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The Exponential Distribution Optimizer (EDO) is a population-based optimizer inspired by exponential distribution theory. It's widely used in real-world scenarios due to its simple architecture and strong optimization capabilities. However, similar to comparable optimizers that rely on swarms, EDO can fall prey to local optima, suffer from premature convergence, and lack diversity when dealing with challenging optimization problems. To address these problems, we propose Modified EDO (MEDO), which combines the Salp Swarm Algorithm (SSA) with Quadratic Interpolation (QI). QI improves MEDO's local search efficiency and solution precision, while SSA helps prevent getting stuck in suboptimal solutions, serving as a global migration mechanism. These combined strategies enhance EDO's performance. Furthermore, MEDO aims to strike a balance between exploiting known information and exploring new possibilities. We evaluated the EDO approach on 27 benchmark functions, including the CEC 2015 and CEC 2022 sets, as well as the four engineering problems and extreme learning machine parameter tuning. Experimental results show that MEDO outperforms other optimizers in 77.78% of the test functions and achieves 97.3% accuracy in fine-tuning ELM parameters. Non-parametric statistical tests demonstrate that MEDO is highly competitive and superior to other algorithms used in research. [ABSTRACT FROM AUTHOR]

The straightness error of hole and shaft parts is one of the important parameters to reflect machining quality. The modeling process of traditional mathematical methods is complex, and the solution precision is not high. The intelligent optimization algorithm has significant advantages in solving this kind of problem. It can depend on random operators jumping out of local optima and does not need to calculate a large gradient information. Therefore, this paper proposes an improved exponential distribution optimization (IEDO) algorithm to achieve the minimum zone evaluation of straightness error. Firstly, the mathematical model of minimum zone method for axis straightness evaluation is established as the objective function. Secondly, the principle of the basic exponential distribution optimization (EDO) algorithm is described, and the exponential distribution optimizer is improved in three aspects: in the initialization, the interval shortening strategy is introduced to solve the problem of uneven initial population distribution; the adaptive switch probability is proposed to replace the constant value (0.5) to balance the ability of global exploration and local exploitation; a guidance strategy based on weight is proposed to guide the search process to reach the global optimal quickly. Then, nine typical benchmark functions are utilized to test the performance of the improved algorithm, which reveals satisfactory results. Finally, IEDO successfully applies to evaluation of axis straightness error with good accuracy. [ABSTRACT FROM AUTHOR]

Population-based meta-heuristic optimization algorithms play a vital role in addressing optimization problems. Nowadays, exponential distribution optimizer (EDO) can be considered to be one of the most recent among these algorithms. Although it has achieved many promising results, it has a set of shortcomings, for example, the decelerated convergence, and provides local optima solution as it cannot escape from local regions in addition to imbalance between diversification and intensification. Therefore, in this study, an enhanced variant of EDO called mEDO was proposed to address these shortcomings by combining two efficient search mechanisms named orthogonal learning (OL) and local escaping operator (LEO). In mEDO, the LEO has been exploited to escape local optima and improve the convergence behavior of the EDO by employing random operators to maximize the search process and to effectively discover the globally optima solution. Then the OL has been combined to keep the two phases (i.e., exploration and exploitation) balanced. To validate the effectiveness and performance of the mEDO algorithm, the proposed method has been evaluated over ten functions of the IEEE CEC'2020 test suite as well as eight real-world applications (engineering design optimization problems), Furthermore we test the applicability of the proposed algorithm by tackling 21 instance of the quadratic assignment problem (QAP). The experimental and statistical results of the proposed algorithm have been compared against seven other common metaheuristic algorithms (MAs), including the basic EDO. The results show the supremacy of the mEDO algorithm over the other algorithms and reveal the applicability and effectiveness of the mEDO algorithm compared to well-established metaheuristic algorithms. The experimental results and different statistical measures revealed the reliability and applicability of the mEDO method in solving the global, engineering design, and combinatorial optimization problems by achieving a reasonable solution in terms of scoring a global optima solutions and avoiding premature convergence by increasing the population's diversity. [ABSTRACT FROM AUTHOR]

