Metaheuristic Algorithms

Nowadays the main usage of the word "heuristic" is mostly the adjective in the sense of "guiding discovery" or "improving problem solving." The greek mathematicians  used two ways to find a solution: They began by assuming the problem solved and worked from there or they started from the admitted body of mathematical knowledge and worked towards the desired result (analysis or synthesis).

There is also a shorter literature extract of this paper in academia.edu.

Genetic algorithm (GA) and differential evolution (DE) are metaheuristic algorithms that have shown a favorable performance in the optimization of complex problems. In recent years, only GA has been widely used for single-objective optimal design of reinforced concrete (RC) structures; however, it has been applied for multiobjective optimization of steel structures. In this article, the total structural cost and the roof displacement are considered as objective functions for the optimal design of the RC frames. Using the weighted sum method (WSM) approach, the two-objective optimization problem is converted to a single-objective optimization problem. The size of the beams and columns are considered as design variables, and the design requirements of the ACI-318 are employed as constraints. Five numerical models are studied to test the efficiency of the GA and DE algorithms. Pareto front curves are obtained for the building models using both algorithms. The detailed results show the accuracy and convergence speed of the algorithms.

Swarm based optimization algorithms are a collection of intelligent techniques in the field of Artificial Intelligence (AI) were developed for simulating the intelligent behavior of animals. Over the years ago, problems complexity increased in a means that it is very difficult for basic mathematical approaches to obtain an optimum solution in an optimal time, this leads the researchers to develop various algorithms base on the natural behaviors of living beings for solving problems. This paper present a review for Cat Swarm Optimization (CSO), which is a powerful metaheuristic swarmbased optimization algorithm inspired by behaviors of cats in the Nature for solving optimization problems. Since its first appearances in 2006, CSO has been improved and applied in different fields by many researchers. In this review, we majorly focus on the original CSO algorithm and some improved branches of CSO family algorithms. Some examples of utilizing CSO to solve problems in engineering are also reviewed.

En este artículo se sistematiza el estado de arte en metaheurísticas inspiradas en la naturaleza y la cultura (primordialmente algoritmo genético y programación evolutiva) aplicadas a la síntesis e inducción gramatical de creaciones artísticas en diversos dominios.

MOFPA--Multi-objective flower pollination algorithm. This demo solves a bi-objective ZDT function of D=30 (dimensions), which can be extended to solve other multi-objective optimization problems. It is relatively straightforward to extend this code to solve other multi-objective functions and optimization problems. You can change the objective functions, dimensionality, various parameters, and simple lower and upper bounds (Lb, Ub).

X.-S. Yang, M. Karamanoglu, X.-S. He, Flower pollination algorithm: A novel approach for multiobjective optimization, Engineering Optimization, vol. 46, no. 9, 1222-1237 (2014).

[Notes: Though this demo should work well using either Matlab (preferred) or Octave (free), Matlab can run more smoothly, whereas Octave can be slower. In addition, for the multi-objective codes, Octave can be very slow for the test problem with 30 dimensions given in the demo codes, so please modify the relevant part of the codes to display results more frequently to show the progress. At the moment, the results are displayed every 100 iterations.]

El problema de enrutamiento de vehículos con recogida y entrega simultánea (VRPSPD por sus siglas en inglés) pertenece a la familia de problemas de enrutamiento de vehículos con restricciones de capacidad en la flota. Dado un conjunto de clientes, con demandas conocidas de recogida y entrega de mercancía, el objetivo del VRPSPD es diseñar un sistema de rutas que permita satisfacer la demanda de todos los clientes al menor costo posible, garantizando que cada cliente sea atendido por unúnico vehículo en uná unica visita y que en todo punto de viaje la mercancía transportada no exceda la capacidad del vehículo. En este trabajo se presenta un estudio del problema, en el que si incluyen además otros elementos como la presencia de una flota heterogénea, restricciones de circulación y horarios de atención en los clientes, con el objetivo de acercar más la modelación y tratamiento teórico del problema a las condiciones de la vida real. También se discuten algunos modelos de programación matemática para el VRPSPD y sus extensiones; se analizan las condiciones de factibilidad y se proponen algunas ideas para su solución.

