Real-world Optimization Problems Research Articles

An Interactive Knowledge-Based Multiobjective Evolutionary Algorithm Framework for Practical Optimization Problems

Experienced users often have useful knowledge and intuition in solving real-world optimization problems. User knowledge can be formulated as inter-variable relationships to assist an optimization algorithm in finding good solutions faster. Such inter-variable interactions can also be automatically learned from high-performing solutions discovered at intermediate iterations in an optimization run – a process called innovization. These relations, if vetted by the users, can be enforced among newly generated solutions to steer the optimization algorithm towards practically promising regions in the search space. Challenges arise for large-scale problems where the number of such variable relationships may be high. This paper proposes an interactive knowledge-based evolutionary multi-objective optimization () framework that extracts hidden variable-wise relationships as knowledge from evolving high-performing solutions, shares them with users to receive feedback, and applies them back to the optimization process to improve its effectiveness. The knowledge extraction process uses a systematic and elegant graph analysis method which scales well with number of variables. The working of the proposed is demonstrated on three large-scale real-world engineering design problems. The simplicity and elegance of the proposed knowledge extraction process and achievement of high-performing solutions quickly indicate the power of the proposed framework. The results presented should motivate further such interaction-based optimization studies for their routine use in practice.

Bayesian Optimisation for Constrained Problems

Many real-world optimisation problems such as hyperparameter tuning in machine learning or simulation-based optimisation can be formulated as expensive-to-evaluate black-box functions. A popular approach to tackle such problems is Bayesian optimisation, which builds a response surface model based on the data collected so far, and uses the mean and uncertainty predicted by the model to decide what information to collect next. In this paper, we propose a generalisation of the well-known Knowledge Gradient acquisition function that allows it to handle constraints. We empirically compare the new algorithm with four other state-of-the-art constrained Bayesian optimisation algorithms and demonstrate its superior performance. We also prove theoretical convergence in the infinite budget limit.

Differential evolution with evolutionary scale adaptation

The performance of differential evolution (DE) algorithm heavily depends on the evolutionary scale, which is controlled by the generation operations including mutation, crossover and the control parameters including mutation factor and crossover rate. Adjusting the evolutionary scale to suit different types of problems is a critical yet challenging open question in DE research. To efficiently address this issue, this paper proposes a novel DE based on evolutionary scale adaptation, termed as ESADE. First, a successful scale estimation mechanism is proposed to measure the appropriate evolutionary scale by utilizing the successful evolutionary feedback from the solution space provided by the trial vectors and the target vectors. With the appropriate evolutionary scale, an evolutionary scale adaptation mechanism pre-selects the closest or the farthest trial vector from each target vector, which corresponds to a small or large evolutionary scale respectively to match the search requirements of different evolutionary stages. The effectiveness of the ESA method is demonstrated by performance comparisons with each single baseline strategy, state-of-the-art DEs and state-of-the-art multi-strategy methods on 29 benchmark functions with three dimensionalities. Further applications on several real-world optimization problems also reveal the competitive performance of ESADE.

Boosting aquila optimizer by marine predators algorithm for combinatorial optimization

Abstract In this study, an improved version of aquila optimizer (AO) known as EHAOMPA has been developed by using the marine predators algorithm (MPA). MPA is a recent and well-behaved optimizer with a unique memory saving and fish aggregating devices mechanism. At the same time, it suffers from various defects such as inadequate global search, sluggish convergence, and stagnation of local optima. However, AO has contented robust global exploration capability, fast convergence speed, and high search efficiency. Thus, the proposed EHAOMPA aims to complement the shortcomings of AO and MPA while bringing new features. Specifically, the representative-based hunting technique is incorporated into the exploration stage to enhance population diversity. At the same time, random opposition-based learning is introduced into the exploitation stage to prevent the optimizer from sticking to local optima. This study tests the performance of EHAOMPA’s on 23 standard mathematical benchmark functions, 29 complex test functions from the CEC2017 test suite, six constrained industrial engineering design problems, and a convolutional neural network hyperparameter (CNN-hyperparameter) optimization for Corona Virus Disease 19 (COVID-19) computed tomography-image detection problem. EHAOMPA is compared with four existing optimization algorithm types, achieving the best performance on both numerical and practical issues. Compared with other methods, the test function results demonstrate that EHAOMPA exhibits a more potent global search capability, a higher convergence rate, increased accuracy, and an improved ability to avoid local optima. The excellent experimental results in practical problems indicate that the developed EHAOMPA has great potential in solving real-world optimization problems. The combination of multiple strategies can effectively improve the performance of the algorithm. The source code of the EHAOMPA is publicly available at https://github.com/WangShuang92/EHAOMPA.