In this paper, an enhanced version of the Exponential Distribution Optimizer (EDO) called mEDO is introduced to tackle global optimization and multi-level image segmentation problems. EDO is a math-inspired optimizer that has many limitations in handling complex multi-modal problems. mEDO tries to solve these drawbacks using 2 operators: phasor operator for diversity enhancement and an adaptive p-best mutation strategy for preventing it converging to local optima. To validate the effectiveness of the suggested optimizer, a comprehensive set of comparative experiments using the CEC'2020 test suite was conducted. The experimental results consistently prove that the suggested technique outperforms its counterparts in terms of both convergence speed and accuracy. Moreover, the suggested mEDO algorithm was applied for image segmentation using the multi-threshold image segmentation method with Otsu's entropy, providing further evidence of its enhanced performance. The algorithm was evaluated by comparing its results with those of existing well-known algorithms at various threshold levels. The experimental results validate that the proposed mEDO algorithm attains exceptional segmentation results for various threshold levels.

In this paper, an enhanced version of the Exponential Distribution Optimizer (EDO) called mEDO is introduced to tackle global optimization and multi-level image segmentation problems. EDO is a math-inspired optimizer that has many limitations in handling complex multi-modal problems. mEDO tries to solve these drawbacks using 2 operators: phasor operator for diversity enhancement and an adaptive p-best mutation strategy for preventing it converging to local optima. To validate the effectiveness of the suggested optimizer, a comprehensive set of comparative experiments using the CEC'2020 test suite was conducted. The experimental results consistently prove that the suggested technique outperforms its counterparts in terms of both convergence speed and accuracy. Moreover, the suggested mEDO algorithm was applied for image segmentation using the multi-threshold image segmentation method with Otsu's entropy, providing further evidence of its enhanced performance. The algorithm was evaluated by comparing its results with those of existing well-known algorithms at various threshold levels. The experimental results validate that the proposed mEDO algorithm attains exceptional segmentation results for various threshold levels. [ABSTRACT FROM AUTHOR]

The emergence of COVID-19 has broken the silence of humanity and people are gradually becoming concerned about pneumonia-related diseases; thus, improving the recognition rate of pneumonia-related diseases is an important task. Neural networks have a remarkable effectiveness in medical diagnoses, though the internal parameters need to be set in accordance to different data sets; therefore, an important challenge is how to further improve the efficiency of neural network models. In this paper, we proposed a learning exponential distribution optimizer based on chaotic evolution, and we optimized Resnet50 for COVID classification, in which the model is abbreviated as IEDO-net. The algorithm introduces a criterion for judging the distance of the signal-to-noise ratio, a chaotic evolution mechanism is designed according to this criterion to effectively improve the search efficiency of the algorithm, and a rotating flight mechanism is introduced to improve the search capability of the algorithm. In the computed tomography (CT) image data of COVID-19, the accuracy, sensitivity, specificity, precision, and F1 score of the optimized Resnet50 were 94.42%, 93.40%, 94.92%, 94.29% and 93.84%, respectively. The proposed network model is compared with other algorithms and models, and ablation experiments and convergence and statistical analyses are performed. The results show that the diagnostic performance of IEDO-net is competitive, which validates the feasibility and effectiveness of the proposed network.

The emergence of COVID-19 has broken the silence of humanity and people are gradually becoming concerned about pneumonia-related diseases; thus, improving the recognition rate of pneumonia-related diseases is an important task. Neural networks have a remarkable effectiveness in medical diagnoses, though the internal parameters need to be set in accordance to different data sets; therefore, an important challenge is how to further improve the efficiency of neural network models. In this paper, we proposed a learning exponential distribution optimizer based on chaotic evolution, and we optimized Resnet50 for COVID classification, in which the model is abbreviated as IEDO-net. The algorithm introduces a criterion for judging the distance of the signal-to-noise ratio, a chaotic evolution mechanism is designed according to this criterion to effectively improve the search efficiency of the algorithm, and a rotating flight mechanism is introduced to improve the search capability of the algorithm. In the computed tomography (CT) image data of COVID-19, the accuracy, sensitivity, specificity, precision, and F1 score of the optimized Resnet50 were 94.42%, 93.40%, 94.92%, 94.29% and 93.84%, respectively. The proposed network model is compared with other algorithms and models, and ablation experiments and convergence and statistical analyses are performed. The results show that the diagnostic performance of IEDO-net is competitive, which validates the feasibility and effectiveness of the proposed network. [ABSTRACT FROM AUTHOR]