Cloud computing is one of the emerging fields in computer science due to its several advancements like on-demand processing, resource sharing, and pay per use. There are several cloud computing issues like security, quality of service (QoS) management, data center energy consumption, and scaling. Scheduling is one of the several challenging problems in cloud computing, where several tasks need to be assigned to resources to optimize the quality of service parameters. Scheduling is a well-known NP-hard problem in cloud computing. This will require a suitable scheduling algorithm. Several heuristics and meta-heuristics algorithms were proposed for scheduling the user's task to the resources available in cloud computing in an optimal way. Hybrid scheduling algorithms have become popular in cloud computing. In this paper, we reviewed the hybrid algorithms, which are the combinations of two or more algorithms, used for scheduling in cloud computing. The basic idea behind the hybridization of the algorithm is to take useful features of the used algorithms. This article also classifies the hybrid algorithms and analyzes their objectives, QoS parameters, and future directions for hybrid scheduling algorithms.

The construction industry, from harvesting raw materials, transport, manufacturing, to the actual construction of buildings, has a significant and negative impact on the environment. The construction of buildings not only produces more waste, but also requires more transport and electricity (emissions), and often results in landscape damage, ecological disruption, habitat destruction, and/or deforestation. Utilizing cold-formed steel frame systems in construction supplies sustainability since this kind of framing are made out of thin-walled sections. Nowadays, there are a variety of metaheuristics developed for minimum weight design of cold-formed steel frames.In this study, the biogeography-based optimization (BBO) algorithm is used to select the cold-formed thin-walled C-sections listed in AISI-LRFD (American Iron and Steel Institution-Load and Resistance Factor Design) in such a way that the design constraints specified by the code are satisfied and the weight of the cold-formed steel frame is the minimum. It is shown that BBO algorithm out performs other metaheuristic technique in the design example considered.

This paper presents a new optimization algorithm called fuzzy adaptive teaching–learning-based optimization (FATLBO) for solving numerical structural problems. This new algorithm introduces three new mechanisms for increasing the searching capability of teaching–learning-based optimization namely status monitor, fuzzy adaptive teaching–learning strategies, and remedial operator. The performance of FATLBO is compared with well-known optimization methods on 26 unconstrained
mathematical problems and five structural engineering design problems. Based on the obtained results, it can be concluded that FATLBO is able to deliver excellence and competitive performance in solving various structural optimization problems.

Scheduling is one of the problems which so many researches have been conducted on it over the years.
The university course timetabling problem which is an NP-hard problem is a type of scheduling problem.
Timetabling process must be done for each semester frequently, which is an exhausting and time consuming task. The allocation of whole of events in timeslots and rooms performs by the university course
timetabling process considering the list of hard and soft constraints presented in one semester, so that no
conflict is created in such allocations. In the university course timetabling problem (UCTTP), the hard
constraints should not be violated under any conditions; soft constraints also should not be violated as
much as possible. The aim of the present paper is to analyze available approaches in the study of university course timetabling problems, including operational researches, metaheuristic methods and intelligent novel methods; also the distributed multi agent systems based approach (Cooperative Search
method) is investigated due to its scalability which enables the timetabling of common events between
departments. In addition, in this work a complete introduction of reliable datasets has been given to test
and evaluation of the structure of considered algorithms.

In the past couple of years, there has been a rapid development of artificial intelligence, specially one of the most popular their branches which is machine learning. The exponential growth of data in the world made a need that algorithms replace humans in analysis and desicion making problems based on that huge amount of data. To all that contributed development of computer performance by which it is now possible in a reasonable time, to get results from some time complex algorithms that use big data and based on that data, they make decisions.