Multi-objective non-linear programming problem with rough interval parameters: an application in municipal solid waste management

In dealing with the real-world optimization problems, a decision-maker has to frequently face the ambiguity and hesitancy due to various uncontrollable circumstances. Rough set theory has emerged as an indispensable tool for representing this ambiguity because of its characteristic of incorporating agreement and understanding of all the involved specialists and producing more realistic conclusions. This paper studies an application of the rough set theory for a multi-objective non-linear programming problem that originates for the management of solid wastes. Municipal solid waste management is a global problem that affects every country. Because of the poor waste management system in many nations, the bulk of municipal solid waste is disposed of in open landfills with no recovery mechanism. Hence, an effective and long term waste management strategy is the demand of the day. This research offers an incinerating, composting, recycling, and disposing system for the long-term management of the municipal solid waste. A model for the municipal solid waste management with the goal of minimizing the cost of waste transportation, cost of waste treatment and maximizing the revenue generated from various treatment facilities is developed under rough interval environment. To tackle the conflicting nature of different objectives, an approach is proposed that gives the optimistic and pessimistic views of the decision-maker for optimizing the proposed model. Also, the biasness/preference of the decision-maker for a specific objective is handled by establishing the respective non-linear membership and non-membership functions instead of the linear ones. Finally, to demonstrates the practicality of the proposed methodology, a case study is solved and the obtained Pareto-optimal solution has been compared to those obtained by the existing approaches.

An evolutionary algorithm based on fully connected weight networks for mixed-variable multi-objective optimization

Multi-objective optimization research has mostly focused on continuous-variable problems. However, real-world optimization problems often involve multiple types of variables (continuous, integer, and discrete) and multiple conflicting optimization objectives, called mixed-variable multi-objective optimization problems (MVMOPs). Discrete variables make the decision space of the problem discrete. In contrast, while different types of variables need different treatments by the evolutionary algorithm, which poses a challenge to the efficient search of the evolutionary algorithm. Therefore, we propose an evolutionary algorithm based on a fully connected weight network (FCWNEA). The fully connected network structure characterizes the entire decision space, the node access count records the frequency of visits to the node, and the weights of connections and the activity of variables estimate the distribution of the decision space. This information assists in generating offspring solutions. To evaluate the performance of the proposed algorithm, we conduct empirical experiments on different types of problems. The results show that the proposed algorithm has a significant advantage in mixed-variable multi-objective problems. Moreover, the proposed algorithm is also quite competitive in continuous problems and can better handle the correlation between variables in optimization problems.

High-Dimensional Multi-Objective Bayesian Optimization With Block Coordinate Updates: Case Studies in Intelligent Transportation System

Many transportation system problems can be formulated as high-dimensional expensive multi-objective problems. They are challenging for Gaussian process-based Bayesian optimization methods to find the Pareto fronts due to the curse of dimensionality and the boundary issue in the acquisition function optimization. This paper presents a multi-objective Bayesian optimization method with block coordinate updates, Block-MOBO, to solve high-dimensional expensive multi-objective problems. Block-MOBO first partitions the decision variable space into different blocks, each of which includes a low-dimensional multi-objective problem. At each iteration, one block is considered and the decision variables not in this block are approximated by context-vector generation embedded with the Pareto prior knowledge thus promoting convergence. To tackle the boundary issue, we present <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> -greedy acquisition function in a Bayesian and multi-objective fashion, which recommends candidates either from the exploitation-exploration trade-off perspective or with probability <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> from the Pareto dominance relationship perspective. We verify the effectiveness of Block-MOBO by comparing it with other multi-objective Bayesian methods on two real-world optimization problems in transportation system and three multi-objective synthetic test suites. The experimental results show that Block-MOBO can find more evenly distributed and non-dominated solutions in the whole search space with lower complexity compared with other state-of-the-art approaches. Our analyses illustrate that block coordinate updates and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> -greedy acquisition function contribute to computational complexity reduction and convergence-diversity trade-offs, respectively.