Exponential distribution optimizer (EDO) is a recently proposed optimization technique that is based on the exponential probability distribution model. As most swarm intelligence algorithms (SIAs), EDO is very good at handling common optimization problems. However, when addressing multimodal and center-bias problems, it exhibits limitations like imbalanced global and local search capabilities and poor solution accuracy. Building upon this, we introduce an improved version of exponential distribution optimizer that incorporates a dimensional perturbation module (DPM) called EDO_DPM. By testing the impact of dimensional perturbation, the K -dimensional evolution strategy is adopted in our approach. Concurrently, to modulate the usage frequency of DPM, an adjustment parameter, named evolutionary state factor (ESF), is designed contingent on the population's evolutionary state. Moreover, to alleviate the deficiency of non full-dimensional perturbation, a bounce out operation is embedded in the algorithm. The efficacy of EDO_DPM has been substantiated through testing on 20 different types of functions and CEC2017 benchmark suite. Comparative analyses with the state-of-the-art algorithms have demonstrated a marked enhancement in EDO_DPM's capability to manage multimodal problems and its proficiency in resolving center-bias problems. Meanwhile, it can achieve excellent results on CEC2017 by comparing excellent improved variants. Furthermore, EDO_DPM is applied to the problem of parameter estimation for photovoltaic (PV) generation systems. Comparison results show that EDO_DPM has good application capability. • The strategy DPM improves EDO's optimization capability. • Bounce out operation helps the algorithm break out of local optimal traps. • EDO_DPM shows excellent performance in numerical experiments and PV problems. [ABSTRACT FROM AUTHOR]

Establishing a precise model for proton exchange membrane fuel cell (PEMFC) is vital to simulate, manage, control, and estimate the optimal parameters accurately. However, the process has some challenges due to the nonlinear nature of fuel cells (FCs) and the missing parameters in datasheet. Also, the reported approaches have some restrictions in their behaviors. This paper proposes a new methodology incorporated exponential distribution optimizer (EDO) to construct PEMFC's equivalent circuit through estimating their parameters with the aid of experimental data. The algorithm is characterized by exploration/exploitation balance that avoids falling in local solutions. Sum square error (SSE) between the measured and estimated terminal voltages is selected as the target to be mitigated. The analysis is performed on four different FCs which are Ballard Mark V 5 kW, BCS-500 W, SR-12 500 W, and NedStack PS6. The proposed EDO is compared to reported approaches of mayfly optimization algorithm (MOA), chaotic mayfly optimization algorithm (CMOA), modified Harris hawks optimizer (MHHO), fractional order modified HHO (FMHHO), hybrid vortex search algorithm and differential evolution (VSDE), and other programmed approaches of sine cosine algorithm (SCA), seagull optimization algorithm (SOA), tunicate swarm algorithm (TSA), and gold rush optimizer (GRO). The best scores are 0.852056, 1.16978E-02, 1.056628, and 2.079166 obtained through the proposed EDO for Ballard Mark V 5 kW, BCS-500 W, SR-12 500 W, and NedStack PS6 cells, respectively. The absolute error ratios of CMOA, MOA, FMHHO, MHHO, VSDE, SOA, SCA, GRO, and TSA attributed to the error obtained by the proposed EDO in case of BSC-500W are 0.17%, 3.49%, 0.62%, 15.50%, 3.78%, 29.12%, 86.30%, 0.90%, and 10.33%, respectively. Despite the nine approaches considered in comparative analysis having some issues with convergence speed, they converged the best solution. Moreover, the dynamic model of PEMFC is established in Simulink and its performance is assessed through applying step load disturbance. The fetched results demonstrated the superiority of the proposed EDO in establishing reliable models of various PEMFCs. • EDO is proposed to estimate the optimal parameters of different PEMFCs. • Comparison to MOA, CMOA, MHHO, FOHHO, VSDE, SCA, SOA, TSA, and GRO is conducted. • The dynamic behavior of the established model is assessed at different demands. • The obtained results demonstrated the efficacy and reliability of the proposed EDO. [ABSTRACT FROM AUTHOR]