Yagi-Uda antenna, a maximum gain of 12.70 dBi and impedance of $50\Omega$ is achieved using
NSBBO that is better than that of reported in [Singh et al., 2010], i.e., 12.69 dBi.

This thesis is outlined as follow: Chapter~\ref{Chapter:1} is devoted to introduction to M.Tech thesis that includes introduction
to Research Topic, Motivation, Methodologies, Contributions, Research findings and Organization of thesis. State-of-the-art study
of the historical research in optimizing Yagi-Uda antenna for single and multi-objectives using AI and non-AI techniques is
represented in Chapter~\ref{Chapter:2}. Chapter~\ref{Chapter:3}, is devoted to multi-objective problems and methods used to find
solution to such problems. Chapter~\ref{Chapter:4} is dedicated to study of biogeography, literature background of BBO, algorithmic
flow and BBO variants reported, till date. Chapter~\ref{Chapter:5} is dedicated to study of PSO, literature background of PSO,
algorithmic flow and PSO variants reported till date. In Chapter~\ref{Chapter:6}, various design parameters of Yagi-Uda antenna and
radiation pattern are represented to formulate antenna design problem as optimization problem. In Chapter~\ref{Chapter:7} firstly,
NEC software is introduced to carry on simulation and analysis of electromagnetic behavior of various antenna designs. Secondly,
implementation flow of NSBBO and NSPSO in C++ along with NEC2. Simulation results of convergence performance of NSBBO as well as
NSPSO algorithm and its variants for maximization of gain and achieving an impedance of $50\Omega$ and $75\Omega$, are represented in
Chapter~\ref{Chapter:8}. Lastly, conclusion and future scope of this research are discussed in Chapter~\ref{Chapter:9}.


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