An improved composite particle swarm optimization algorithm for solving constrained optimization problems and its engineering applications

&lt;abstract&gt;&lt;p&gt;In the last few decades, the particle swarm optimization (PSO) algorithm has been demonstrated to be an effective approach for solving real-world optimization problems. To improve the effectiveness of the PSO algorithm in finding the global best solution for constrained optimization problems, we proposed an improved composite particle swarm optimization algorithm (ICPSO). Based on the optimization principles of the PSO algorithm, in the ICPSO algorithm, we constructed an evolutionary update mechanism for the personal best position population. This mechanism incorporated composite concepts, specifically the integration of the $ \varepsilon $-constraint, differential evolution (DE) strategy, and feasibility rule. This approach could effectively balance the objective function and constraints, and could improve the ability of local exploitation and global exploration. Experiments on the CEC2006 and CEC2017 benchmark functions and real-world constraint optimization problems from the CEC2020 dataset showed that the ICPSO algorithm could effectively solve complex constrained optimization problems.&lt;/p&gt;&lt;/abstract&gt;

Multi-operator opposition-based learning with the neighborhood structure for numerical optimization problems and its applications

Opposition-based learning (OBL) is an effective strategy that adjusts the population to accelerate the convergence of the algorithm. However, OBL involves two phases (generation and calculation) that are seldom mentioned simultaneously. Besides, individual information in OBL is not fully used to guide evolution. First, a novel neighborhood generation strategy is proposed to fully use individual information. There are numerous variants of the neighborhood structure. Three prominent neighborhood structures are designed to demonstrate their benefits in various dimensions. Second, a multi-operator calculation method with two distributions is introduced to reach the equilibrium between diversification and intensification. Consequently, this paper proposes three multi-operator neighborhood-based OBL variants (MNOBLs). Compared with the traditional OBL variants, MNOBLs generate the opposite population by using a neighborhood of the individuals. A well-balanced calculation method can lead to good convergence behavior. Subsequently, the proposed MNOBLs are embedded into the basic differential evolution (DE) algorithm to obtain the proposed algorithms. The extensive and rigorous numerical experiments are designed at three levels: strategies, algorithms, and functions. Specifically, the effectiveness and efficiency of the proposed algorithms are verified by comparing them with 13 state-of-the-art DE variants and four metaheuristics on the CEC 2017, and CEC 2022 test suites, and two real-world optimization problems. The comprehensive results show that the proposed OBL variants provide promising results for most problems.

Quantum Computing Algorithms for Nonlinear Optimization Problems

The increasing complexity of real-world optimization problems highlights the importance of this research since classical algorithms are unable to provide efficient answers in these cases. Innovative methods for fast and scalable resolution of nonlinear optimization problems are required because these problems are prevalent in many fields. The potential for quantum computing to speed up optimization processes and overcome classical limitations is great, owing to its superposition principles and intrinsic parallelism. The integration of quantum algorithms (I-QA) into real-world applications, however, will not always be smooth sailing. There are significant challenges associated with preserving quantum coherence, correcting errors, and working within hardware limits. To enable the simultaneous exploration of solution spaces through quantum parallelism, this research proposes the Hybrid Quantum Gradient -Classical Approach (HQG-CA), which makes use of parameterized quantum circuits to represent probable solutions. Additionally, improves convergence rates through applying quantum gradient information to direct optimization in the quantum state space. Optimization of portfolios in finance, adjustment of model parameters in machine learning, and optimization of routes in logistics are a few examples of the many industries that find use for HQG-CA. These applications are explored in this abstract, which highlights the revolutionary potential of HQG-CA to solve optimization problems in the real world. The effectiveness of HQG-CA is assessed through a thorough simulation experiment. Performance measures such algorithmic speedup, solution accuracy, and scalability are discussed, which is based on extensive testing and comparison with classical alternatives. The present research provides a comprehensive evaluation of HQG-CA's potential for tackling nonlinear optimization problems.

