Impact of initialization of a modified particle swarm optimization on cooperative source searching

ABSTRACT


INTRODUCTION
Target searching is an important task but very challenging to solve in real world scenarios.Target searching is usually associated with complex and time-consuming processes despite strict constraints to be met.For example, the searching mission for black box of Malaysian Airlines MH370 in the Indian Ocean took huge efforts and involved a complex and challenging search environment.In this case, the boundary of the searching environment based on global positioning system (GPS) coordinates was set before the searching process took place.In addition to complex operations and huge challenges, the rescuers have a very limited time to search for the black box before the battery of the black box dies out.This real scenario demonstrates the importance of target searching and the need for a better target searching strategy and solution in dealing with real world searching problems [1].Other examples of target searching include search Int J Elec & Comp Eng ISSN: 2088-8708  Impact of initialization of a modified particle swarm optimization on cooperative … (Mad Helmi Ab.Majid) 219 and rescue of earthquake victims, demining operation, radioactive leakage source detection, environmental monitoring and surveillance [2]- [4].The primary objective of target searching is to locate the source to its proximity location within a specified boundary (e.g., search space dimension) and operational constraints (e.g., time, accuracy) [5].Autonomous robots have been researched for the purpose of target searching tasks for a very long time.However, searching using a single autonomous robotic platform is difficult to achieve optimal searching result.Alternatively, cooperative searching using a group of robots has been proven to be more efficient and able to give optimal searching results compared to a single robot searching [6].From this perspective, the concept of swarm robotics using relatively simple robots offered greater advantages for solving complex target searching as a result of its robustness, scalability and flexibility characteristics [7].Additionally, incorporating intelligence algorithms allow swarm robots to make automatic decisions intelligently with minimal interruption from humans while ensuring optimal accuracy of the search output [8].
PSO is the most common SI based algorithm for swarm robotic target searching.Initially PSO was implemented for target searching in its original form but many modifications have been proposed to improve the original PSO performance in target searching tasks.The implementation in its original form includes for example by Hereford et al. [25] and Ab Aziz et al. [26].On the other hand, the modifications of PSO were performed for the following purposes: inclusion of obstacles avoidance capability [27], avoid trapping into local optima or premature convergence [28], [29], incorporate multi target searching [30], [31], integrate mobile target searching capability [32].However, to the best of the author's knowledge, the analysis of target overshooting and the impact of different initialization strategies have not been deeply studied.In this paper, we proposed a modified PSO algorithm to minimize target overshooting in addition to fast convergence and avoiding premature convergence.Additionally, we also evaluate and compare the performance of the modified PSO with three different initialization strategies.The rest of this paper is organized as follows: Section 2 for research methodology, Section 3 for results and discussion and Section 4 for conclusion and recommendations of future work.

RESEARCH METHOD
In this research, a modified PSO is proposed to improve PSO convergence speed, avoid robots stuck in a local optimum or premature convergence and minimize target overshooting.Additionally, three initialization strategies were designed for the proposed modified PSO.To validate the performance of the modified PSO and evaluate the effect of different initialization strategies, a series of simulations using MATLAB was performed.For the testing purpose, we implemented the algorithm on a swarm of autonomous surface vehicles (ASV) which was represented by a complete kinematic and dynamic mathematical model and a complete control system.

