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\title{}
\author[1]{Ishwarya Anand}%
\affil[1]{GGSIPU}%
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\date{\today}
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\section*{Introduction}
\label{intro}
Optimization is the method of maximizing or minimizing a given function using a given set of all possible solutions available at a certain point in time. The "best" solution out of these solutions becomes the answer. The primary goals of Optimization are Minimum Cost, Maximum Profit, Minimum error, Minimum Effort Optimum Design. Nature has always fascinated us in innumerable ways. \hyperref[csl:1]{[1]}The scientists from several years have studied the patterns and occurrences in nature and then these patterns are then adopted in artificial computational systems. Optimization refers to an act or a methodology of making a system, product, design or an action completely accurate, perfect and functional.
Carpooling is the concept of sharing vehicles between people with similar travel needs. The idea has achieved an impressive public attention in recent years. The use of shared vehicles has economic aspects and
environmental benefits, individually and collectively. Having less vehicles on the streets leads to less traffic jams, resulting in smoother, therefore more efficient traffic.\hyperref[csl:2]{[2]} This helps to minimize the impact of transport on the environment, which at the moment is one of the major concerns, especially due to the large city sizes. From an economic point of view, significantly sharing travel between passengers reduces transport costs
\section*{Basic Steps of a Nature Inspired Algorithm}\hyperref[csl:3]{[3]}
\begin{itemize}
\item A population of competing solutions (agents such as ants, bees, fireflies etc.) is taken in each algorithm.
\item The best solution is selected out of the above solutions based on the fitness function value.
\item The population is evolved, (that is, new solutions are found) using operators such as mutation, crossover in terms of mathematical equations and formulas.
\item The population keeps on evolving until all the solutions converge, that is, all the solutions become somewhat similar.
\item The movement of the particles is a combination of stochastic (random moves) and deterministic moves (the agents are attracted towards the current best solution g* and its own previous best solution). So, in other words, the particles move in quasi deterministic fashion which allows the particles to escape the condition of getting stuck in local optima region.
\item The algorithm carries out both global (exploration) as well as local (exploitation) search to find out optimal solutions.
\item The best solutions are selected by the "Survival of the Fittest" phenomenon.
\end{itemize}
\section*{Optimization Algorithms}\hyperref[csl:4]{[4]}
The optimization algorithms can be categorized into the following two types :
\begin{itemize}
\item Traditional Algorithms
\item Non- Traditional Algorithms
\end{itemize}
\subsection*{Traditional Algorithms}
They refer to the analytical methods which use the concept of differential calculus to find optimal solutions of continuous and differentiable functions. These algorithms undergo iterations until an optimal solution is obtained. They can be further categorized into :
\begin{itemize}
\item \textbf{Direct Method : }In Direct method, only the objective function and the constraints are used to guide the search process. It includes methods such as Bracketing methods, Exhaustive search method ,Bounding phase method, Region-elimination method, Interval halving method, Fibonacci search method, Point estimation method, Successive quadratic method.
\item \textbf{Gradient Method :}In Gradient method, 1st and/or 2nd derivative of objective function and/or constraints are used to guide the search process. It include methods such as Newton raphson method, Bisection method, Secant method, Cubic search method
\end{itemize}
\subsection*{Non-Traditional Algorithms}
They refer to the approximation methods which converge quickly towards a solution but there would be no guarantee that the solution obtained would be optimal.They include :
\begin{itemize}
\item Evolutionary Algorithms such as Genetic Algorithms(GA)
\item Trajectory Based Methods such as Simulated Annealing
\item Swarm Intelligence(SI) such as Particle Swarm Optimiation(PSO)
\item Local Search Techniques such Ant Colony Optimization(ACO), Artificial Bee Colony Optimization(ABC), Bat Algorithm
\end{itemize}
\section*{Bio-Inspired Algorithms}
\subsection*{Ant Colony Optimization}
Ants select the shortest path depending on the pheromone chemical deposit in the way from nest to food. Each ant follows the way of previous ants with higher pheromone deposit. This swarm activity of ants improves the routing performance in term of delay. Moreover, energy consumption of each sensor can also be reduced according to the foraging activity of real ants. Swarm intelligence behavior significantly improves network lifetime and packet delivery ratio.
\subsection*{Particle Swarm Optimization}
Particle swarm optimization is an effective, simple, and efficient algorithm for optimization. PSO compares the fitness of particles to select the cluster head depending on the higher fitness value. Reduced energy consumption is obtained through the fitness evaluation.
\subsection*{Cuckoo Search Algorithm}
Cuckoo search algorithm depends on the selection of the best routing solution to achieve the network lifetime and reduced energy consumption. It is a probabilistic method for selecting the cuckoo's egg from host bird eggs. Cuckoo drops their eggs in the host birds nest, and both are more similar to see. If the host bird identifies the difference of egg, it throws away or rebuilds their nest in another place. Cuckoos egg represents the best routing solution. CSA leads the higher energy conservation, and it enhances the network efficiency.
\subsection*{Firefly Algorithm}
WSN contains more sensors in large geographic region that can communicate with other sensors and transmit the sensed data to the base station. Minimum energy routing is the most important one during communication. The sensor routing protocols can improve the network lifetime using a firefly routing algorithm. Firefly produces flashes of light in short duration to attract prey or other fireflies. More attractiveness depends on the intensity of light flashes. Fireflies move toward another firefly with high-intensity light. This attractively based routing is used in sensor communication to attain the limited energy consumption.