A novel optimization approach based on unstructured evolutionary game theory

Proposing new metaheuristic methods is crucial for continuous algorithmic improvement and the ability to effectively address increasingly complex real-world optimization problems. On the other hand, Evolutionary Game Theory analyzes how trough competition is possible to modify the strategies of individuals within a population in order to spread successful mechanisms and reduce or remove less successful strategies. This paper introduces a novel optimization approach based on the principles of evolutionary game theory. In the proposed method, all individuals are initialized using the Metropolis–Hasting technique, which sets the solutions at a starting point closer to the optimal or near-optimal regions of the problem. An original strategy is then assigned to each individual in the population. By considering the interactions and competition among different agents in the optimization problem, the approach modifies the strategies to improve search efficiency and find better solutions. To evaluate the performance of the proposed technique, it is compared with eight well-known metaheuristic algorithms using 30 benchmark functions. The proposed methodology demonstrated superiority in terms of solution quality, dimensionality, and convergence when compared to other approaches.

Design-space adaptation method for multiobjective and multidisciplinary optimization

This paper developed a new method that adaptively adjusts a design space by considering the actual solution distribution of a problem to overcome the conventional design-space adaptation method that assumes the solutions distribution to be a normal distribution because the distributions of solutions are rarely normal distributions for real-world problems. The developed method was applied to nineteen multiobjective test functions that are widely used to evaluate the characteristics and performance of optimization approaches. The results showed that this method adapted the design space to an appropriate design space where the solution existence probability was high. The optimization performance achieved using the developed method was higher than that of the conventional methods. Furthermore, the developed method was applied to the conceptual design of an unmanned spacecraft to confirm its validity in real-world design and multidisciplinary-optimization problems. The results showed that the Pareto solutions of the developed method were superior to those of conventional methods. Additionally, the optimization efficiency with the developed method was improved by more than 1.4 times over that of the conventional methods. In this regard, the developed method has the potential to be applied to complicated real-world optimization problems to achieve better performance and efficiency.

INTEGRATING ENHANCED OPTIMIZATION WITH FINITE ELEMENT ANALYSIS FOR DESIGNING STEEL STRUCTURE WEIGHT UNDER MULTIPLE CONSTRAINTS

Real-world optimization problems are ubiquitous across scientific domains, and many engineering challenges can be reimagined as optimization problems with relative ease. Consequently, researchers have focused on developing optimizers to tackle these challenges. The Snake Optimizer (SO) is an effective tool for solving complex optimization problems, drawing inspiration from snake patterns. However, the original SO requires the specification of six specific parameters to operate efficiently. In response to this, enhanced snake optimizers, namely ESO1 and ESO2, were developed in this study. In contrast to the original SO, ESO1 and ESO2 rely on a single set of parameters determined through sensitivity analysis when solving mathematical functions. This streamlined approach simplifies the application of ESOs for users dealing with optimization problems. ESO1 employs a logistic map to initialize populations, while ESO2 further refines ESO1 by integrating a Lévy flight to simulate snake movements during food searches. These enhanced optimizers were compared against the standard SO and 12 other established optimization methods to assess their performance. ESO1 significantly outperforms other algorithms in 15, 16, 13, 15, 21, 16, 24, 16, 19, 18, 13, 15, and 22 out of 24 mathematical functions. Similarly, ESO2 outperforms them in 16, 17, 18, 22, 23, 23, 24, 20, 19, 20, 17, 22, and 23 functions. Moreover, ESO1 and ESO2 were applied to solve complex structural optimization problems, where they outperformed existing methods. Notably, ESO2 generated solutions that were, on average, 1.16%, 0.70%, 2.34%, 3.68%, and 6.71% lighter than those produced by SO, and 0.79%, 0.54%, 1.28%, 1.70%, and 1.60% lighter than those of ESO1 for respective problems. This study pioneers the mathematical evaluation of ESOs and their integration with the finite element method for structural weight design optimization, establishing ESO2 as an effective tool for solving engineering problems.

