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\chapter{Review of Related Literature}  \label{sec:relatedlit}  \setcounter{secnumdepth}{5}  \section{Review of Related Paper}  \subsection{Transit Route Generation}  \label{sec:transitroutegeneration} 
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  \begin{table}[]  \centering  \caption{Overview of Past Research on Transit Network Design \cite{Foletta_2010}} \protect\cite{Foletta_2010}}  \label{tab:routing}  \begin{tabular}{|l|l|}  \hline 
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\end{tabular}  \end{table}  \subsubsubsection \emph{Contiuous \subsubsection {Continuous  \& Discrete Approach}\\ Approach}  \label{sec:continuousdiscreteapproach}  Continuous approach formulates a problem on a solution space with certain completeness. This approach works well for small problems, but as the size of the problem increases, solution time quickly reaches unreasonable values. While discrete approach formulates the problem on possible solution subspaces defined based on domain specified heuristic guidelines. Discrete solution requires less computing time \cite{Foletta_2010}.\\  \subsubsection{\emph{Hybrid Routing Model}}   \label{sec:hybridrouting}    Before the Hybrid Routing Model became the result of He et al. studies, random networks, scale-free networks, small-world networks and a square lattice was used to study efficient generation of routing methods to mitigate congestion. Square lattices are typically used as the base model to study road networks. All four generated networks have the number of nodes \emph{N} = 400 with an average degree $\emph{k} \approx{4}$. Transport demand was assumed to be homogeneously distributed. The total transport volume \emph{V} was increased to 10,000 to 35,000 to simulate different levels of congestion in the networks. The transport cost of a link was defined by the Bureau of Public Roads function, which is widely used in civil engineering where Transport cost \emph{Cij} between two neighboring nodes \emph{i} and \emph{j} is defined as :  \begin{center}  $cij(f) = lij + \alpha(f /Capacity)  \beta  lij$\end{center}  where lij is the distance between the two nodes, f is the link flow, Capacity is the link capacity, and α and β determine the  correlation between congestion cost and f . Noting that the volume over capacity VOC = f /Capacity, can be written as:  \begin{center}  $cij(f) = lij + \alpha(VOC)  \beta  lij.$\end{center}  Combining shortest path (SP) routing and minimum cost (MC) routing, a hybrid routing model was created by He et al. This model requires only a small fraction of the total number of agents to use MC routes, and mitigates congestion under heterogeneous or homogeneous transport demand. \cite{He_2015} Usually, if it concerns network flow, the agent's first choice is the shortest path. MC routing mitigate networks in congestion, but it is difficult to induce all agents to choose MC routes. Using the hybrid routing model, targeted agents are forced to use MC routes. This is generated by calculating transport cost for each agent in SP routing scenario then the fraction of agents with the largest transport cost were assigned as a target to use MC routes. The remaining agents use SP routes, while the link flow is calculated. With the updated link cost, targeted agents are kept to use MC routes until the condition of convergence is satisfied.  \subsection{Microsimulation}  \label{sec:microsimulation}  The study of \cite{Ljubovic_2009} stated four approaches of traffic modeling. The study’s objective was to compare a non-coordinated system with a coordinated one to prove their hypothesis being that the latter would be more efficient. One of the approaches used was microsimulation and in utilizing this method they had to understand the basic element of the system which was a single vehicle in the traffic. A differential equation was formulated for each vehicle to provide the data that will produce results needed to evaluate the effect of the current vehicle being studied on the overall structure of the system.\\  A class of this approach is called a car-following model and it takes a number of factors such as the distance between the car being studied and the one in front of it, the speed of each of the vehicles and the behavior of the drivers involved. Microsimulation as by its name, is able to take the most basic part of the traffic system and simulate it so that a situation may be analyzed in greater detail. Therefore, this model helped to a better understand the possible scenarios in a traffic system.