Metaheuristic Approaches in Path Finding and Optimization

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Metaheuristic Approaches in Path Finding and Optimization

Shikhar Trivedi Department of Computer Science

and Engineering,

Pandit Deendayal Energy University Email:[email protected]

Rajeev Gupta Department of Computer Science

and Engineering

Pandit Deendayal Energy University Email:[email protected]

Santosh Bharti Department of Computer Science

and Engineering

Pandit Deendayal Energy University Email:[email protected]

Abstract—Navigation planning is a critical component in the operation of mobile systems such as robots, autonomous vehicles, and unmanned aerial vehicles (UAVs). As the complexity of these systems increases, the need for robust and efficient pathfind- ing algorithms becomes more significant. Traditional heuristic approaches often struggle in dynamic environments, prompting the adoption of metaheuristic algorithms inspired by natural phenomena. This study evaluates five widely used metaheuristic algorithms: Ant Colony Optimization (ACO), Artificial Bee Colony (ABC), Firefly Algorithm (FA), Moth Flame Optimization (MFO), and Tabu Search (TS). The performance of these algorithms is compared across multiple scenarios, including static shortest-path calculations, the Traveling Salesperson Problem (TSP), and randomized environment. Results indicate that ACO consistently identifies optimal paths but incurs relatively high computational time. Tabu Search offers a balanced trade-off between computational efficiency and solution quality, while ABC delivers suboptimal paths with faster execution times. In contrast, MFO and FA exhibit excessive exploration, leading to higher costs and inefficiencies in specific scenarios.

Keywords—MetaHeuristic, Path finding, Optimization

I. INTRODUCTION

Navigation is an important factor in not only automobiles but also in robotics and any mobile object in general. With the rise of automation throughout the current decade, not only various different vehicles are produced but self-driving vehicles are also present. Many meta heuristic algorithms like genetic algorithm which work on natural phenomena came to rise [1] . The navigation planning or path planning is not only limited to vehicles but also unmanned aerial vehicles (UAVs) [2][3][4], underwater vehicles [2]. The processes of finding the most optimal path or in general path finding can be carried out through different algorithms, whether they be heuristics algorithms or meta-heuristic algorithms.

Algorithms like Genetic Algorithm, Ant Colony Optimiza- tion, Artificial Bee Colony, and Moth Flame provide optimal solutions but each has its own shortcomings, whether it be getting trapped in local minima, rampant increase in computational resources requirement with respect to the increase in inputs. Meta-heuristic algorithms usually follow the behavior of certain animal kingdoms, for example, Ant Colony Optimization follows the behavior of ants, their tendency to

lay pheromones, how moths are attracted to a light source, artificial bee colony working on food sources [5] etc.

II. HEURISTIC ALGORITHMS

A. Dijkstra’s Algorithm

Calculates the shortest path from the current node to the next node, compares all nodes, while this will confirm the optimal solution the cost increases the more nodes are present [6].

B. A* Algorithm

Calculates the best path based on best-first search from origin node to final node, will always take the least costly path from the current node , does combine breadth first search [13] and dijkstra . Dynamic A* algorithm calculates the shortest distance from each node to enable quick switching of paths [6].

III. METAHEURISTIC ALGORITHMS

A. Artificial Bee Colony

The food search process of a bee colony is simulated by the ABC algorithm. A population of food positions exists in the ABC algorithm, and over time, the artificial bees alter these food positions. The quantity of food positions in the colony is double its size. Half of the colony consists of employed bees, while the other half consists of observer bees. An employed bee turns into a scout bee after failing several attempts to enhance a food position. While the spectator bees wait for information from the employed bees on the amount of nectar at the food spots, the employed bees take use of the food positions. Using the employed bee knowledge, the spectator bees choose food spots and take advantage of the chosen food which scout bees take [5].

B. Particle Swarm Optimization

It mimics the coordinated movements of flocks of birds searching for food in the absence of a leader; the birds follow the bird that is closest to the food source. The PSO algorithm determines the best course while taking into account a number of factors, including smoothness, length, and collision risk [8][9].

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C. Genetic Algorithm

The underlying idea of this strategy is that the strongest individuals in a population survive while the weaker individuals are left behind. A population’s members are defined as chromosomes, and each chromosome is a potential solution to an optimization issue. The fitness function of the chromosomes is measured in order to assess their viability. Through a variety of procedures or operators, including crossover and mutation, GA produces offspring based on their best chromosomes, updating its population and fortifying its discovered solutions (chromosomes).

