A Comprehensive Guide to Optimization Algorithms in Modern Computing

A BSTRACT: The learning process , which was made by the model observer lecturers , w as success in increasing the students learning process. Based on the result and the discussion of some research ers , it can be concluded that the learning process , in the basic subject of mathematics learning process through applying “ l esson s tudy” , can help in increasing the learning students ’ motivation. The learning model modification was done based on the students need. Meanwhile, the role of intrinsic and extrinsic motivation s are needed in the learning process. The intrinsic motivation is the encouragement coming from the students themselves , such as the desire and the willingness to be success, the encouragement and the learning need, and the dream of the future. The extrinsic motivation is the encourag e ment coming from the outside of the students themselves , which are shown by the existence of the reward, the interesting activity, the conducive learning environment in the learning process, so that the students are able to learn well. This research aimed at describing the students learning motivation in the subject of mathematics learning basic and process through applying the “ l esson s tudy”. The research consisted of 4 cycles, and every cycle consisted of 3 steps, they are “plan, do , and see ” . The subject of research was the Class D mathematics education study program students of UMP (Muhammadiyah University of Purwokerto) in academic year 2012. The data were got from the observation sheet, video recording , and questionnaire. The data analysis techniques were data reducing, data presenting, and concluding. The research showed that the students learning motivation was different in every cycle and the highest average motivation score was the fourth cycle. KEY WORDS : L earning motivation, lesson study , intrinsic and extrinsic motivation s, basic subject of mathematics , and students learning process . About the Authors: Anggun Badu Kusuma, M.Pd., Fitrianto Eko Subekti, M.Pd ., and Reni Untarti, M.Pd. are the Lecturers at the Department of Mathematics Education, Faculty of Education and Teacher Training UMP (Muhammadiyah University of Purwokerto) in Central Java, Indonesia. The authors can be reached at: anggun.badu@gmail.com , efitrians@ymail.com , and reniuntarti@gmail.com How to cite this article? Kusuma, Anggun Badu, Fitrianto Eko Subekti & Reni Untarti. (2015). “Description of the Students Learning Motivation in the Subject of Mathematics Learning Basic and Process Using the Lesson Study” in EDUCARE: International Journal for Educational Studies , Vol.7(2) February, pp.103-110. Bandung, Indonesia: Minda Masagi Press and UMP Purwokerto, ISSN 1979-7877. Chronicle of the article: Accepted (January 9, 2015); Revised (February 10, 2015); and Published (February 28, 2015).

The mathematical process is one part of mathematical literacy that students need to have in solving mathematical problems. Therefore, students who have good mathematical processing skills will find it easier to solve mathematical problems related to the real world. This article aims to determine students' mathematical literacy skills in solving story problems based on mathematical processes. The story problem in question is a math problem related to the real world. This research is a qualitative research with descriptive method. Data analysis techniques in this study consist of data collection, data reduction, display data, and verification. The subjects of this study were three students from the ninth grade in one of the junior high schools in Banyuwangi. Subjects were selected based on three considerations, namely academic ability, teacher recommendations, and students' willingness. The story questions given consist of two story questions about Quadrilateral material. The indicators of mathematical literacy ability used in this study include: (1) understanding the problem, (2) selecting knowledge, (3) outlining plans, (4) solving and reasoning, and (5) evaluating results in problem solving. The results showed that the mathematical literacy ability of the ninth graders in solving the story problems of the quadrilateral material had not met all the indicators of the mathematical literacy process. In addition, the results of the study also showed that students were not accustomed to writing down the information contained in the questions, and did not describe the completion plan clearly. From these results it is suggested that teachers train to involve the mathematical process in the learning process so that students are accustomed to solving problems related to the real world and can improve their mathematical literacy skills.

