Fitness Dependent Optimizer: Inspired by the Bee Swarming Reproductive Process (1904.05226v1)

Abstract: In this paper, a novel swarm intelligent algorithm is proposed, known as the fitness dependent optimizer (FDO). The bee swarming reproductive process and their collective decision-making have inspired this algorithm; it has no algorithmic connection with the honey bee algorithm or the artificial bee colony algorithm. It is worth mentioning that FDO is considered a particle swarm optimization (PSO)-based algorithm that updates the search agent position by adding velocity (pace). However, FDO calculates velocity differently; it uses the problem fitness function value to produce weights, and these weights guide the search agents during both the exploration and exploitation phases. Throughout the paper, the FDO algorithm is presented, and the motivation behind the idea is explained. Moreover, FDO is tested on a group of 19 classical benchmark test functions, and the results are compared with three well-known algorithms: PSO, the genetic algorithm (GA), and the dragonfly algorithm (DA), additionally, FDO is tested on IEEE Congress of Evolutionary Computation Benchmark Test Functions (CEC-C06, 2019 Competition) [1]. The results are compared with three modern algorithms: (DA), the whale optimization algorithm (WOA), and the salp swarm algorithm (SSA). The FDO results show better performance in most cases and comparative results in other cases. Furthermore, the results are statistically tested with the Wilcoxon rank-sum test to show the significance of the results. Likewise, FDO stability in both the exploration and exploitation phases is verified and performance-proofed using different standard measurements. Finally, FDO is applied to real-world applications as evidence of its feasibility.

• The paper introduces a novel swarm intelligence algorithm (FDO) that leverages a fitness function-derived weight for dynamic control of agent velocities.
• Empirical evaluations using 19 benchmark functions and IEEE CEC-C06 2019 tests confirm FDO’s competitive performance and robustness against local optima.
• The research demonstrates FDO's practical applications in optimizing antenna arrays and sound wave parameters, paving the way for hybrid and multi-objective extensions.

Analysis of the Fitness Dependent Optimizer Algorithm

The paper under analysis presents a novel swarm intelligence algorithm called the Fitness Dependent Optimizer (FDO). Inspired by the decision-making process during bee swarming reproductive events, FDO introduces a distinct velocity calculation technique compared to traditional Particle Swarm Optimization (PSO) models. This unique methodology relies on generating weights using a fitness function to guide search agents in both exploration and exploitation phases. Unlike its predecessors such as the honey bee or artificial bee colony algorithms, FDO distinguishes itself through its implementation and performance. In this essay, we will examine the algorithmic structure, performance evaluations, and implications for future optimization techniques.

Algorithmic Design and Innovation

FDO operates by simulating scout bees' behavior in searching for optimal hives, which essentially translates to finding optimal solutions. The innovative approach of FDO lies in its employment of a weight factor derived from the fitness function of the problem being addressed. This factor dictates the pace and direction of the agents’ movements, thus ensuring both diversified exploration and precise exploitation of the solution space. A particular highlight is FDO's ability to memorize and reuse past agent velocities which can enhance its search efficacy over successive iterations. Utilizing a randomization mechanism akin to the Levy flight ensures that the exploration space is adequately sampled.

The complexity analysis presented in the paper indicates that for each iteration, the time complexity is proportional to O(p*n + p*CF), where 'p' is the population size, 'n' is the dimension, and 'CF' is the function cost. This renders the algorithm competitive in scenarios requiring numerous iterations without incurring excessive computational overhead.

Empirical Evaluation

The paper extensively evaluates FDO using 19 classical benchmark functions and additional IEEE CEC-C06 2019 benchmarks. In comparative studies with PSO, Genetic Algorithm (GA), Dragonfly Algorithm (DA), Whale Optimization Algorithm (WOA), and Salp Swarm Algorithm (SSA), FDO demonstrates superior or comparable performance, particularly excelling in real-number, continuous domain problems. Its performance on multimodal benchmark functions affirms its robustness against local optima entrapment—a typical challenge in complex optimization landscapes.

Statistical significance testing via Wilcoxon rank-sum test corroborates the algorithm's reliability and effectiveness. Moreover, FDO was benchmarked against computationally intensive problems such as the Lennard-Jones minimum energy cluster and modified Schwefel's function, further supporting its adaptability across varied problem domains.

Practical Implications and Future Directions

The paper validates FDO's applicability in real-world scenarios via two practical implementations: optimizing the element positions in aperiodic antenna arrays and tuning parameters in frequency-modulated sound waves. This practical application signifies its potential in engineering applications where solution quality and convergence speed are critical.

The research suggests possible extensions into multi-objective and binary optimization problems. Given the modular nature of FDO, it offers a promising foundation for hybridization with other optimization techniques, which could enhance its efficiency even further. As more complex and higher-dimensional problems emerge, metaheuristic algorithms like FDO may hold the key to developing effective, generalized solutions.

Conclusion

The introduction of the Fitness Dependent Optimizer represents an advancement in swarm intelligence algorithms, particularly in the way it synergizes global exploration with local exploitation. Its empirical effectiveness suggests that FDO holds promise for expansion into broader optimization contexts. While the current findings substantiate its competitive edge against existing algorithms, continued research into hybrid models and multi-faceted objective problems could unlock further capabilities inherent in this innovative approach.