Source-linked AI summary
New directional bat algorithm for continuous optimization problems
Asma Chakri, Rabia Khelif, Mohamed Benouaret, Xin-She Yang
TL;DR
The paper addresses premature convergence and weak exploration in standard BA, especially as problem dimensionality increases. It proposes dBA with directional echolocation and three additional modifications, and reports superiority across benchmark comparisons using non-parametric tests.
Problem
Standard BA can prematurely converge under some conditions, and its performance may diminish as problem dimensionality increases.
Method
dBA embeds directional echolocation and three other modifications into standard BA to enhance exploration and exploitation, evaluating it across classical and CEC’2005 benchmarks.
Results
Non-parametric statistical comparisons and extensive benchmarking report dBA as superior to other algorithms in accuracy, search efficiencies, and BA performance.
Takeaways & Limitations
Directional guidance from better bats and adaptive control of pulse rates, loudness, and search scales provide the proposed basis for balancing exploration and exploitation.
Takeaways & Limitations
The reviewed prior BA variants had been tested on classical benchmarks, while dBA’s reported evaluation includes CEC’2005 and repeated benchmark experiments.
Abstract
from arXiv · showhide
Bat algorithm (BA) is a recent optimization algorithm based on swarm intelligence and inspiration from the echolocation behavior of bats. One of the issues in the standard bat algorithm is the premature convergence that can occur due to the low exploration ability of the algorithm under some conditions. To overcome this deficiency, directional echolocation is introduced to the standard bat algorithm to enhance its exploration and exploitation capabilities. In addition to such directional echolocation, three other improvements have been embedded into the standard bat algorithm to enhance its performance. The new proposed approach, namely the directional Bat Algorithm (dBA), has been then tested using several standard and non-standard benchmarks from the CEC2005 benchmark suite. The performance of dBA has been compared with ten other algorithms and BA variants using non-parametric statistical tests. The statistical test results show the superiority of the directional bat algorithm.
1 Introduction
Real-world optimization often involves nonlinear, multimodal problems with many variables and constraints, motivating nature-inspired algorithms. This section identifies premature convergence and reduced performance in standard BA as problems addressed by dBA.
- Real-world optimization commonly involves highly nonlinear problems with many design variables and complex constraints.
- Nature-inspired algorithms emerged partly because deterministic methods cope poorly with many practical optimization problems.
- BA uses swarm intelligence inspired by micro-bats’ echolocation behavior during hunting.
- BA performance can diminish as dimensionality increases, and premature convergence can occur under certain conditions.
- dBA introduces directional echolocation and other modifications to improve BA’s exploration and exploitation, then evaluates it on CEC’2005 benchmarks against other algorithms.
2 The standard bat algorithm
The standard BA represents candidate solutions as bat positions and updates positions, velocities, frequency, loudness, and pulse rates during search. Its rules combine frequency-based movement, local random walks, and iteration-dependent control parameters.
- Each bat’s position encodes a candidate solution, while its velocity and position are updated in a d-dimensional search space.
- Bats vary frequency, wavelength, loudness, and pulse-emission rate while searching for prey.
- The velocity update moves each bat according to frequency and the difference between its position and the global best solution.
- A new local solution is generated using a random walk based on average loudness and a random vector.
- Loudness decreases and pulse rate increases as iterations proceed, modeling bats approaching prey.
3 Related works
Prior BA variants modify control parameters, movement, local search, encoding, or hybridization, but the reviewed methods were mainly evaluated on classical benchmarks. The paper targets this evaluation gap with directional echolocation and four modifications.
- BA performance may diminish as problem dimension increases, motivating remedies explored through BA variants.
- Existing variants use self-adaptation, differential evolution, inertia factors, mutation, sound speed, complex encoding, or hybrid algorithms.
- Some variants improve low-dimensional performance but show limited gains in high dimensions.
- Prior variants were tested on classical functions, whereas CEC’2005 functions are shifted, rotated, and displaced so optima are not centered.
- dBA instead uses directional echolocation, better-bat guidance, controlled step sizes, and modified pulse rates and loudness.