\\  In the objective of wanting to learn microsimulation, a research by \cite{sbyati_roden} named “Best Practices in the Use of Micro Simulation Models”, has discovered the advantages and disadvantages of using Microsimulation. Through their research, they have found that one study by \cite{austroads_2006} concluded that there are three characteristics which make microsimulation desirable. The first chracteristic of microsimulation is clarity because its visual attribute makes the information acquired from the method more understandable. Secondly, the characteristic which makes the gathered data valid is because microsimulation is accurate. The approach studies an individual vehicle and it has allowed for a more detailed analysis since each vehicle makes different decisions and this enables exploration of more scenarios than having fixed parameters on the system such as travel time for an expanse of road. Lastly, the method was said to be flexible because by diving into more specific scenarios, looking for solutions to the issues regarding traffic may be easier since one will be able to pinpoint the problem areas. \\  Microsimulation having its pros does have its cons and these were presented in the form of an opinion by \cite{Fox_2008}. According to the study, using microsimulation purely will not be able to provide the best results so it is better to use a multi-resolution approach. One method has its strengths which may be the other method’s weakness. Thus, combining approaches helped learning traffic in a more accurate sense since the aspects of a single resolution approach may be targeted by another one to examine almost all possible factors that may need to be given thought when trying to improve a system. Another study which used observations to state what may need to be considered in using microsimulation was by Dr. May (1990). Some of the observations on the paper were to think of all possible alternatives that may yield best results to a problem, the cost and time to utilize the method and the amount of data to make the generated output precise and close to what may actually happen in the real world.\\  \subsection{Skip-Stop Design Model under Mixed Traffic Conditions}  \label{sec:skipstopmodel}  \subsubsubsection{Optimization Process using Genetic Algorithm}\\  \label{sec:optimizationusinggeneticalgorithm} This model was the result of the study by Sun et al. from analyzing and optimizing the Travel Time model.It is Travel time is affected by traffic volume and capacity links which is influenced by the number of stopping buses at a stop \cite{feng_wen-tao_ying_dian-hai_2013}.With mathematical functions included in the study, the researchers compared the equation formulated from both the travel time model and skip-stop model adaptation. The study states that bus stops make an impact on traffic interfering with flow. \\  The Skip-Stop model can be taken as a nonlinear 0-1 integer programming problem, with the binary integer variables representing which stops to be skipped by the control vehicles.In analyzing the new model, the researchers used the run time model which is usually used in understanding existing service and evaluating transit planning and strategies.\\  \subsection{Based on Cellular Automata}  \label{sec:cellularautomata}  Cellular automata (CA) is an alternative to microsimulation and other traffic flow models based on continuous values. CA models have the distinction of being able to capture micro-level dynamics and still relate traffic flow in a macro level. Additionally, CA models are able to represent vehicle and its interactions relating it to traffic flow metrics: throughput, travel time and vehicle speed. Using CA models in modeling roads are powerful either in a single or multi-lane traffic \cite{Benjaafar}.  A famous model of this approach is based from the works of Nagel-Schreckenberger model \cite{Benjaafar} \cite{Ljubovic_2009}. His work is known for the term "jam from nothing" where traffic appear for no apparent and particular reason, noting that models based on differential equations failed to describe the phenomenon.\\  \subsection{Agent Based Models}  \label{sec:agentbasedmodels}  Agent based modeling is a powerful method to form simulations that models autonomous units to make decisions called agents. Agents create decisions like a human, has its own perspective and bound by certain decision rules but realistically also lacks the complete picture of the system. Agent based models can have rules and behaviors that could not have been predicted mathematically \cite{Ljubovic_2009} and one example in application to the research paper is the instance of traffic congestion.\\ 
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Model of an individual agent can be separately modified and tested. In the example of using traffic models, measuring the behavior of individual drivers and compare it with an encoded agent model is possible. Afterwards, the agent can be placed into a simulation to calibrate the whole system's behavior through the use of the measured values.\\  Aside from using Agent-based simulations in road traffic itself, it can further be used in designing a passenger-centered design of buses to enhance concepts designs of buses to improve service to different passengers. An approach discussed by Schelenz et al. was to use a passenger model where passengers' preferences and behavior are modeled with modern bus layouts considering seat typologies and orientations, types and number of doors, ticketing machines and the fact that passengers are not only classified by gender, age and ethnicity but also by their physical needs and psychological features \cite{Schelenz_2012}. \cite{Schelenz_2012}.