Today, the machine learning algorithms are widely used in many areas and some tasks they perform are for example spam messages classification, product recommendations, machine translation, generation of fake images and videos (deepfakes), object or person recognition, navigation of autonomous machines, discovery of new drugs, reading thoughts using brain signals, etc. In addition to these areas, machine learning algorithms are used widely in the financial sector starting from an calculating of a person’s creditworthiness, detecting fraudulent transactions and other anomalies, analyzing huge amounts of data and making some business decisions based on
them, predicting the movement of stock prices and their trading, which is the main topic of this master thesis.

The main idea of this thesis is to present some machine learning algorithms that can be used for stock movement prediction and the decision making for trading them. The focus will be placed more on the description of the algorithms themselves and analysis of results, and less on the financial concepts and theory related to the finance.
This work can be useful for anyone who is interested in machine learning, especially those who work with time series, because stock prices are shown in the form of time series, and one of the ideas of the work is to present a wide range of classical machine learning algorithms, primarily intended for classification, starting from logistic regression, decision tree, random forest, support vector machine, boosting algorithms, neural networks and reinforcement learning. In
addition, the paper will describe some optimization techniques, including the genetic algorithm as well as some other metaheuristics.

Keywords: Machine learning, Financial time series, Classification, Reinforcement learning, Neural networks, Metaheuristics

Optimisation has attracted the attention of human since ancient times, during which the activities were inconsiderable and resources were unlimited. Extension of activities and their cost, time and resources limitations have caused researchers pay their attention to optimising the activities. Optimum alternative should be feasible, economical, functional and effective as possible. "Structural optimisation" is the technical term for the application of optimisation on structures. The last decades has seen a rapid development in optimisation techniques to solve related problems in structural design. However, recent surveys have shown insufficient penetration of optimisation methods in concrete structures. Due to the complexities of the design and construction of structures, optimisation techniques faced serious obstacles until the modern (meta-heuristic) methods of optimisation were developed. Applying such methods became quite widespread in various problems, including those of concrete structures, the optimisation of which were highly problematic and sometimes impossible before the introduction of these methods. The goal of concrete structure optimisation is often the minimization of the costs including the costs of concrete material, reinforcing bars, formwork, and pre-stressed cables. In a limited number of cases, the geometry and shape of structures were optimised. In this paper, an updated and extensive literature review is presented and due to the wide variety of meta-heuristic algorithms, appropriate concrete structure optimisation algorithms for practical practitioner are addressed. This research illustrated shortage of the concrete structure optimisation cases, researches and required direction of future studies in this regards. Researchers have been seeking the best responses to human problems for ages and optimization has been utilized as a set of principles and approaches to find the most appropriate answer in this regard. Approaches applied in optimization of complex problem have been developed through knowledge improvements. Meta-heuristics algorithms (MAs) are the latest category of approaches used by researchers to optimize complex and non-linear polynomial (NP-Hard) problems. These approaches are not able to provide global optimum, but they provide an acceptable solution for problems at a reasonable cost in a short time. Main difference of various meta-heuristic methods is their ability to solve certain types of problems and achieve closer answer to the global optimum at a lower cost in a shorter time (Cercevic,2014). Today, application domain of optimization techniques has been spread due to the development of knowledge and computer numerical analysis techniques; so that optimization objectives have changed from one target to multiple targets and subjects of problems have got closer to the reality. In primary problems, the main purpose of optimization solving problem was finding the minimum weight, while structural optimization is not only aimed at the weight and factors such as construction cost, time and quality, different construction methods, etc. could also be considered as objects. The development and many introduced techniques have caused a difficulty in selecting appropriate MAs to optimize a problem. Lots of existing methods (Figure 1), the diversity of their names (Table 1) and the provision of new algorithms have made the user confuse while solving a optimization problem; so that selection of appropriate algorithm for a

A novel population-based algorithm based on the mine bomb explosion concept, called the mine blast algorithm (MBA), is applied to the constrained optimization and engineering design problems. A comprehensive comparative study has been carried out to show the performance of the MBA over other recognized optimizers in terms of computational effort (measured as the number of function evaluations) and function value (accuracy). Sixteen constrained benchmark and engineering design problems have been solved and the obtained results were compared with other well-known optimizers. The obtained results demonstrate that, the proposed MBA requires less number of function evaluations and in most cases gives better results compared to other considered algorithms.