Additionally, GA features an elitism mech- anism that safeguards the fittest, highest-performing chromosome which provide the best result, it is based on evolutionary behavior/survival of the fittest [1][10].

D. Ant Colony Optimization

A chemical compound known as ”pheromone” is left behind by ants along their path. The amount of pheromone is inversely proportional to the length of the path, so if the route is short, the ant will leave some behind to attract additional ants. Ants are also capable of sensing pheromones when they pass by, and the concentration of pheromones may have an impact on their behavior. They would choose a path whose likelihood was proportionate to the pheromone’s concentration. In this sense, the more often ants visit a shorter path, the more pheromones collect on the trail. This procedure will continue until every ant chooses the shortest route [3].

E. Moth Flame Optimization

Moth flame optimization is inspired by the behavior of moths in nature by mimicking the attraction of moths towards a light source, this specific nature of moths is used for solving optimization problems. Where moths are the candidate solution, which is attracted to flame which are reference points of the best solution found during the optimization process, flame attraction parameter can be set to select a range where moth will be more attracted to flame [8].

F. Firefly Algorithm

The Firefly Algorithm (FA) is a nature-inspired optimization approach that replicates fireflies’ mating behavior, in which their flashing lights serve as messages to other fireflies. In the method, each firefly symbolizes a possible solution to an optimization issue, and the intensity of its light indicates the quality of that solution.

Fireflies are drawn to brighter col- ors, therefore solutions with higher objective function values (such as reduced prices or more efficiency) will receive more attention. The program employs two essential mechanisms: attraction, in which less suited fireflies gravitate toward brighter ones, and exploration, in which a random component prevents premature convergence [11]. This dual method enables FA to efficiently explore and utilize the search space, making it ideal for complicated and multidimensional issues. By repeatedly modifying firefly positions and updating the best solutions, FA seeks to converge on optimum or near-optimal solutions while balancing the requirement to explore new options.

This

makes it a versatile and strong tool for tackling a wide range of optimization issues [2].

G. Tabu Search

Tabu Search is a sophisticated metaheuristic optimization technique that improves classic local search methods by combining memory-based processes to more efficiently explore complicated solution spaces. The method replicates an iterative process in which a solution is optimized by investigating surrounding solutions obtained by movements. Tabu Search relies on a Tabu List to keep track of recently visited solutions or movements, preventing them from being revisited and being caught in local optima. This list, together with ambition criteria that let specific tabu actions if they considerably enhance the solution, maintains a balance between exploration and exploitation. The algorithm constantly adapts its search strategy by focusing on promising locations (intensification) and investigating new areas (diversification), thereby improving its robustness and versatility. Tabu Search is excellent for tackling a wide range of optimization issues, including scheduling, routing, and resource allocation, since it can explore huge and complicated search spaces while avoiding premature convergence [12].

IV. LITERATURE REVIEW

Ant colony optimization performs well when it comes to route planning. However, there are still issues, such as the tendency to settle into local optimal states, sluggish convergence, and the incapacity of real-time obstacle avoidance in global planning.

To better handle the search process and to make convergence fast, the paper proposes modifications to traditional ant colony algorithm by improving update rules and various other enchancement whose goal is to ultimately perform better than to traditional ones, and the result show the same by providing improved path quality and computing efficiency [9].

Introduction of path planning strategy integrated adaptive ant colony optimization with enhanced dynamic window approach (DWA) , where parameters are adjusted through adapting with environmental changes and collision avoidance and path planning is enhanced by dynamic window approach which optimizes not only global space but also local space search for improved efficiency and accuracy in dynamic environments [7].

The study indicates that in comparison to conventional control tactics, metaheuristic approaches such as Genetic Algo- rithms and Particle Swarm Optimization—offer considerable advances in vehicle speed control. The findings suggest that these optimization strategies can result in more adaptable and seamless speed control, improving the overall efficiency and security of self-driving cars [9].

Analysis on various navigation algorithm, thier strengths and weakness/limitations , for a safe and secure autonomous driving car through path planning and navigation abilities [11].

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TABLE I

LITERATURE SURVEY OF DIFFERENT ALGORITHMS USED, THEIR FINDINGS, AND LIMITATIONS.

Algorithm Findings Limitations

Adaptive ant colony with

enhanced window [7] Works well in dynamic environments, and provides better solution quality in dynamic environment by enhancement of ACO

Sensor dependent, heuristic factor plays a vital role, and is computationally expensive due to calculation of window, can be combined with other algorithms for better results.