\\    \subsection{Optimization Process }  \label{sec:optimization}  \subsubsubsection \emph{Hybrid Routing Model}\\  Before \subsubsection{{\emph{Using Genetic Algorithm}}}  \label{sec:geneticalgorithm}    Optimization from  the Hybrid Routing study on Skip Stop Design  Model became uses  the result of He et al. studies, random networks, scale-free networks, small-world networks and Genetic Algorithm. Since the model is considered  a square lattice was used nonlinear 0-1 integer problem where its parameters are close  to study efficient generation of routing each other, conventional  methods to mitigate congestion. Square lattices are typically used as solve  the base model to study road networks. All four generated networks have problem will hardly accomplish  the number of nodes \emph {N} = 400 with an average degree {\emph{k}} \approx 4. Transport demand was assumed to be homogeneously distributed. The total transport volume \emph{V} was increased to 10,000 to 35,000 to simulate different levels task. Thus, the use  ofcongestion in  the networks. Genetic Algorithm which is a heuristic search method that imitates the process of natural evolution.  The transport cost principles  of a link was defined natural evolution is followed  by the Bureue subject  of Public Roads function, which natural selection and survival of the fittest individual. It  iswidely  used in civil engineering where Transport cost \emph{Cij} between two neighboring nodes \emph{i} on bi-level programming model  and \emph{j} is defined as : \\ cij(f) = lij + α(f /Capacity)  β  lij\\ in finding the optimal coordination of the stopping stations in order to minimize inconveniences for passengers\cite{feng_wen-tao_ying_dian-hai_2013}.  where lij Genetic algorithms In using genetic algorithms to solve an optimization problem,each solution is coded as a string called a \emph{"chromosome"} and denoted as an individual while a collection is known as a population. The process starts by randomly generating a population and for each iteration a new population of same size  is generated from  the distance between current population using three basic operations on the individuals of the population. The operators are (i) Reproduction/Selection, (ii) Crossover and (iii) Mutation \cite{bhandari_murthy_pal_2012}.\\  To determine the global optimal solution in defining a stopping variance using the algorithm, starting to represent a solution in chromosomal form is followed. Following the work of Holland found under the research paper of Bhandari et al.,where for every iteration  the evaluation or fitness function \emph{fit} for a string \emph{S} is equivalent to the function \emph{f}:  \begin{center}  $\emph{fit(S)} = \emph{f(x)}$  \end{center}  Next is the process of Natural selection which is based on the fitness function, where the weaker members are weeded out, and new members are generated to replace them either by mutation or reproduction of stronger members \cite{bhandari_murthy_pal_2012}. Crossover and Mutation steps follows the process. Crossover step is where  two nodes, f potential string/chromosome exchanges information and generates and offspring. Mutation then creates alteration into the character creating variability in the population to be iterated.\\  There  is such a thing as convergence of genetic algorithms. Once  the link flow, Capacity proof of convergence for an algorithm exists to an optimal solution it  is an assurance that the optimal solution has infinite iterations, thus the shift focuses on  the link capacity, determination  and α exploration of stopping time or criterion.Today, the biggest challenge in the implementation of GAs is to decide when to stop the algorithm keeping in mind that there is no a-prior information regarding the objective function \cite{bhandari_murthy_pal_2012}.\\  \subsubsection{{\emph{Using Ant Colony Optimization}}}  \label{sec:antcolony}  Ant colony optimization is an algorithm influenced by observing the social insects which are ants. Ants live in colonies  andβ determine  the correlation sole goal of surviving as a whole. The foraging behavior of ants are interesting to scientists. The insects find the shortest path  between congestion cost their food sources  and f . Noting that their ant nest. The process is done by leaving trail of their pheromones which are chemical hormones on  the volume over capacity VOC = f /Capacity, ground followed by their fellow ants.\\  The main idea of the subject is to present how indirect communication between individuals of a population of ants are done, which  can be written as:\\  cij(f) = lij + α(VOC)  β  lij. \\ imitated artificially.This behavior is made to solve optimization problems. This optimization algorithm is further discussed under the paper \emph{"An Ant Colony Optimization Algorithm for Area Traffic Control"} \cite{haldenbilen_baskan_oz_2013}.  