Modified PSO
Firstly, one of the criteria for good searching is a fast convergence.The faster the convergence, the faster the location of the source can be determined and thus, meet the timing constraint of the searching task.From the PSO perspective, fast convergence can be achieved through fast information sharing and update among the robots in the swarm.Typically, this problem is associated with waiting periods using a synchronous update.In this study, asynchronous updates will be used to improve the convergence speed.Secondly, due to the nature of the PSO, robots may get stuck at local optima due to premature convergence.Premature convergence occurs because of rapid decreasing of velocity as the robots rapidly approach or converge to a local optima position where the updated velocity approaches zero and cause robots to lose their exploration capability (i.e., decrease of swarm diversity) before finally stop moving.Once robots are trapped into local optima, they have no capability to escape and are permanently stuck and fail to reach global convergence.As a result, an inaccurate solution is obtained which affects the accuracy of the source's position estimation.Thirdly, target overshooting will result in inaccurate approximation of the target's location.Target overshooting primarily happened due to large velocity assigned to the robots as they approached the optimal position.Consequently, more control effort is necessary to accommodate the backand-forth movements especially for a robot with limited turning capability before robots can reach a stable convergence.Typically, this problem is caused by excessive velocity magnitude due to non-optimal or fixed value of inertia weight and inappropriate selection of velocity limit,   .To resolve these problems, asynchronous dynamically adjustable particle swarm optimization (ADAPSO) is proposed in this study.The velocity, v and position, p update equations of the proposed ADAPSO are given by ( 1) and ( 2): (  + 1) =   (  ) +   (  + 1) +   ( + 1) where ω is the inertia weight, c is the acceleration coefficient, r is the random number between 0 and 1, pBest is the personal best position, gBest is the global best position, k is the iteration number and i is the robot's index.The vector q is used to adjust position of the robot such that communication between robots is maintained.In this formulation, the velocity update is set as ||v|| ≤ Vmax to avoid explosion.The inertia weight is defined as (3).
where the evolutionary speed factor, h, and aggregation degree, s (defined according to [33]) and the convergence speed factor, g are defined as: where f is the fitness function of the robot expressed as measured source signal intensity.If the corresponding robot is the best robot (i.e., robot with highest fitness value or highest source intensity measurement), the second and the third terms of (1) become zero or close to zero due to the fact that robot current position is close to pBest and gBest positions.As a result, the exploration capability of that robot temporarily (i.e., as long as it is the best robot) dies out.For this reason, the inertia weight adjustment equation is further modified as (7).
Small cognitive component (i.e., the term with pBest) and large social component (i.e., the term with gBest) promotes search exploration space at the beginning and in the later stage, when cognitive component becomes larger and social component becomes smaller, the possibility of convergence to global optima is improved.The acceleration coefficients are defined as ( 8) and ( 9): where cini is the initial acceleration coefficient, t is current time, tT is the total time taken to complete the previous operation (i.e., sum of time taken for searching) process and tmax is the maximum searching time allowed (i.e., limited by robot power resource).

Initialization strategies
In this study, three different initialization strategies were proposed relevant to the source searching task which are known as random initialization, equidistant initialization and centralized initializations as illustrated in Figure 1.Firstly, for a random initialization, robots are randomly distributed in a search space such that their initial position can be expressed as (10): where xmin and ymin are the minimum initialization positions and xmax and ymax are the maximum initialization positions.The rand is the random number between 0 and 1 and i is the index of the individual robot.Random initialization is a realistic initialization method in source searching because the proposed algorithm involves stochastic elements and robots can perform source searching when there is no initial guest of the source location.Secondly, for an equidistance initialization strategy, robots are dispersed at an equal angle and radius surrounding the possible source location, rrs such that where N is the total number of robots used in the searching process.In a real implementation, this method is not practically feasible because of difficulty in setting the exact robot arrangement at desired angle but it can be useful for evaluating and benchmarking performance of the tested algorithm.Thirdly, in a centralized deployment, robots are deployed from the same site (i.e., typically a known reference coordinate) of the search space.This initialization method is typically useful for evaluating performance of the algorithm when high similarity in terms of measured source signal intensity among the robots exists.Mathematically, a centralize initialization is defined by (12).
where p0,i is the initial position of the robot i, p0 is the initial position of deployment of the first robot and rini is the initialization radius.In case none of the robots detect the source once they are deployed, each robot will move randomly in the search space.
Figure 1.Different strategies of initializations

Termination criteria
In swarm robotics source searching tasks, robot physical limit and accuracy of the estimated source position must be considered in order to set proper termination conditions.To obtain accurate estimation, only converged robots are considered for the purpose of estimating the source position based on average value.Notice that since rcon is not physically measurable because the source's position is unknown and needs to be estimated, the number of converged robots should be decided based on the intensity difference between the converged robots.Let the final intensity measured by robot i is Ii,f(t), the position of the converge robots can be defined as: where Λ ∈ [0,100] is the threshold of percentage intensity difference and If,max is the maximum intensity or fitness of the gBest robot.Any robot in the swarm is classified as a converged robot if its percentage intensity difference is less than certain percentage.A small value of Λ provides a better approximation of the source's position compared to a large value of Λ.Once terminated, the source position can be estimated from the average position of the converge robots or taken to be equal to the final gBest position.In this study, the following termination conditions are used to terminate the searching process: − Maximum operating time is reached, t > tmax, or − At least 3 robots successfully converge where fitness difference among the converged robots should be less than Λ ≤ 5%, and, − No improvement of gBest value is observed for the last 10 iterations