Several conventional and artificial algorithms have been used to find the location of distributed generation DG in power systems. Particle swarm optimization PSO is one of the
most used, but some convergence problems have been reported in literature. In this paper, the use of the metaheuristic Bat-inspired algorithm BA is proposed to place different number and capacities of DG for meshed and radial distribution networks. The aim of this work was to solve an optimization problem defined as minimization of power losses installing generators at load busses. A binary combination is included to represent the states and locations of generators. The search for the minimum value is achieved using the movement of bats at iterations, considering location and size. IEEE 14-bus, IEEE 30-bus and IEEE 33-node systems were used to test the metaheuristic techniques using five cases of power increasing considering from 1 to 5 generators. Results showed that bat algorithm is a good method to locate and find size of DG and maintain convergence to improve power losses. Voltage level and power losses were improved for all cases maintaining consistent results.

In this paper, we propose a new metaheuristic algorithm based on Lévy flight called Lévy flight distribution (LFD) for solving real optimization problems. The LFD algorithm is inspired from the Lévy flight random walk for exploring unknown large search spaces (e.g., wireless sensor networks (WSNs). To assess the performance of the LFD algorithm, various optimization test bed problems are considered, namely the congress on evolutionary computation (CEC) 2017 suite and three engineering optimization problems: tension/compression spring, the
welded beam, and pressure vessel. The statistical simulation results revealed that the LFD algorithm provides better results with superior performance in most tests compared to several well-known metaheuristic algorithms such as simulated annealing (SA), differential evolution (DE), particle swarm optimization (PSO), elephant
herding optimization (EHO), the genetic algorithm (GA), moth-flame optimization algorithm (MFO), whale optimization algorithm (WOA), grasshopper optimization algorithm (GOA), and Harris Hawks Optimization (HHO) algorithm. Furthermore, the performance of the LFD algorithm is tested on other different optimization problems of unknown large search spaces such as the area coverage problem in WSNs. The LFD algorithm shows high performance in providing a good deployment schema than energy-efficient connected dominating set (EECDS), A3, and CDS-Rule 𝐾 topology construction algorithms for solving the area coverage problem in WSNs. Eventually, the LFD algorithm performs successfully achieving a high coverage rate up to 43.16 %, while the A3, EECDS, and CDS-Rule 𝐾 algorithms achieve low coverage rates up to 40% based on network sizes used in the simulation experiments. Also, the LFD algorithm succeeded in providing a better deployment
schema than A3, EECDS, and CDS-Rule 𝐾 algorithms and enhancing the detection capability of WSNs by minimizing the overlap between sensor nodes and maximizing the coverage rate. The source code is currently
available for public from: https://www.mathworks.com/matlabcentral/fileexchange/76103-lfd.

Computer graphics and animation have has become a key technology in determining future research and development activities in many academic and industrial branches. The aim of this journal is to be an international peer-reviewed open access forum for scientific and technical presentations and discus the latest advances in Computer graphics and animation.

Handbook of Research on Metaheuristics for Order Picking Optimization in Warehouses to Smart Cities is a novel, innovative and adequate source of information that compiles interdisciplinary perspectives about diverse issues related with Order Picking Optimization in Warehouses on different ways about Intelligent Optimization, Industrial Applications on real-world, Social applications and Technology applications each one with a different perspective about the correct solution of this kind of methodologies.