Battle Royale Optimizer (BRO) is a recently proposed optimization algorithm that has added a new category named game-based optimization algorithms to the existing categorization of optimization algorithms. Both continuous and binary versions of this algorithm have already been proposed. Generally, optimization problems can be divided into single-objective and multi-objective problems. Although BRO has successfully solved single-objective optimization problems, no multi-objective version has been proposed for it yet. This gap motivated us to design and implement the multi-objective version of BRO (MOBRO). Although there are some multi-objective optimization algorithms in the literature, according to the no-free-lunch theorem, no optimization algorithm can efficiently solve all optimization problems. We applied the proposed algorithm to four benchmark datasets: CEC 2009, CEC 2018, ZDT, and DTLZ. We measured the performance of MOBRO based on three aspects: convergence, spread, and distribution, using three performance criteria: inverted generational distance, maximum spread, and spacing. We also compared its obtained results with those of three state-of-the-art optimization algorithms: the multi-objective Gray Wolf optimization algorithm (MOGWO), the multi-objective particle swarm optimization algorithm (MOPSO), the multi-objective artificial vulture's optimization algorithm (MOAVAO), the optimization algorithm for multi-objective problems (MAOA), and the multi-objective non-dominated sorting genetic algorithm III (NSGA-III). The obtained results approve that MOBRO outperforms the existing optimization algorithms in most of the benchmark suites and operates competitively with them in the others.

After the teaching–learning-based optimization (TLBO) algorithm was proposed, many improved algorithms have been presented in recent years, which simulate the teaching–learning phenomenon of a classroom to effectively solve global optimization problems. In this paper, a cyclical non-linear inertia-weighted teaching–learning-based optimization (CNIWTLBO) algorithm is presented. This algorithm introduces a cyclical non-linear inertia weighted factor into the basic TLBO to control the memory rate of learners, and uses a non-linear mutation factor to control the learner’s mutation randomly during the learning process. In order to prove the significant performance of the proposed algorithm, it is tested on some classical benchmark functions and the comparison results are provided against the basic TLBO, some variants of TLBO and some other well-known optimization algorithms. The experimental results show that the proposed algorithm has better global search ability and higher search accuracy than the basic TLBO, some variants of TLBO and some other algorithms as well, and can escape from the local minimum easily, while keeping a faster convergence rate.

Several optimization problems from various types of applications have been efficiently resolved using available meta-heuristic algorithms such as Particle Swarm Optimization and Genetic Algorithm. Recently, many meta-heuristic optimization techniques have been extensively reported in the literature. Nevertheless, there is still room for new optimization techniques and strategies since, according to the literature, there is no meta-heuristic optimization algorithm that may be considered as the best choice to cope with all modern optimization problems. This paper introduces a novel meta-heuristic optimization algorithm named Dynamic Group-based Optimization Algorithm (DGCO). The proposed algorithm is inspired by the cooperative behavior adopted by swarm individuals to achieve their global goals. DGCO has been validated and tested against twenty-three mathematical optimization problems, and the results have been verified by a comparative study with respect to state-of-the-art optimization algorithms that are already available. The results have shown the high exploration capabilities of DGCO as well as its ability to avoid local optima. Moreover, the performance of DGCO has also been verified against five constrained engineering design problems. The results demonstrate the competitive performance and capabilities of DGCO with respect to well-known state-of-the-art meta-heuristic optimization algorithms. Finally, a sensitivity analysis is performed to study the effect of different parameters on the performance of the DGCO algorithm.

Single and multi-objectives based on an improved golden jackal optimization algorithm for simultaneous integration of multiple capacitors and multi-type DGs in distribution systems

Nowadays, structural health monitoring has attracted much attention, due to the construction of important and complex structures and their safety. One branch of structural health monitoring is damage detection, estimating the location and extent of eventual damages in the structural systems. In this study, an efficient method is introduced to determine the location and extent of damage in the frame, beam and truss structures using time domain response and an optimization algorithm. First of all, the structural damage detection problem is formulated as a standard optimization problem. So that, the optimization objective function is defined by using the acceleration of damaged structures and analytical model acceleration. The acceleration is obtained using Newmark method. Damage is simulated by reducing the elasticity modulus of structural members. Then, damage problem converted to an optimization problem are solved by teaching–learning-based optimization (TLBO) algorithm therefore, the exact location and extent of damage in structure can be determined. In order to show the capabilities of the proposed approach for identifying structural damage, four illustrative test examples are considered with considering measurement noise effect. The results clearly show that the proposed method is as a powerful method to detect multiple damage in structures.

