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A well-regarded as well as powerful method named the ‘analytic hierarchy process’ (AHP) uses mathematics and psychology for making and analysing complex decisions. This article aims to present a brief review of the consistency measure of the judgments in AHP. Judgments should not be random or illogical. Several researchers have developed different consistency measures to identify the rationality of judgments. This article summarises the consistency measures which have been proposed so far in the literature. Moreover, this paper describes briefly the functional relationships established in the literature among the well-known consistency indices. At last, some thoughtful research directions that can be helpful in further research to develop and improve the performance of AHP are provided as well.

Reliable recognition of geochemical anomalies linked to ore deposits is one of the most significant challenges in mineral exploration. Several advanced machine learning (AML) algorithms have recently been applied to recognize multi-element geochemical anomalies. Performance of the AML algorithms are extremely dependent to values of their hyperparameters. Because, conclusions of their application can significantly be differed tuning hyperparameters. Tuning hyperparameters through trial-and-error way is a labor-intensive and time-consuming procedure which is not mostly eventuated to reliable results. In this regard, applying an AML model decreases training time and assists to achieve optimized values of hyperparameters yielding reasonable potential maps. Hence, execution of an AML model mitigates the biasness problem and uncertainties with recognition of multi-element geochemical anomalies. In this study, Harris hawks optimization (HHO) algorithm was employed to optimize known hyperparameters of the random forest (RF) method for detecting multi-element geochemical anomalies related to mineralization occurrences in the Feyzabad district of the Razavi Khorasan province, NE Iran. This research demonstrates that Harris hawks optimized random forest (HHORF) model is a vigorous procedure to identify multi-element geochemical anomalies. Because, the HHORF model has recognized 86.53% mineralization occurrences through 30% corresponding area while the RF method has catched 80.14% mineralization occurrences up via same corresponding area.

The growing penetration of renewable energy sources (RES) in power markets poses several operational issues, such as price volatility, transmission congestion, and voltage instability. In response to these issues, this work suggests an optimal power flow (OPF) method that considers renewable energy generation (REG) and demand response strategies to reduce system cost and enhance voltage stability. The IEEE-30 bus system is utilized as the test case, and the optimization problem is addressed using the Whale Optimization Algorithm (WOA). The outcomes show that incorporating an electricity market lowers generation costs from 798.86 $/h to 707.35 $/h with an 11.5% decrease, and system losses from 8.63 MW to 8.16 MW. Further, the inclusion of REG in the market-based model lowers the operational cost to 706.96 $/h, and system losses to 7.21 MW, an overall improvement of 16.5%. The total voltage deviation (VD) which is an important stability index, decreases from 0.1060 pu to 0.0803 pu, enhancing voltage stability by 24.2%. In addition, a multi-objective optimization approach is implemented that balances minimizing the cost and the reduction of voltage deviation. Convergence behavior reveals that WOA can find a good solution at 300 iterations and is faster and more accurate than traditional algorithms. The research proves that optimal scheduling of active and reactive power and effective participation of the demand side can improve economic efficiency and voltage stability. These results set WOA as a strong and effective method for power system performance optimization in deregulated electricity markets, enabling large-scale renewable integration while maintaining system reliability and economic viability.

In the last decade, we observe an increasing number of nature-inspired optimization algorithms, with authors often claiming their novelty and their capabilities of acting as powerful optimization techniques. However, a considerable number of these algorithms do not seem to draw inspiration from nature or to incorporate successful tactics, laws, or practices existing in natural systems, while also some of them have never been applied in any optimization field, since their first appearance in literature. This paper presents some interesting findings that have emerged after the extensive study of most of the existing nature-inspired algorithms. The need for irrationally introducing new nature inspired intelligent (NII) algorithms in literature is also questioned and possible drawbacks of NII algorithms met in literature are discussed. In addition, guidelines for the development of new nature-inspired algorithms are proposed, in an attempt to limit the misleading appearance of variation of metaheuristics as nature inspired optimization algorithms.

Optimization is an important and fundamental challenge to solve optimization problems in different scientific disciplines. In this paper, a new stochastic nature-inspired optimization algorithm called Pelican Optimization Algorithm (POA) is introduced. The main idea in designing the proposed POA is simulation of the natural behavior of pelicans during hunting. In POA, search agents are pelicans that search for food sources. The mathematical model of the POA is presented for use in solving optimization issues. The performance of POA is evaluated on twenty-three objective functions of different unimodal and multimodal types. The optimization results of unimodal functions show the high exploitation ability of POA to approach the optimal solution while the optimization results of multimodal functions indicate the high ability of POA exploration to find the main optimal area of the search space. Moreover, four engineering design issues are employed for estimating the efficacy of the POA in optimizing real-world applications. The findings of POA are compared with eight well-known metaheuristic algorithms to assess its competence in optimization. The simulation results and their analysis show that POA has a better and more competitive performance via striking a proportional balance between exploration and exploitation compared to eight competitor algorithms in providing optimal solutions for optimization problems.