Simulation setup
For the purpose of evaluating the performance of the proposed PSO and initialization strategy, a series of simulations were conducted.In this simulation, robots are a swarm of Autonomous Surface Vehicles (ASVs) described by a complete kinematics and dynamics model with a proper speed and heading controllers.To simulate performance of the proposed source searching strategy using ASV swarming platform, a swarm robotic simulator was developed by using MATLAB TM as shown in Figure 2.This simulator integrates the localization algorithm, control laws and ASV model as illustrated in Figure 3.The outputs from the proposed source searching algorithm were used to generate the desired waypoint and thus, the desired robot path.From the desired path, the reference control signals were computed which were then fed into speed and heading controllers.The output of the controller was fed into an ASV model where the states of the ASV can be determined.The controller keeps tracking the path until the robot reaches the desired waypoint within an acceptable radius.Once the robot reaches the desired waypoint, a new waypoint is generated and the process is repeated.This is a continuous loop process where it runs until the desired task is completed (i.e., robot successfully reaches convergence) or the desired termination conditions are satisfied or terminated by the user.The source used in this simulation is an underwater acoustic source represented by a mathematical model representing a signal intensity decaying model.
where Pa is the power of the source, r is the radius from the source (i.e., distance from ASV to the source), hs is depth of the source (assumed to be constant) and I is the intensity of the source.By the energy conservation law, the intensity of the acoustic source can be derived as (15): and solving for I gives: where r=drs is the distance between source position and current robot position, w is the added parameter representing white Gaussian noise generated using MATLAB function wgn(), r0 is the reference radius and I0 is the corresponding acoustic source level.Note that this approximation model is a simplified model where it does not consider refraction, reflection and propagation effect of the sound wave.White Gaussian noise is considered since it closely represents the noise model in actual environment measured by the sensor.The illustration of the source intensity with and without noise effect is shown in Figure 4(a) and 4(b), respectively.

RESULTS AND DISCUSSION
Based on the proposed algorithm and methodology, a series of simulations were performed in order to evaluate the fulfilment of the research objectives.The first objective of this research as previously stated is to evaluate performance of the proposed PSO for source searching in terms of target overshooting and impact of parameters on searching capability.The second objective is to evaluate the impact of different initialization strategies on source searching performance.

Modified PSO performance
The ADAPSO velocity limit, Vmax, should be examined as one of the ADAPSO parameters since it has a direct impact on the efficiency of the source searching.In this study, the value of Vmax is independent of the maximum robot velocity since the position update of the ADAPSO represents the desired waypoint instead of the robot position update step.To ensure quick convergence and reduce target overshooting (i.e., oscillation around the source), which necessitates additional control efforts, it is essential to find the optimal value Vmax.A choice of a small Vmax value may result in a slow convergence (indicated by actual searching time), as shown in Figure 5, and may cause the robot to become trapped in local optima because robots lose its capability to explore the searched area.On the other hand, a choice of a large Vmax may result in large target overshooting or a continuous oscillation around the source, which is ineffective in terms of the desired control, as shown in Figure 6. Figure 7 depicts the potential ideal convergence, which is quick with nearly no oscillation convergence.Notice that equidistant initialization was used in this analysis to obtain consistent initialization position for different repetition of the simulations.
A simulation was executed with various Vmax values to ascertain the best value, and the time it takes to attain convergence for various initialization types (such as centralize, equidistance, and random) was noted.Figure 7 displayed the amount of time required for various values of Vmax to converge for various types of initializations in a search space with a size of 25x50 m 2 .The best value for Vmax, which may be used with various initialization procedures is 1.0 as shown in Figure 8.As a result, for the remaining simulation experiments, this value is set as the velocity limit for ADAPSO velocity update.