Nature-inspired optimization techniques have been applied in various fields of study to solve optimization problems. Since designing a Fuzzy System (FS) can be considered one of the most complex optimization problems, many meta-heuristic optimizations have been developed to design FS structures. This paper aims to design a Takagi–Sugeno–Kang fuzzy Systems (TSK-FS) structure by generating the required fuzzy rules and selecting the most influential parameters for these rules. In this context, a new hybrid nature-inspired algorithm is proposed, namely Genetic–Grey Wolf Optimization (GGWO) algorithm, to optimize TSK-FSs. In GGWO, a hybridization of the genetic algorithm (GA) and the grey wolf optimizer (GWO) is applied to overcome the premature convergence and poor solution exploitation of the standard GWO. Using genetic crossover and mutation operators accelerates the exploration process and efficiently reaches the best solution (rule generation) within a reasonable time. The proposed GGWO is tested on several benchmark functions compared with other nature-inspired optimization algorithms. The result of simulations applied to the fuzzy control of nonlinear plants shows the superiority of GGWO in designing TSK-FSs with high accuracy compared with different optimization algorithms in terms of Root Mean Squared Error (RMSE) and computational time.

With the development of science and technology, many optimization problems in real life have developed into high-dimensional optimization problems. The meta-heuristic optimization algorithm is regarded as an effective method to solve high-dimensional optimization problems. However, considering that traditional meta-heuristic optimization algorithms generally have problems such as low solution accuracy and slow convergence speed when solving high-dimensional optimization problems, an adaptive dual-population collaborative chicken swarm optimization (ADPCCSO) algorithm is proposed in this paper, which provides a new idea for solving high-dimensional optimization problems. First, in order to balance the algorithm’s search abilities in terms of breadth and depth, the value of parameter G is given by an adaptive dynamic adjustment method. Second, in this paper, a foraging-behavior-improvement strategy is utilized to improve the algorithm’s solution accuracy and depth-optimization ability. Third, the artificial fish swarm algorithm (AFSA) is introduced to construct a dual-population collaborative optimization strategy based on chicken swarms and artificial fish swarms, so as to improve the algorithm’s ability to jump out of local extrema. The simulation experiments on the 17 benchmark functions preliminarily show that the ADPCCSO algorithm is superior to some swarm-intelligence algorithms such as the artificial fish swarm algorithm (AFSA), the artificial bee colony (ABC) algorithm, and the particle swarm optimization (PSO) algorithm in terms of solution accuracy and convergence performance. In addition, the APDCCSO algorithm is also utilized in the parameter estimation problem of the Richards model to further verify its performance.

Metaheuristic optimization algorithms continue to be essential for solving complex real-world problems, yet existing methods often struggle with balancing exploration and exploitation across diverse problem landscapes. This paper proposes a novel nature-inspired metaheuristic optimization algorithm named the Painted Wolf Optimization (PWO) algorithm. The main inspiration for the PWO algorithm is the group behavior and hunting strategy of painted wolves, also known as African wild dogs in the wild, particularly their unique consensus-based voting rally mechanism, a behavior fundamentally distinct from the social dynamics of grey wolves. In this innovative process, pack members explore different areas to find prey; then, they hold a pre-hunting voting rally based on the alpha member to determine who will begin the hunt and attack the prey. The efficiency of the proposed PWO algorithm is evaluated by a comparison study with other well-known optimization algorithms on 33 test functions, including the Congress on Evolutionary Computation (CEC) 2017 suite and different real-world engineering design cases. Furthermore, the algorithm’s performance is further tested across a spectrum of optimization problems with extensive unknown search spaces. This includes its application within the field of cybersecurity, specifically in the context of training a machine learning-based intrusion detection system (ML-IDS), achieving an accuracy of 0.90 and an F-measure of 0.9290. Statistical analyses using the Wilcoxon signed-rank test (all p<0.05) indicate that the PWO algorithm outperforms existing state-of-the-art algorithms, providing superior solutions in diverse and unpredictable optimization landscapes. This demonstrates its potential as a robust method for tackling complex optimization problems in various fields. The source code for the PWO algorithm is publicly available at https://github.com/saeidsheikhi/Painted-Wolf-Optimization.

A novel distributed optimal dispatch algorithm is proposed for coordinating the operation of multiple micro units in a microgrid, which has incorporated the distributed consensus algorithm in multi-agent systems and the λ-iteration optimization algorithm in the economic dispatch of power systems. Specifically, the proposed algorithm considers the global active power constraint by adding a virtual pinner and it can deal with the optimization problem with any initial states. That is, it can realize the global optimization and avoid the defect of the initial conditions' sensitivity in the optimization problem. On the other hand, the proposed optimization algorithm can either be used for off-line calculation or be utilized for online operation and has the ability to survive single-point failures and shows good robustness in the iteration process. Numerical studies in a seven-bus microgrid demonstrate the effectiveness of the proposed algorithm.