Combining shortest path (SP) routing and minimum cost (MC) routing, a hybrid routing model was created by He et al. This model requires only a small fraction of the total number of agents to use MC routes, and mitigates congestion under heterogeneous or homogeneous transport demand. \cite{He_2015} Usually, if it concerns network flow, the agent's first choice is the shortest path. MC routing mitigate networks in congestion, but it is difficult to induce all agents to choose MC routes. Using the hybrid routing model, targeted agents are forced to use MC routes. This is generated by calculating transport cost for each agent in SP routing scenario then the fraction of agents with the largest transport cost were assigned as a target to use MC routes. The remaining agents use SP routes, while the link flow is calculated. With the updated link cost, targeted agents are kept to use MC routes until the condition of convergence is satisfied.    \section{Review of Related Software}  This section contains a review of software systems that:  \begin{itemize}  \item Belongs to Theoretically, the tool found in Table \ref{tab:modeltool} below is the most ideal software for analyzing  a design for bus/public utility vehicle networks. However, to be able to use,  research area similar and explore on different algorithms flexibly modeled from previous researches the researchers will use one of the agent based modeling and simulation tools found in Table \ref{tab:agenttools}. While the table does not present an extensive list for related software, Allan \cite{allan} strongly suggest the list  to yours  \item Addresses a need be of particular relevance to scientific modeling and simulation.\\  Before using the following tools, the following terminology differences among most platforms are also presented in Table \ref{tab:agentterminology}.  \begin{table}[!htbp]  \centering  \caption{A Tool for Evaluating and Optimizing Bus Stop Location Decisions }  \label{tab:modeltool}  \begin{tabular}{|l|c|c|c|c|c|}  \hline  \multicolumn{1}{|c|}{Tool} & \begin{tabular}[c]{@{}c@{}}Plotting/Removing\\ Stops\end{tabular} & Evaluating & Optimizing & \begin{tabular}[c]{@{}c@{}}Demand\\ Parameters\end{tabular} & \begin{tabular}[c]{@{}c@{}}Roadway and\\ Traffic Parameters\end{tabular} \\ \hline  \begin{tabular}[c]{@{}l@{}}Transit IDEA \\ J-04/IDEA 31\end{tabular} & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\ \hline  \end{tabular}  \end{table}  \begin{table}[!htbp]  \centering  \caption{Agent Based Terminology \protect \cite{allan}}  \label{tab:agentterminology}  \begin{tabular}{|l|c|c|c|}  \hline  \multicolumn{1}{|c|}{Concept/Term} & MASON & NetLogo & Repast \\ \hline  \begin{tabular}[c]{@{}l@{}}Object that builds\\ and controls simulation\\ objects\end{tabular} & Model & Observer & Model \\ \hline  \begin{tabular}[c]{@{}l@{}}Object that builds \\ and controls screen \\ graphics\end{tabular} &   \begin{tabular}[c]{@{}c@{}}model with\\ UI\end{tabular} & Interface & - \\ \hline  \begin{tabular}[c]{@{}l@{}}Object that represents\\ space and agent locations\end{tabular} & Field & World & Space \\ \hline  \begin{tabular}[c]{@{}l@{}}Graphical display \\ of spatial information\end{tabular} & Portrayal & View & Display \\ \hline  \begin{tabular}[c]{@{}l@{}}User-opened display\\ of an agent's state\end{tabular} & Inspector & Monitor & Probe \\ \hline  \begin{tabular}[c]{@{}l@{}}An agent behaviour \\  or domain similar to yours  \item Is your predecessor  \end{itemize} event to be executed\end{tabular} & Steppable & Procedure & Action \\ \hline  \begin{tabular}[c]{@{}l@{}}Queue of events\\ executed repeatedly\end{tabular} & Schedule & \begin{tabular}[c]{@{}c@{}}Forever\\ Procedure\end{tabular} & Schedule \\ \hline  \end{tabular}  \end{table}  \begin{table}[]  \centering  \caption{Agent Based Platforms}  \label{tab:agenttools}  \begin{tabular}{|c|c|c|}  \hline  Platform & \begin{tabular}[c]{@{}c@{}}Primary\\ Domain\end{tabular} & \begin{tabular}[c]{@{}c@{}}Programming\\ Language\end{tabular} \\ \hline  \begin{tabular}[c]{@{}c@{}}Agent Execution \\ Framework (AXF)\end{tabular} & \begin{tabular}[c]{@{}c@{}}The execution framework \\ provides services and \\ UI for model management, \\ execution, and views.\end{tabular} & JAVA \\ \hline  \begin{tabular}[c]{@{}c@{}}Agent Graphics \\ Framework (AGF)\end{tabular} & \begin{tabular}[c]{@{}c@{}}The graphics framework extends\\ GEF, GEF3D, Zest, and the BIRT\\ charting engine to support real-time \\ visualization of and interaction \\ with agent models.\end{tabular} & JAVA \\ \hline  Escape & \begin{tabular}[c]{@{}c@{}}It allows modelers to code in Java \\ and/or generate models with AMF \\ andthen execute those models \\ within the same development \\ environment.\end{tabular} & JAVA \\ \hline  MASON & \begin{tabular}[c]{@{}c@{}}MASON is a fast discrete-event \\ multiagent simulation library core in \\ Java,designed to be the foundation \\ for largecustom-purpose Java \\ simulations.\end{tabular} & JAVA \\ \hline  NetLogo & \begin{tabular}[c]{@{}c@{}}A cross-platform multi-agent \\ programmable modeling\\ environment.\end{tabular} & Logo \\ \hline  Repast & \begin{tabular}[c]{@{}c@{}}A free and open source agent-based\\ modeling toolkit that simplifies \\ model creation and use.\end{tabular} & JAVA \\ \hline  AnyLogic & \begin{tabular}[c]{@{}c@{}}The simulation framework provides\\ the ability to use both agent-based and\\ event-based methods to describe \\ the stochastic behavior of machine\\ -controlled and human-controlled objects.\end{tabular} & JAVA \\ \hline  \end{tabular}  \end{table}