Ant-colony optimization [9] Updated pheromone/pheromone rule works well compared to traditional ant colony algorithm / optimization thus shedding light on parameter tuning and its importance.

Situational improvement, needs to be compared with other algorithms.

Ant colony, Firefly algo-

rithm [14] ACO performs well in optimizing alternative routes in traffic-heavy areas, while Firefly algorithm suffers from excessive exploration.

Firefly algorithm fine tuning of parameters, ACO requires high resources in large scale scenarios, more heuristic algorithms can be explored.

ACO, Genetic algorithm, PSO and Simulated an- nealing [15]

Comparison between algorithms highlighting thier strong aspects in unstructured environment.

More meta-heuristic algorithms can be applied.

A. Exploitation v/s Exploration

Exploitation and exploration are two fundamental strategies present in almost all optimization algorithms for navigating solution space , exploitation refers to refining and improving known good solutions by searching around them to enhance said good solution , exploitation uses existing knowledge , for example path length in meters , connecting edges , speed limit of nodes to find optimal solutions but risks getting trapped into local minima if too much weightage is applied on exploitation

, while exploration refers to discovering of new areas present in solution spaces which gives rise to different solutions or innovative solutions for better outcomes this not only helps avoiding local minimas but also allows algorithm to explore potential better solution spaces which may have been missed out although too much exploration can cause increase in resource consumption and computational time increment , thus balancing of exploitation and exploration is very crucial and is one of the initial trade-offs in optimization algorithms , most of them have mechanisms which allow tuning of exploration and exploitation.

V. PROPOSED WORK

A. Problem Scenarios

In the first scenario, various optimization algorithms are performed on different scenarios, one consisting of simple shortest path length from one coordinate to another coordinate.

TABLE II

COMPARISON OF META-HEURISTIC ALGORITHMS. Algorithm Time Taken (seconds) Path Length (meters)

ACO 17.748007 754.800

ABC 25.039150 754.800

FireFly 18.362422 754.800

MFO 21.179950 1241.005

Tabu 18.004962 754.800

The findings of the optimization algorithms show comparison of both time taken (computational efficiency) and path

length while handling the task at hand. The Ant Colony Optimization (ACO), Artificial Bee Colony (ABC), and Firefly Algorithm (FA) all reached the same path length of 754.800 meters, demonstrating that they converge to identical solutions in terms of overall distance. However, their time taken varied as following: ACO was the fastest, taking 17.75 seconds, followed by FA (18.36 seconds) and ABC (25.04 seconds). In comparison, the Moth Flame Optimization (MFO) method had a greater path length of 1241.005 meters but was the most efficient in terms of time, requiring only 16.16 seconds The findings indicate that whereas ACO, ABC, and FA offer ideal or comparable path lengths, MFO outperforms them in terms of speed at the expense of solution quality, emphasizing the trade-off that optimization algorithms have between computing efficiency and solution correctness.

Second scenario consists of Travelling salesman problem , where 50 cities are randomly selected from Sector 2 of Gandhinagar, India through usage of Osmnx and Optimization algorithms are used to find best route for each algorithm. No dynamic / real time traffic is applied, all iterations and candidate values are set to 100 for an attempt at fair comparison between algorithms.

TABLE III

COMPARISON OF META-HEURISTIC ALGORITHMS. Algorithm Path Length (meters) Time Taken (seconds)

ACO 4387.883 49.532256

ABC 15697.296 2.363077

FireFly 23910.611 150.174779

MFO 24482.997 154.502197

Tabu 6207.343 19.062977

The findings here provide a better insight on performance of algorithms, Ant Colony Optimization finds the best path (4387.883) for this Travelling salesman problem , while time taken is on higher end , while Firefly and moth flame optimization algorithms provide worst solutions both distance and time taken wise , which might be a result of too much exploration ,

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Artificial bee colony finds sub optimal solution very quickly, tabu search displays almost perfect scenario of balanced tradeoffs as compared with other metrics. Strengths and Weakness of each algorithm can be seen through this.

Third scenario deals with randomly generated 50 cities for 50 instances (i.e 50 cities will be randomized for each instance to provide diverse tsp test case scenarios) with no correlation to real life locations, euclidean distance is used to create a distance matrix of the city to assign costs .

Fig. 1. Cost per instance comparison for TSP (50 cities randomly generated, 50 instances) , Consistent performance of ACO in finding lower cost routes, followed by Tabu search.

