A hybridization of differential evolution and monarch butterfly optimization for solving systems of nonlinear equations
Bibliographic record
Abstract
Abstract In this study, we propose a new hybrid algorithm consisting of two meta-heuristic algorithms; Differential Evolution (DE) and the Monarch Butterfly Optimization (MBO). This hybrid is called DEMBO. Both of the meta-heuristic algorithms are typically used to solve nonlinear systems and unconstrained optimization problems. DE is a common metaheuristic algorithm that searches large areas of candidate space. Unfortunately, it often requires more significant numbers of function evaluations to get the optimal solution. As for MBO, it is known for its time-consuming fitness functions, but it traps at the local minima. In order to overcome all of these disadvantages, we combine the DE with MBO and propose DEMBO which can obtain the optimal solutions for the majority of nonlinear systems as well as unconstrained optimization problems. We apply our proposed algorithm, DEMBO, on nine different, unconstrained optimization problems and eight well-known nonlinear systems. Our results, when compared with other existing algorithms in the literature, demonstrate that DEMBO gives the best results for the majority of the nonlinear systems and unconstrained optimization problems. As such, the experimental results demonstrate the efficiency of our hybrid algorithm in comparison to the known algorithms. Highlights This paper proposes a new hybridization of differential evolution and monarch butterfly optimization. Solve system of nonlinear equations and unconstrained optimization problem. The efficiency and effectiveness of our algorithm are provided. Experimental results prove the superiority of our algorithm over the state-of-the-arts.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".