The increased speed and accuracy in solving optimization problems of gas allocation in the gas lift process are of high importance. Solving gas allocation optimization problems generally involves two steps: (1) The gas lift performance curve (GLPC) fitting (gas lift modeling) and (2) optimizing the allocation of gas between wells. Therefore, in order to increase the speed and accuracy of solving gas allocation optimization problems, both steps need to be improved. In order to increase the accuracy of the first step, a new correlation was proposed in which, in addition to increasing the accuracy of fit, the optimization speed was improved by decreasing the number of constants used in the correlation. Besides, in order to improve the performance of the second step, water cycle optimization algorithm was used and the results obtained from this algorithm were compared with the results obtained from previous studies on teaching–learning-based optimization (TLBO) algorithm, continuous ant colony (CACO) algorithm, genetic algorithm (GA) and particle swarm optimization algorithm (PSO) for solving the five-well Nishikiori index problem. The results suggested that the water cycle optimization algorithm has a very good performance in terms of convergence rate, non-capture at local optimum points and repeatability. Finally, as a new problem, the gas allocation between the wells of one of the heavy oil fields in the southwest of Iran was optimized with predetermined oil production rates. The goal of optimization was to obtain the minimum amount of gas required to produce the predetermined oil rates using the water cycle optimization algorithm. The results showed that optimization is of higher importance in lower oil production targets, resulting in higher additional oil production.

The paper reviews and introduces the state-of-the-art nature-inspired metaheuristic algorithms in optimization, including Firefly algorithm, PSO algorithms and ABC algorithm. By implementing these algorithms in Matlab, we will use worked examples to show how each algorithm works. Firefly algorithm is one of the evolutionary optimization algorithms, and is inspired by the flashing behaviour of fireflies in nature. There are many noisy non-linear mathematical optimization problems that can be effectively solved by Metaheuristic Algorithms. Mathematical optimization or programming is the study of such planning and design problems using mathematical tools. Nowadays, computer simulations become an indispensable tool for solving such optimization problems with various efficient search algorithms. Nature-inspired algorithms are among the most powerful algorithms for optimization. Firefly algorithm is one of the new metaheuristic algorithms for optimization problems. The algorithm is inspired by the flashing behaviour of fireflies. A Firefly Algorithm (FA) is a recent nature inspired optimization algorithm, which simulates the flash pattern and characteristics of fireflies. It is a powerful swarm intelligence algorithm inspired by the flash phenomenon of the fireflies. In this context, three types of meta-heuristics called Artificial bee Colony algorithm, Particle Swarm Optimization (PSO) and Firefly algorithms were devised to find optimal solutions of noisy non-linear continuous mathematical models. A series of computational experiments using each algorithm were conducted. The stimulation result of this experiment were analyzed and compared to the best solutions found so The Firefly algorithm in each noisy non linear optimization function seems to perform better and efficient.

Applying multi-objective ant colony optimization algorithm for solving the unequal area facility layout problems

This research proposed an integrated strategy for building performance optimization from the whole life cycle perspective to explore the optimal building scheme. After the feature elimination, the ensemble learning model (ELM) was trained to obtain a high-precision model for predicting life cycle carbon emissions (LCCE), life cycle costs (LCC), and indoor discomfort hours (IDH). Then, the optimal optimization algorithm was selected among three different optimization algorithms. Finally, the best building scheme was chosen according to the newly proposed solution. The results showed that the ELM could achieve high prediction efficiency by combining input feature evaluation and screening, multi-sampling methods, and hyperparameter optimization. The R2 value of ELM can reach 0.980, while the Two-Archive Evolutionary Algorithm for Constrained multi-objective optimization (C-TAEA) was the optimal optimization algorithm. The best equilibrium solution proposed in this study solved the problem of different optimization ranges of different objectives and maximized the optimization value. Finally, the best equilibrium scheme reduced the LCCE by 34.7%, the LCC by 13.9%, and the IDH by 26.6%. Therefore, this strategy can efficiently optimize building objectives and produce a more balanced and optimal building scheme, thus making it widely applicable in building performance optimization.