This book is a collective effort to introduce new ideas and paradigms from a variety of perspectives using innovative techniques related with Bioinspired Algorithms, metaheuristics and methodologies associated with Artificial Intelligence. An innovative Handbook specialized on optimization considers different aspects to realize this “Intelligent Optimization” tries to improve with innovative techniques and methodologies different daily aspects of our lives, in each one of them is possible to understand the
necessity of improve scenarios, distances, time, costs, spaces and a plethora of features associated with the modern life (labor associated with organize, kept, and delivery of goods, materials or products). We received manuscripts from renowned researchers from all around the world associated with Theoretical foundations of Order Picking Optimization algorithms to understand many paradigms on different Optimization implementation kind. In addition, we receive many manuscripts with expertise on improving optimization related with Order Picking Optimization of deliveries associated with products and services, Optimization of different elements in the time and location, Social Applications to enjoy our life of a better way to improve the life in a Smart City, and finally, Technologies Applications of diverse ways to increase our Life Quality. The book starts with a section entitled “Mathematical Operation of the Order Picking Problem,” featuring six chapters on the theoretical and mathematical ideas
related with the correct implementation of diverse range of Order Picking optimization algorithms and Logistics applications on real world. The next section is named “Innovative Aspects of Applied Metaheuristics for the Resolution of Order Picking,” featuring five chapters related with different comparatives of metaheuristics used in order picking optimization algorithms and intelligent logistics in the search to improve resources in diverse aspects of our transportations or improve process to this. The third section is named “Avant-Garde Applications in the Use of Order Picking Models to Improve Competitiveness in the Supply Chain Sector of Companies in the Manufacturing Industry,” featuring six chapters related with different comparatives of order picking optimization algorithms and intelligent logistics models in the search to improve resources in diverse aspects of companies and to improve our lives. And finally, the section entitled “Innovation in the Context of Industry 4.0 and Applications Beyond the Technology Associated With Smart Manufacturing” grouped nine different papers related with solutions derived of
specific aspects try to improve daily activities on optimization with real applications to social topics.

An accessible introduction to metaheuristics and optimization, featuring powerful and modern algorithms for application across engineering and the sciences

From engineering and computer science to economics and management science, optimization is a core component for problem solving. Highlighting the latest developments that have evolved in recent years, Engineering Optimization: An Introduction with Metaheuristic Applications outlines popular metaheuristic algorithms and equips readers with the skills needed to apply these techniques to their own optimization problems. With insightful examples from various fields of study, the author highlights key concepts and techniques for the successful application of commonly-used metaheuristc algorithms, including simulated annealing, particle swarm optimization, harmony search, and genetic algorithms.

Esta planilla de Excel posee referencias a piezas de software mayormente gratuitas disponibles en la Web. Se ha seleccionado exclusivamente el software que se ciñe a las algorítmicas de la complejidad organizada. Comprende generadores de fractales, sistemas de análisis de dimensión fractal, sistemas de Lindenmayer, sistemas de funciones iteradas, sistemas de modelación de simetrías de frisos y superficies, sistemas de análisis de redes complejas, modelos de análisis de series temporales no lineales, simulación de procesos no lineales, etcétera.

Se indica en cada caso el fabricante, programador y el URL desde donde puede bajarse y se asigna a cada programa un puntaje más bien subjetivo que califica su utilidad científica.

Los datos están actualizados a noviembre de 2021. Requiere Microsoft Excel o Excel Viewer. Es a la fecha el repositorio más amplio existente de software de complejidad.