From fig 1 It can be determined that Ant Colony optimization algorithm (ACO) performs better and is more consistent in finding lower cost routes per instances, Artificial Bee colony (ABC) providing decent / sub-optimal results, while Moth flame optimization algorithm and Firefly algorithm finding paths with higher costs, these results do correlate with previous ones.

Fourth scenario is similar to third scenario, but only one set of 50 cities are randomly generated for better comparison of a singular instance.

TABLE IV

COMPARISON OF META-HEURISTIC ALGORITHMS. Algorithm Path Length (Cost) Ant Colony Optimization 5.681070421354115

Artficial Bee Colony 16.47337363183926 FireFly Algorithm 21.383884301258192 Moth-Flame Optimization 19.051897269431883 Tabu Search 9.158221724792812

Below are the figures which represent optimal path found by the respective algorithm in a defined space.

Fig. 2. Ant colony optimization path of minimal length (5.68), representing proper node traversal resulting in a optimal path.

Fig. 2 represents the optimal path obtained by ant colony algorithm with cost of 5.68. The nodes are traversed in a manner that minimizes the overall distance traveled, avoiding unnecessary crossings and tours which results in a considerably lower path length and displays efficiency in solving of this problem.

Fig. 3. Artificial bee colony path, suboptimal path due to inefficient node traversal (16.47).

Fig. 3 represents the optimal path obtained by Aritficial Bee colony with cost of 16.47 which is due to nodes traversed in suboptimal manner which increases overall cost for this path.

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Fig. 4. Firefly algorithm path. Chaotic node traversal results in a high cost of 21.38, highlighting the inefficiency of the algorithm in this scenario and the need for fine- tuning.

Fig. 4 represents the optimal path obtained by Fire fly algorithm with cost of 21.38 which is due to nodes traversed in chaotic manner which increases overall cost for this path, displaying low efficiency in this problem.

Fig. 5. Moth flame optimization Path, suboptimal path suffering from the same inefficient node traversal as Firefly algorithm.

Fig. 5 represents the optimal path obtained by Moth flame optimization with cost of 19.05 which is due to nodes traversed in chaotic manner which increases overall cost for this path similar to Fire fly algorithm, displaying low efficiency in this problem.

Fig. 6. Tabu Search path, achieving a balanced trade-off between optimal path length and computational efficiency through effective node traversal.

Fig. 6 represents the optimal path obtained by Tabu Search algorithm with cost of 9.15 which is due to nodes traversed in somewhat efficient manner which decreases overall cost for this path , as seen in previous scenarios tabu search performs perfect on trade-off between optimal path and time taken to calculate .

The results may vary when parameters are tuned but may require lot of time to find perfect set of parameters to get most optimal path for each algorithm which are not performing good.

B. Evaluation and Performance

Ant colony optimization provides shortest results in this problem although time taken by ACO is a bit high , Artificial bee colony although fast , provides sub-optimal result , Tabu search provides perfect trade-off scenario where both shortest path and time taken are within acceptable range , Fire fly Algorithm and Moth flame optimization explore too much and need to be fine-tuned more accurately to provide acceptable results . Conclusion can be made that tradeoffs are necessary for meta heuristic algorithms and fine tuning algorithm is a key to provide best / optimal results, the type of problem also pay a vital role as some algorithms may or may not perform well on certain problems. Comparison under dynamic environment may provide better results for these base line Meta-Heuristic and evolutionary algorithms.

VI. CONCLUSION

By imitating natural behaviors, meta-heuristic algorithms such as Artificial Bee Colony (ABC), Particle Swarm Opti- mization (PSO), Moth flame optimization, Firefly algorithm Genetic Algorithm (GA), and Ant Colony Optimization (ACO) greatly improve path planning for mobile robots and are useful

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in dynamic environments where traditional heuristics might not work as well as these algorithms provide optimal solution for NP hard problems.

By combining strong aspects of multiple algorithms, the loopholes of algorithms may vanish, but computational resources and execution time does affect in cases where dynamic and real time / quick results are required. Conclusion can be made that metaheurstic models will in near future be able to solve dynamic tasks much faster and in a reliable manner.

VII. FUTURE WORK

More advanced meta heursitic algorithms can be imple- mented ,real-time traffic, dynamic environment can be added

, not only do advanced algorithms provide good measures for comparison but also the fine tuning can be understood which helps in setting trade-off between exploration and exploitation of various algorithms, built upon base line meta heuristics

, further more comparison at perfectly tuned parameters can also be done to provide even more accurate results, as parameters inherently affect the behaviour of these evolutionary algorithms and will impact the solutions / efficiency.

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