Impact of ADAPSO parameters
In this section, the effect of various ADAPSO parameters on source searching performance will be examined.Depending on where the source signal is possibly detected, source searching can start from a variety of initialization configurations.For instance, if the source signal is discovered only after a few 225 iterations of random movement, the robots must execute source searching from the random position initialization.Similarly, if the source signal is discovered only after the robots have been deployed into the search space.Therefore, by taking into account various initialization strategies, a general overview of the ADAPSO performance in terms of fitness differences between the robots (i.e., robot similarity) was provided.Thus, the robustness of the proposed algorithm can be assessed taking into account a variety of initial source signal strengths by evaluating various initialization strategies of the ADAPSO.For various starting procedures, the effect of various ADAPSO parameters (see ( 1) through ( 9)) on the searching performance is depicted by histograms as in Figure 9.When its effect on the source searching performance was assessed, the appropriate parameter was relaxed (i.e., set to zero) for this reason.Despite the fact that robots were deployed using various initialization techniques, it is clear from the figure that each parameter has a favorable effect on the overall ADAPSO performance.Even when the distance between the source position and first deployment site is similar, it takes more time to obtain convergence since the initial degree of similarity among the robots in a centralized initialization strategy is high.This is due to the fact that velocity update is minimal and the cognitive and social components of the ADAPSO become small when gBest and pBest are near to each other.Because robots were initialized at equal radial distances from the source, the equidistance initialization strategy also has the fastest convergence speed.The equally distributed beginning pattern quickens the robots' convergence rate even though their initial fitness is equivalent.On the other hand, random initialization has a medium rate of convergence since the robots' similarity depends on their initial random positions.The pace of convergence increases with the proximity of the robots to the source and with their random distribution.For the source searching task, however, only random and centralized initializations are feasible and can easily be employed.
Figure 10 illustrates how ADAPSO parameters affect the search results in terms of swarm best fitness, or gBest.The outcome demonstrated the beneficial effects of several ADAPSO parameters in terms of convergence speed and accuracy.As shown in Figure 10, deactivating one of the parameters decreases the ADAPSO's effectiveness.The combination of those parameters in the suggested ADAPSO algorithm, it is evidence from this finding, aids the robots in achieving a faster convergence speed and greater accuracy.

Impact of initialization
Similar to the preceding part, three initialization strategies: random, equidistant, and centralized or initialization from the same region were taken into consideration to study the impact of initialization strategy.The goal of this section is to evaluate the proposed algorithm's performance and robustness to other benchmark methods under various initial robot configurations and robot counts.Benchmarking of ADAPSO's performance is done using the basic PSO algorithms listed in Table 1.This simulation takes into account a search space of 25×50 m 2 .Figure 11 displays the simulations' outcomes.Figure 12 displays the success rate for various initialization techniques and for various robot counts.The dashed line indicates no convergence is observed.
According to the findings, the ADAPSO algorithm performs better than other algorithms in each of the three different initialization setups.Due to their poor ability to escape local optima, particularly when a small number of robots were taken into account, especially in a random and centralized initialization, conventional PSO algorithms such as IWPSO and CFPSO for small numbers of robots fail to achieve convergence compared to other algorithms.Because of its weak capacity to escape local optima caused by constant inertia weight, the IWPSO completely fails in the centralized initialization.Although the CFPSO can typically reach convergence, its rate of convergence is slow, especially when there are many robots that share characteristics, as was seen in the centralized initialization.However, as shown in Figure 12, the CFPSO has a greater propensity to trap into local optima when there are fewer robots present.It should be noted that IWPSO and CFPSO are non-adaptive PSOs, which is the fundamental cause of the two algorithms' inability to escape local optima when there is a significant degree of robot similarity.An example of a complete illustration of a source searching using ADAPSO is shown in Figure 13.In this figure, the robot traces during a complete source searching process when a source is positioned at ps = (20, 0) in an obstacle's free environment.In this example, robots were deployed close to each other using a centralized initialization.Robots cooperatively search the target based on detected source signal and exchange the information within the swarm to reach convergence.

CONCLUSION
In this study, source searching based on a modified PSO has been proposed and tested using a swarm of ASVs.The findings of the study showed that the proposed ADAPSO algorithm has successfully achieved better searching capability after the velocity limit is optimized by avoiding excessive oscillation.In addition, the impact of each parameter of ADAPSO has been evaluated and the result showed that each parameter has significant impact on the searching effectiveness.Moreover, it is also shown that each initialization strategy has a different impact on the searching operation.For future work, further improvement will be considered.In some searching scenarios multiple sources may exist within the same search space.In this situation, robots must be able to partition themselves into multiple sub swarms if all targets are the targets of interest or otherwise, they must be able to differentiate a correct target from the false targets.This process involves task distribution among the robots in the swarm may improve capability of the algorithm which may bring a step further towards real world implementation.

Figure 9 .
Figure 9. Impact of parameters on the overall ADAPSO performance

Figure 11 . 227 Figure 12 .Figure 13 .
Figure 11.Performance of ADAPSO for different initialization methods in a search space of 25×50 m 2 using N=5

Table 1 .
Selected benchmark PSO algorithms