4 The new directional bat algorithm
dBA retains the standard BA procedure while adding directional movement, adaptive local-search scales, revised pulse and loudness schedules, and a changed acceptance rule. These mechanisms shift emphasis from exploration early to exploitation later.
- 4 The new directional bat algorithm: dBA keeps the standard BA flowchart but introduces four modifications to enhance exploration and exploitation.
- 4.1 The 1st modification (the directional echolocation): Each bat emits pulses toward the best bat and a randomly selected bat, using their fitness feedback to choose movement.
- 4.1 The 1st modification (the directional echolocation): Directional movement diversifies early search directions and gathers bats around the best bat later, reducing local-trapping risk while strengthening exploitation.
- 4.1 The 2nd modification: The local-search scale w_i decreases over iterations, producing broader exploration initially and a smaller region around the best solution later.
- 4.1 The 2nd modification: Sampling found approximately 50%, 25%, and 12.5% of generated solutions outside bounds for w_i0 equal to the domain width, half-width, and quarter-width.
- 4.1 The 2nd modification: The revised pulse-rate and loudness schedules regulate switching between global search and local random walks across iterations.
- 4.1 The 2nd modification: A new solution is accepted when it improves the current solution and a random number is below its corresponding loudness.
5 Experiments and discussions
Three comparison experiments evaluated dBA against standard algorithms, advanced optimizers, and bat-algorithm variants; results generally favored dBA across benchmark functions, statistical tests, and parameter settings.
- First experiment: dBA achieved better results on 9 of 20 classical functions, plus the best median on F2 and best solution on F16.GA performed better on five functions, DE on three, HS on one, and BA on one.
- First experiment: dBA significantly outperformed BA, PSO, HS, and CS by Sign-test comparisons, and outperformed these algorithms plus GA and DE under Wilcoxon testing.The Wilcoxon comparisons used α = 0.05 for BA, PSO, HS, CS, and GA, and α = 0.1 for DE.
- Statistical comparisons: dBA held the lowest rank in Friedman, Aligned Friedman, and Quade tests, with adjusted analyses showing superiority over several competing algorithms.The Quade analysis indicated better results than HS, PSO, and BA on harder problems, with similar or better behavior than CS, GA, and DE on most difficult problems.
- Second experiment: On CEC’2005 functions, dBA was best or tied for best on 12 of 25 functions, representing 48% of the problems.The comparison used mean errors after 1E+5 function evaluations at dimension D = 10.
- Further comparisons: In broader comparisons, dBA outperformed several advanced algorithms, obtained positive contrast differences, and won 26 of 32 tested benchmarking scenarios.The 26 wins represented 81.25% of the evaluated scenarios; dBA also achieved 100% success on the spherical function and for Zakharov’s function with populations ≤ 100.
6 Conclusions
The paper concludes that dBA improves the standard bat algorithm through four modifications, including directional echolocation, and reports superior benchmark performance. The authors link the directional strategy to stronger exploration and exploitation and propose further real-world study.
- Conclusions: The proposed dBA embeds four modifications into standard BA to increase exploration and exploitation capabilities.The approach uses two pulse-emission sets in different directions and guidance from the best bats toward promising regions.
- Conclusions: Across three experiment sets, non-parametric tests supported dBA’s superiority over standard algorithms, advanced optimizers, and many BA variants.The comparisons included classical benchmarks, CEC’2005 functions, and improved bat algorithms.
Algorithm 1
The directional bat algorithm combines directional echolocation and modified update rules with benchmark-based comparisons against classical and advanced optimization algorithms. Across the reported statistical analyses, dBA is identified as the strongest-performing algorithm in the comparisons.
- Algorithm 1: dBA modifies standard BA with directional echolocation and additional rules intended to improve exploration and exploitation.The algorithm initializes pulse rates, loudness, and a weight, then selects another bat, generates frequencies, updates solutions, performs local search, and conditionally accepts new solutions.
- Algorithm 1: The first experiment compares dBA with standard BA, PSO, HS, CS, GA, and DE on 20 classical benchmark functions.The functions are divided into F01-F10 and F11-F20, with convergence evolution reported for both groups.