As the world moves towards industrialization, optimization problems become more challenging to solve in a reasonable time. More than 500 new metaheuristic algorithms (MAs) have been developed to date, with over 350 of them appearing in the last decade. The literature has grown significantly in recent years and should be thoroughly reviewed. In this study, approximately 540 MAs are tracked, and statistical information is also provided. Due to the proliferation of MAs in recent years, the issue of substantial similarities between algorithms with different names has become widespread. This raises an essential question: can an optimization technique be called ‘novel’ if its search properties are modified or almost equal to existing methods? Many recent MAs are said to be based on ‘novel ideas’, so they are discussed. Furthermore, this study categorizes MAs based on the number of control parameters, which is a new taxonomy in the field. MAs have been extensively employed in various fields as powerful optimization tools, and some of their real-world applications are demonstrated. A few limitations and open challenges have been identified, which may lead to a new direction for MAs in the future. Although researchers have reported many excellent results in several research papers, review articles, and monographs during the last decade, many unexplored places are still waiting to be discovered. This study will assist newcomers in understanding some of the major domains of metaheuristics and their real-world applications. We anticipate this resource will also be useful to our research community.

This paper innovatively proposes the Black Kite Algorithm (BKA), a meta-heuristic optimization algorithm inspired by the migratory and predatory behavior of the black kite. The BKA integrates the Cauchy mutation strategy and the Leader strategy to enhance the global search capability and the convergence speed of the algorithm. This novel combination achieves a good balance between exploring global solutions and utilizing local information. Against the standard test function sets of CEC-2022 and CEC-2017, as well as other complex functions, BKA attained the best performance in 66.7, 72.4 and 77.8% of the cases, respectively. The effectiveness of the algorithm is validated through detailed convergence analysis and statistical comparisons. Moreover, its application in solving five practical engineering design problems demonstrates its practical potential in addressing constrained challenges in the real world and indicates that it has significant competitive strength in comparison with existing optimization techniques. In summary, the BKA has proven its practical value and advantages in solving a variety of complex optimization problems due to its excellent performance. The source code of BKA is publicly available at https://www.mathworks.com/matlabcentral/fileexchange/161401-black-winged-kite-algorithm-bka .

From the past few decades many nature inspired algorithms have been developed and gaining more popularity because of their effectiveness in solving problems of distinct application domains. Undoubtedly, Particle swarm optimization (PSO) algorithm is the most successful optimization algorithm among the available nature inspired algorithms such as simulated annealing, genetic algorithm, differential evolution, firefly, cuckoo etc., because of its high efficiency and capability to adjust in different dynamic environments. This year marks its 25th anniversary of PSO, one of the base inspirations for many modern-day metaheuristics development. Because of its simple structure and few number of algorithmic parameters, PSO from its origin has acquired widespread popularity amongst researchers, technocrats and practitioners and has been proven to provide better performance in various functional areas such as networking, robotics, image segmentation, power generation and controlling, fuzzy systems and so on. PSO is a population based global heuristic optimization approach motivated by the social behavior of animals chasing for food such as flock of birds, schools of fish. PSO attempts to stabilize exploration and exploitation by combining local search capabilities with global search capabilities. In this article, an in-depth analysis of PSO with its developments from 1995 to 2020 has been presented. Mainly, the improved variants of PSO along with solvable application areas are discussed in detail to provide a scope for the further development. At the end of the paper, the growth of the PSO in various application areas has been presented with factual representation. The main motive of this survey is to inspire the researchers, practitioners and technocrats to develop improved and innovative solutions for solving complex problems in various domains using PSO.

Real-world problems are complex as they are multidimensional and multimodal in nature that encourages computer scientists to develop better and efficient problem-solving methods. Nature-inspired metaheuristics have shown better performances than that of traditional approaches. Till date, researchers have presented and experimented with various nature-inspired metaheuristic algorithms to handle various search problems. This paper introduces a new nature-inspired algorithm, namely butterfly optimization algorithm (BOA) that mimics food search and mating behavior of butterflies, to solve global optimization problems. The framework is mainly based on the foraging strategy of butterflies, which utilize their sense of smell to determine the location of nectar or mating partner. In this paper, the proposed algorithm is tested and validated on a set of 30 benchmark test functions and its performance is compared with other metaheuristic algorithms. BOA is also employed to solve three classical engineering problems (spring design, welded beam design, and gear train design). Results indicate that the proposed BOA is more efficient than other metaheuristic algorithms.

Nature-inspired metaheuristics comprise a compelling family of optimization techniques. These algorithms are designed with the idea of emulating some kind natural phenomena (such as the theory of evolution, the collective behavior of groups of animals, the laws of physics or the behavior and lifestyle of human beings) and applying them to solve complex problems. Nature-inspired methods have taken the area of mathematical optimization by storm. Only in the last few years, literature related to the development of this kind of techniques and their applications has experienced an unprecedented increase, with hundreds of new papers being published every single year. In this paper, we analyze some of the most popular nature-inspired optimization methods currently reported on the literature, while also discussing their applications for solving real-world problems and their impact on the current literature. Furthermore, we open discussion on several research gaps and areas of opportunity that are yet to be explored within this promising area of science.