The difficulty and complexity of the real-world numerical optimization problems has grown manifold, which demands efficient optimization methods. To date, various metaheuristic approaches have been introduced, but only a few have earned recognition in research community. In this paper, a new metaheuristic algorithm called Archimedes optimization algorithm (AOA) is introduced to solve the optimization problems. AOA is devised with inspirations from an interesting law of physics Archimedes’ Principle. It imitates the principle of buoyant force exerted upward on an object, partially or fully immersed in fluid, is proportional to weight of the displaced fluid. To evaluate performance, the proposed AOA algorithm is tested on CEC’17 test suite and four engineering design problems. The solutions obtained with AOA have outperformed well-known state-of-the-art and recently introduced metaheuristic algorithms such genetic algorithms (GA), particle swarm optimization (PSO), differential evolution variants L-SHADE and LSHADE-EpSin, whale optimization algorithm (WOA), sine-cosine algorithm (SCA), Harris’ hawk optimization (HHO), and equilibrium optimizer (EO). The experimental results suggest that AOA is a high-performance optimization tool with respect to convergence speed and exploration-exploitation balance, as it is effectively applicable for solving complex problems. The source code is currently available for public from: https://www.mathworks.com/matlabcentral/fileexchange/79822-archimedes-optimization-algorithm

The complexity of real-world problems motivated researchers to innovate efficient problem-solving techniques. Generally natural Inspired, Bio Inspired, Metaheuristics based on evolutionary computation and swarm intelligence algorithms have been frequently used for solving complex, real-world optimization and Nondeterministic polynomial hard (NP-Hard) problems because of their ability to adjust to a variety of conditions. This paper describes Grey Wolf Optimizer (GWO) as a Swarm Based metaheuristic algorithm inspired by the leadership hierarchy and hunting behavior of the grey wolves for solving complex and real-world optimization problems. Since the appearance of GWO many modifications for improving the performance of the algorithm and have been applied to various applications in several fields. At the end of this paper, the improvements are listed.

The assignment of products to storage locations has a major impact on the performance of a warehouse, especially if the warehouse is not automated, but serviced by human pickers. Although the static storage location assignment problem has been studied for more than fifty years, the interrelations with up- and downstream processes and the effects of dynamic fluctuations in demand are still not well under- stood. In this thesis, we model and optimise dynamic and integrated storage assignment problems based on real-world data from the auto- motive and steel industry. Order picking is the main bottleneck in both scenarios, therefore the quality of a warehouse assignment is evaluated via picker travel distance required to supply products to downstream processes.
Affinity based slotting strategies place products that are frequently ordered together closer to each other. Part i of this thesis focuses on the formalisation of the novel Pick Frequency / Part Affinity score, which combines popularity and affinity measures. The new score is coupled with various metaheuristics and compared to standard assignment strategies in two empirical case studies.
The downside of the algorithms studied in the first part of this work is that implementing the generated assignments in a fully operational warehouse requires extensive movements of products. Part ii therefore focuses on the development of a generic multi-period model of the storage location assignment problem. By considering storage, re-location, and picking efforts, the costs and benefits of extensive re- locations versus iteratively moving a small number of products per period are analysed. Greedily selecting re-locations has a couple of disadvantages, which were mitigated by switching to a "robust" selection strategy.
In Part iii, we model an integrated warehouse assignment, order scheduling, and in-house transport problem and solve it sequentially via metaheuristics and simulation. Trade-offs between space requirements, picker performance, and overall performance are analysed. Finally, we model a slab yard assignment problem, which is unexpectedly difficult to solve to optimality. Fitness Landscape Analysis reveals a high level of neutrality in the search space, i.e. there are many re-locations that do not affect the solution quality. By incorporating strategies that explore neutral plateaus into the metaheuristics, we were able to find the global optimum for the benchmark.

Because of successful implementations and high intensity, metaheuristic research has been extensively reported in literature, which covers algorithms, applications, comparisons, and analysis. Though, little has been evidenced on insightful analysis of metaheuristic performance issues, and it is still a "black box" that why certain metaheuristics perform better on specific optimization problems and not as good on others. The performance related analyses performed on algorithms are mostly quantitative via performance validation metrics like mean error, standard deviation, and co-relations have been used. Moreover, the performance tests are often performed on specific benchmark functions - few studies are those which involve real data from scientific or engineering optimization problems. In order to draw a comprehensive picture of metaheuristic research, this paper performs a survey of metaheuristic research in literature which consists of 1222 publications from year 1983 to 2016 (thirty three years). Based on the collected evidence, this paper addresses four dimensions of metaheuristic research: introduction of new algorithms, modifications and hybrids, comparisons and analysis, and research gaps and future directions. The objective is to highlight potential open questions and critical issues raised in literature. The work provides guidance for future research to be conducted more meaningfully that can serve for the good of this area of research.