\subsection*{Bat Algorithm}
The main aim of bat algorithm is achieving the packet routing through the optimal paths which depend on the cluster formation and the cluster head selection. Bat algorithm depends on the echolocation based food searching of real bats. Bats make the sound louder and it can adjust its frequency depends on the received echo from prey or obstacles.
\subsection*{Genetic Algorithm}
Genetic algorithm motivates the routing methodology of biological evaluation such as crossover and mutation of various fittest chromosomes (solutions). In a genetic algorithm, individuals are selected for crossover (breeding) depending on their fitness amount. By combining these solutions, significantly produce a new individual solution. The new individual represents the new generation. This process is repeated for achieving the more fitness solutions. In sensor networks, it saves more energy and increases the lifetime using reproduction process.
\subsection*{Artificial Algae Algorithm}
Artificial algae algorithm (AAA), which is one of the recently developed bio-inspired optimization algorithms, has been introduced by inspiration from living behaviors of microalgae. In AAA, the modification of the algal colonies, i.e. exploration and exploitation is provided with a helical movement.
\subsection*{Chicken Swarm Optimization}
A new bio-inspired algorithm, Chicken Swarm Optimization (CSO), is proposed for optimization applications. Mimicking the hierarchal order in the chicken swarm and the behaviors of the chicken swarm, including roosters, hens and chicks, CSO can efficiently extract the chickens' swarm intelligence to optimize problems.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Capture/Capture}
\caption{{Example of solution representation for the taxi sharing
problem.\protect\hyperref[csl:5]{[5]}
{\label{328243}}%
}}
\end{center}
\end{figure}
\subsection*{Algorithm}\hyperref[csl:6]{[6]}
The proposed encoding has specific characteristics and restrictions, which is why we apply ad-hoc search operators.
\begin{itemize}
\item Initialization of the population: the initial population consists of two individuals representing greedy cost and delay solutions and the rest of the population are generated by applying to random number of disturbances (ie exchange of two elements) on copies of these two individuals.\hyperref[csl:7]{[7]}
\item Feasibility check and correction process: the initialization method may violate some of the restrictions defined for the coding of the solution. Therefore, a corrective function is applied to guarantee the solution's feasibility. The method searches for sequences of digits that are not zero greater than the maximum capacity of the vehicle
At the moment So, the correction algorithm identifies the first pair of consecutive zeros, moves the first zero to a random position in the non-zero sequence to stop the invalid sequence. The search for invalid sequences continues until the end of the solution; at that point, the individual meets all the restrictions related to the problems.
\item Selection: a selection of the tournament (tournament size: 2 persons) is applied to provide a selection pressure. Initial experiments confirmed that the standard proportional selection technique
It has not provided enough diversity, which leads to premature convergence.
\item Recombination: we apply an ad hoc variant of the position-based crossover operator (PBX).
\end{itemize}\selectlanguage{english}
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\includegraphics[width=1.00\columnwidth]{figures/Capture1/Capture1}
\caption{{\protect\hyperref[csl:5]{[5]}
{\label{502575}}%
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\section*{References}\sloppy
\phantomsection
\label{csl:1}[1]``{Nature Inspired Algorithms}''. \url{https://econ.ubbcluj.ro/~rodica.lung/taco/literatura/Yang_nature_book_part.pdf} [Online]. Available at: \url{https://econ.ubbcluj.ro/~rodica.lung/taco/literatura/Yang_nature_book_part.pdf}
\phantomsection
\label{csl:2}[2]``{Nature-Inspired Algorithms: State-of-Art, Problems and Prospects}''. \url{https://pdfs.semanticscholar.org/fe0d/8e06d1e09a3fc86098b984def4d406b8f336.pdf} [Online]. Available at: \url{https://pdfs.semanticscholar.org/fe0d/8e06d1e09a3fc86098b984def4d406b8f336.pdf}
\phantomsection
\label{csl:3}[3]R. Kapur, ``{Review of nature inspired algorithms in cloud computing}'', in \textit{International Conference on Computing Communication {\&} Automation}, 2015, doi: 10.1109/ccaa.2015.7148476 [Online]. Available at: \url{https://doi.org/10.1109\%2Fccaa.2015.7148476}
\phantomsection
\label{csl:4}[4]I. F. jr. Xin-She Yang, ``{A Brief Review of Nature-Inspired Algorithms for Optimization}'', 2013.
\phantomsection
\label{csl:5}[5]S.-C. Huang, M.-K. Jiau, and C.-H. Lin, ``{A Genetic-Algorithm-Based Approach to Solve Carpool Service Problems in Cloud Computing}'', \textit{{IEEE} Transactions on Intelligent Transportation Systems}, vol. 16, no. 1, pp. 352–364, Feb. 2015, doi: 10.1109/tits.2014.2334597. [Online]. Available at: \url{https://doi.org/10.1109\%2Ftits.2014.2334597}
\phantomsection
\label{csl:6}[6]S. Yan and C.-Y. Chen, ``{A model and a solution algorithm for the car pooling problem with pre-matching information}'', \textit{Computers {\&} Industrial Engineering}, vol. 61, no. 3, pp. 512–524, Oct. 2011, doi: 10.1016/j.cie.2011.04.006. [Online]. Available at: \url{https://doi.org/10.1016\%2Fj.cie.2011.04.006}
\phantomsection
\label{csl:7}[7]C. Ma, R. He, and W. Zhang, ``{Path optimization of taxi carpooling}'', \textit{{PLOS} {ONE}}, vol. 13, no. 8, p. e0203221, Aug. 2018, doi: 10.1371/journal.pone.0203221. [Online]. Available at: \url{https://doi.org/10.1371\%2Fjournal.pone.0203221}
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