Dynamic ε-multilevel hierarchy constraint optimization with adaptive boundary constraint handling technology

Real-world optimization problems are often difficult to solve because of the complexity of the objective function and the large number of constraints that accompany it. To solve such problems, we propose Adaptive Dynamic ε-Multilevel Hierarchy Constraint Optimization (εMHCO). Firstly, we propose the dynamic constraint tolerance factor ε which can change dynamically with the feasible ratio and the number of iterations in the current population. This ensures a reasonable proportion of virtual feasible solutions in the population. Secondly, we propose adaptive boundary constraint handling technology (ABCHT). It can reshape the current individual position adaptively according to the size of constraint violation and increase the diversity of the population. Finally, we propose multi-level hierarchy optimization, whose multiple population structure is beneficial to solve real-world constraint optimization problems (COPs). To validate and analyze the performance of εMHCO, numerical experiments are conducted on the latest real-world test suite CEC’2020, which contains a set of 57 real-world COPs, and compared with four state-of-the-art algorithms. The results show that εMHCO is significantly superior to, or at least comparable to the state-of-the-art algorithms in solving real-world COPs. Meanwhile, the effectiveness and feasibility of εMHCO are verified on the real-world problem of the pipeline inner detector speed control.

Triple competitive differential evolution for global numerical optimization

As optimization problems become more and more complex in real-world scenarios, the effectiveness of many existing differential evolution (DE) methods is critically challenged. To circumvent this predicament, this paper proposes a triple competitive DE (TCDE) to tackle increasingly complicated optimization problems. Specifically, a triple competition mechanism is devised to first randomly arrange individuals into exclusive triples and then let individuals in each triple compete with each other. Subsequently, heterogeneous mutation schemes are designed to update the three individuals in each triple based on the competition results. With the cooperation between these two techniques, on the one hand, better individuals in the triples tend to exploit the areas where they lie to find high-accuracy solutions, while worse individuals in the triples prefer to explore the intricate problem space to locate promising regions. On the other hand, different individuals are mutated by following the guidance of different leading exemplars, which ensures that individuals traverse the sophisticated solution space in diverse directions along with slight intensification to optimal regions. Furthermore, a modified adaptive parameter adjustment scheme is designed for individuals in each triple by considering their differences so as to meet the expectation that better individuals focus on exploitation while worse individuals concentrate on exploration. Finally, experiments are performed to first compare TCDE with totally 10 advanced DE variants and then further compare it with totally 10 CEC winners and their latest variants on the CEC'2014 and the CEC'2017 problem suites with totally 4 different dimensionality settings. Experimental results prove that TCDE achieves highly competitive or even much better performance than the totally 20 compared methods. Particularly, TCDE is demonstrated to be especially capable of solving complicated optimization problems. Furthermore, the efficacy of TCDE in tackling real-world optimization problems is substantiated through experiments conducted on the CEC'2011 real-world optimization problem set.

A local correlation estimation surrogate-assisted bi-objective evolutionary algorithm for heterogeneous objectives

Most existing evolutionary algorithms for solving bi-objective optimization problems are based on the assumption that both objectives can be evaluated once at the same time. However, in real-world optimization problems, there is a significant difference in function evaluation time between objectives, and these problems are defined as the problems with heterogeneous objectives. To utilize the latency of objectives, we propose a local correlation estimation based surrogate-assisted bi-objective evolutionary algorithm for problems with heterogeneous objectives. In the proposed algorithm, surrogate models are employed to approximate the objective functions. The proposed local correlation estimation (LCE) method is used to analyze the correlation between objectives within a local region, guiding the search direction for one objective while identifying promising solutions for the other objective. Finally, the ablation experiment for the LCE method validates the effectiveness of the proposed strategy, and the comparative results on various expensive bi-objective test problems demonstrate that the proposed algorithm is promising on heterogeneous bi-objective optimization problems.

A Contemporary Systematic Review on Meta-heuristic Optimization Algorithms with Their MATLAB and Python Code Reference

AbstractOptimization is a method which is used in every field, such as engineering, space, finance, fashion market, mass communication, travelling, and also in our daily activities. In every field, everyone always wants to minimize or maximize something called the objective function. Traditional and modern optimization techniques or Meta-Heuristic (MH) optimization techniques are used to solve the objective functions. But the traditional optimization techniques fail to solve the complex and real-world optimization problem consisting of non-linear objective functions. So many modern optimization techniques have been proposed exponentially over the last few decades to overcome these challenges. This paper discusses a brief review of the different benchmark test functions (BTFs) related to existing MH optimization algorithms (OA). It discusses the classification of MH algorithms reported in the literature regarding swarm-based, human-based, physics-based, and evolutionary-based methods. Based on the last half-century literature, MH-OAs are tabulated in terms of the proposed year, author, and inspiration agent. Furthermore, this paper presents the MATLAB and python code web-link of MH-OA. After reading this review article, readers will be able to use MH-OA to solve challenges in their field.