Whale optimization algorithm (WOA) is a recently developed swarm-based meta-heuristic algorithm that is based on the bubble-net hunting maneuver technique-of humpback whales-for solving the complex optimization problems. It has been widely accepted swarm intelligence technique in various engineering fields due to its simple structure, less required operator, fast convergence speed and better balancing capability between exploration and exploitation phases. Owing to its optimal performance and efficiency, the applications of the algorithm have extensively been utilized in multidisciplinary fields in the recent past. This paper investigates further into WOA of its applications, modifications, and hybridizations across various fields of engineering. The description of the strengths, weaknesses and opportunities to support future research are also explored. The Systematic Literature Review is opted as a method to disseminate the findings and gap from the existing literature. The authors select eighty-two (82) articles as a primary studies out of nine hundred and thirty-nine (939) articles between 2016 and 2020. As per our result, WOA-based techniques are applied in 5 fields and 17 subfields of various engineering domains. 61% work has been found on modification, 27% on hybridization and 12% on multi-objective variants of WOA techniques. The growing research trend on WOA is expected to continue into the future. The review presented in the paper has the potential to motivate expert researchers to propose more novel WOA-based algorithms, and it can serve as an initial reading material for a novice researcher.

This paper uses the concept of algorithmic efficiency to present a unified theory of intelligence. Intelligence is defined informally, formally, and computationally. We introduce the concept of dimensional complexity in algorithmic efficiency and deduce that an optimally efficient algorithm has zero time complexity, zero space complexity, and an infinite dimensional complexity. This algorithm is used to generate the number line.

Metaheuristic algorithms have been an interesting and widely used area for scientists, researchers and academicians because of their specific and significant characteristics and capabilities in solving optimization problems. Metaheuristic algorithms are developed base on inspiration of some real world phenomenon in nature or on the behavior of living being (animal, insects, organic living beings). On the past many metaheuristic algorithms have been introduced and applied on various problems of various domains including real world optimization problems. This paper is aimed to provide a historical Survey on metaheuristic algorithms, it will provide a list of metaheuristic based algorithms ordered according to the foundation year, with the name of Authors and the algorithm abbreviations.

This paper provides an in-depth review of the optimal design of type-1 and type-2 fuzzy inference systems (FIS) using five well known computational frameworks: genetic-fuzzy systems (GFS), neuro-fuzzy systems (NFS), hierarchical fuzzy systems (HFS), evolving fuzzy systems (EFS), and multiobjective fuzzy systems (MFS), which is in view that some of them are linked to each other. The heuristic design of GFS uses evolutionary algorithms for optimizing both Mamdani-type and Takagi-Sugano-Kang-type fuzzy systems; whereas, the NFS combines the FIS with neural network learning method to improve the approximation ability. HFS combines two or more low-dimensional fuzzy logic units in a hierarchical design to overcome the curse of dimensionality. EFS solves the data streaming issues by refining (evolving) the system incrementally, and MFS solves the multi-objective trade-offs like the simultaneous maximization of both interpretability and accuracy. The overall synthesis of these dimensions explores the FIS's potential challenges and opportunities ; the complex relations among the dimension; and the FIS's potential to combining one or more computational frameworks adding another dimension: deep fuzzy systems.

El problema de las n-Reinas (n-Queens Problem) es muy antiguo. Propuesto por primera vez en el año 1848, consiste en encontrar una asignación a n reinas en un tablero de ajedrez de n x n de modo tal, que éstas no se ataquen. El presente trabajo presenta el problema en cuestión, muestra un ejemplo sencillo
de él y profundiza en distintos métodos de resolución basados en técnicas incompletas de optimización.

Nature-inspired algorithms take inspiration from living things and imitate their behaviours to accomplish robust systems in engineering and computer science discipline. Symbiotic organisms search (SOS) algorithm is a recent metaheuristic algorithm inspired by symbiotic interaction between organisms in an ecosystem. Organisms develop symbiotic relationships such as mutualism, commensalism, and parasitism for their survival in ecosystem. SOS was introduced to solve continuous benchmark and engineering problems. The SOS has been shown to be robust and has faster convergence speed when compared with genetic algorithm, particle swarm optimization, differential evolution, and artificial bee colony which are the traditional metaheuristic algorithms. The interests of researchers in using SOS for handling optimization problems are increasing day by day, due to its successful application in solving optimization problems in science and engineering fields. Therefore, this paper presents a comprehensive survey of SOS advances and its applications, and this will be of benefit to the researchers engaged in the study of SOS algorithm.

This paper proposes the African Buffalo Optimization (ABO) which is a new meta-heuristic algorithm that is derived from careful observation of the African buffalos, a species of wild cows, in the African forests and savannahs. This animal displays uncommon intelligence, strategic organizational skills and exceptional navigational ingenuity in its traversal of the African landscape in search for food. The African Buffalo Optimization builds a mathematical model from the behavior of this animal and uses the model to solve 33 benchmark symmetric Traveling Salesman's Problem and six difficult asymmetric instances from the TSPLIB. This study shows that buffalos are able to ensure excellent exploration and exploitation of the search space through regular communication, cooperation and good memory of its previous personal exploits as well as tapping from the herd's collective exploits. The results obtained by using the ABO to solve these TSP cases were benchmarked against the results obtained by using other popular algorithms. The results obtained using the African Buffalo Optimization algorithm are very competitive.

In this research, monthly solar radiation is predicted in semi-dry, dry, and wet climates. Adaptive neurofuzzy interface system (ANFIS), radial basis function neural network (RBFNN), and multi-layer perceptron (MLP) models are used for predicting solar radiation (SR). Grasshopper algorithm (GOA) is utilized to improve the performance of ANFIS, RBFNN, and MLP models. Three stations in Iran, namely Rasht (humid climate), Yazd (semi-arid) and Tehran (slightly arid), are considered as the case studies. The accuracy of GOA is benchmarked against particle swarm optimization (PSO) and salp swarm algorithm (SSA). The results reveal that the best-input combination is relative humidity, wind speed, rainfall, and temperature at these three stations. A comprehensive study is performed to select the best-input combination. The main contribution of paper is to create new hybrid ANFIS models for predicting monthly solar radiation in different climates. Besides, effects of different parameters are comprehensively investigated on solar radiation. This study indicates that temperature is the most effective parameter for estimating SR in dry and semi-dry climate. It is found that rainfall plays a key role for estimating SR in a wet region. The main finding of this paper is that the determination of the most suitable input scenario for predicting SR is an important issue because different input scenarios in different climates provide different performances. Besides, the use of a robust optimization algorithm as a training method is a significant step of the modeling process of SR. Results indicate that mean absolute error (MAE) of ANFIS-GOA is 3.8% and 8.9% less in comparison with that of MLP-GOA and RBFNN-GOA, respectively during the training stage at Yazd station. Besides, MAE of ANFIS-GOA is 26% and 31% less than that of MLP-GOA and RBFNN-GOA, respectively during the training stage at Tehran station. Results indicate that NSE values of ANFIS-GOA, ANFIS-SSA, ANFIS-PSO, and ANFIS models are 0.94, 0.88, 0.84, and 0.79, respectively during the testing stage at Rasht station. It is found that ANFIS-GOA attains higher accuracy in predicting SR under different climates.