Dual-Fuzzy-Classifier-Based Evolutionary Algorithm for Expensive Multiobjective Optimization

Multiobjective evolutionary algorithms (MOEAs) have been widely used to solve multiobjective optimization problems (MOPs). Conventional MOEAs usually require a large number of function evaluations (FEs) for evaluating the quality of solutions. However, only a limited number of FEs are affordable in many real-world optimization problems where the FEs are computationally or economically expensive. The use of a large number of FEs decreases the effectiveness of MOEAs in solving these problems. This article proposes a dual fuzzy classifier-based surrogate model (DFC) and a DFC-based multiobjective evolutionary algorithm framework (DFC-MOEA) for expensive optimization problems. The DFC model is used for offspring pre-selection to choose high-quality offspring solutions and for categorization to divide unevaluated solutions into three categories. In the proposed framework, two fuzzy classifiers are built to predict the quality of each unevaluated solution. To strike a balance between convergence and diversity, one classifier is designed for predicting the dominance relation of unevaluated solutions (i.e., convergence), and another classifier is designed for predicting the crowdedness of unevaluated solutions (i.e., diversity). The integration of the proposed framework in three different types of MOEAs (i.e., a dominance-based MOEA, an indicator-based MOEA, and a decomposition-based MOEA) demonstrates its usefulness in handling expensive optimization problems. Comprehensive experiments on four well-known test suites and several real-world optimization problems demonstrate that the proposed framework is able to improve the performance of MOEAs under a limited number of FEs.

TPPSO: A Novel Two-Phase Particle Swarm Optimization

Particle swarm optimization (PSO) is a stout and rapid searching algorithm that has been used in various applications. Nevertheless, its major drawback is the stagnation problem that arises in the later phases of the search process. To solve this problem, a proper balance between investigation and manipulation throughout the search process should be maintained. This article proposes a new PSO variant named two-phases PSO (TPPSO). The concept of TPPSO is to split the search process into two phases. The first phase performs the original PSO operations with linearly decreasing inertia weight, and its objective is to focus on exploration. The second phase focuses on exploitation by generating two random positions in each iteration that are close to the global best position. The two generated positions are compared with the global best position sequentially. If a generated position performs better than the global best position, then it replaces the global best position. To prove the effectiveness of the proposed algorithm, sixteen popular unimodal, multimodal, shifted, and rotated benchmarking functions have been used to compare its performance with other existing well-known PSO variants and non-PSO algorithms. Simulation results show that TPPSO outperforms the other modified and hybrid PSO variants regarding solution quality, convergence speed, and robustness. The convergence speed of TPPSO is extremely fast, making it a suitable optimizer for real-world optimization problems.

I-CPA: An Improved Carnivorous Plant Algorithm for Solar Photovoltaic Parameter Identification Problem.

The carnivorous plant algorithm (CPA), which was recently proposed for solving optimization problems, is a population-based optimization algorithm inspired by plants. In this study, the exploitation phase of the CPA was improved with the teaching factor strategy in order to achieve a balance between the exploration and exploitation capabilities of CPA, minimize getting stuck in local minima, and produce more stable results. The improved CPA is called the I-CPA. To test the performance of the proposed I-CPA, it was applied to CEC2017 functions. In addition, the proposed I-CPA was applied to the problem of identifying the optimum parameter values of various solar photovoltaic modules, which is one of the real-world optimization problems. According to the experimental results, the best value of the root mean square error (RMSE) ratio between the standard data and simulation data was obtained with the I-CPA method. The Friedman mean rank statistical analyses were also performed for both problems. As a result of the analyses, it was observed that the I-CPA produced statistically significant results compared to some classical and modern metaheuristics. Thus, it can be said that the proposed I-CPA achieves successful and competitive results in identifying the parameters of solar photovoltaic modules.