Solving Complex Optimization Problems Research Articles

Training mode of university dance performers based on sequential quadratic programming algorithm

Dance performance is an art form, which needs to cultivate students’ dance skills, artistic accomplishment and stage performance ability. Sequential quadratic programming algorithm is an optimization algorithm that can be used to solve complex optimization problems. In this paper, Sequential Quadratic Programming (SQP) is applied to explore the training mode of dance performers in colleges to help dance performers develop the optimal training plan and program. Aiming at the problems existing in the training mode of dance performance talents in colleges, this paper put forward an optimization method based on SQP algorithm, and implemented its optimization scheme in actual colleges. In the planning of dance performance talent training mode, particle swarm optimization (PSO) is used to optimize SQP algorithm, so that it can have higher planning efficiency. This paper studied the goal and index system of the training of dance performance talents in colleges, generated a personalized training program, and further improved the scientific and practical effectiveness of the training mode. This paper investigated the current situation of dance performance talent training in several dance schools in a certain province of China. The survey data include practical curriculum planning, teachers’ teaching philosophy and teaching content. Combined with SQP algorithm, the teaching and training program is optimized. After evaluation, it can be concluded that the SQP algorithm optimized by PSO shows good stability and accuracy. It can calculate the optimal solution of the cultivation scheme, and when calculating the optimal solution, the running time of the Central Processing Unit (CPU) was only 5.6 s, which can further improve the efficiency of the planning. Finally, through the satisfaction and resource utilization test, it can be found that the number of people who are very satisfied with the teaching content of the dance performance talent training program optimized by SQP increased from 38.4% to 52.4%. After optimization, the average utilization rate of teaching resources reached 88.1%. It can be concluded that SQP algorithm can provide scientific basis for dance education institutions to improve the training mode of dance talents. This can help dance education institutions better improve the training mode, and improve the overall quality and dance skills of dance students.

ANÁLISIS COMPARATIVO DE METAHEURÍSTICAS DE BASE BIOLÓGICA

This article reviews the metaheuristics published in the literature, emphasizing their usefulness in solving complex optimization problems. The review highlights inspiration's relevance in the metaheuristics design, being the main classification in multiple taxonomies existing in the literature. After reviewing the state of the art, six of the most relevant metaheuristics used to solve problems of various types (engineering, logistics, economics, data science, ...) were selected. This selection of metaheuristics will be subjected to an analysis of their performance using a set of problems selected from different authors. The problems selected for this analysis include problems with a single minimum or multiple minima, different sizes in terms of dimensions, and different types of mathematical functions such as polynomial, trigonometric, or exponential. The analysis offers a discussion of which scenarios are the best for each metaheuristic, analyzing aspects such as the ability of metaheuristics to explore and escape local minima. The article concludes by summarizing which metaheuristic is best for each type of problem. Keywords: Metaheuristics, benchmark, optimization problems, biological-based metaheuristics

A Modified Sine Cosine Algorithm for Numerical Optimization

Sine cosine algorithm (SCA) is a recently developed meta-heuristic method based on the characteristics of sine and cosine functions. However, SCA algorithm may suffer premature convergence in solving complex optimization problems. To mitigate this limitation, a modified SCA (MSCA) is developed to achieve an effective balance between exploration and exploitation. Specifically, the conversion parameter can be configured adaptively by using the individual fitness information in the evolution process to guide the individual search behavior. After that, an inertia weight is embedded in the position updating equation to further improve the search accuracy and accelerate the convergence speed. The performance of MSCA algorithm is investigated on 13 benchmark functions and the chaotic time series prediction problem. Experimental results demonstrate that MSCA algorithm is more effective than the other optimization methods.

An adaptive differential evolution algorithm with multi-strategy for solving complex optimization problem

In this paper, an adaptive differential evolution algorithm with multi-strategy, namely ESADE is proposed to solve the premature convergence and high time complexity for complex optimization problem. In the ESADE, the population is divided into several sub-populations after the fitness value of each individual is sorted. Then different mutation strategies are proposed for different populations to balance the global exploration and local optimization. Next, a new self-adaptive strategy is designed adjust parameters to avoid falling into local optimum while the convergence accuracy has reached its maximum value. And a complex airport gate allocation multi-objective optimization model with the maximum flight allocation rate, the maximum near gate allocation rate, and the maximum passenger rate at near gate is constructed, which is divided into several single-objective optimization model. Finally, the ESADE is applied solve airport gate allocation optimization model. The experiment results show that the proposed ESADE algorithm can effectively solve the complex airport gate allocation problem and achieve ideal airport gate allocation results by comparing with the current common heuristic optimization algorithms.

A GAN-based genetic algorithm for solving the 3D bin packing problem

The 3D bin packing problem is a challenging combinatorial optimization problem with numerous real-world applications. In this paper, we present a novel approach for solving this problem by integrating a generative adversarial network (GAN) with a genetic algorithm (GA). Our proposed GAN-based GA utilizes the GAN to generate high-quality solutions and improve the exploration and exploitation capabilities of the GA. We evaluate the performance of the proposed algorithm on a set of benchmark instances and compare it with two existing algorithms. The simulation studies demonstrate that our proposed algorithm outperforms both existing algorithms in terms of the number of used bins while achieving comparable computation times. Our proposed algorithm also performs well in terms of solution quality and runtime on instances of different sizes and shapes. We conduct sensitivity analysis and parameter tuning simulations to determine the optimal values for the key parameters of the proposed algorithm. Our results indicate that the proposed algorithm is robust and effective in solving the 3D bin packing problem. The proposed GAN-based GA algorithm and its modifications can be applied to other optimization problems. Our research contributes to the development of efficient and effective algorithms for solving complex optimization problems, particularly in the context of logistics and manufacturing. In summary, the proposed algorithm represents a promising solution to the challenging 3D bin packing problem and has the potential to advance the state-of-the-art in combinatorial optimization.

Evolutionary Multitasking for Costly Task Offloading in Mobile-Edge Computing Networks

The offloading of computation-intensive tasks to an edge server near resource-constrained mobile devices can provide improved application performance and user experience. However, with the rapid growth of mobile devices connected to the edge server, it is challenging to directly obtain an optimal task offloading scheme due to increasing computational cost and problem scale. In this study, we model the costly task offloading problem (CTOP) in mobile edge computing networks to achieve efficient joint optimization of energy consumption and processing latency for mobile devices. Inspired by the success of evolutionary multitasking in solving complex optimization problems by leveraging the experience of simple optimization problems, we develop a novel multitasking framework whose effectiveness is demonstrated in solving the CTOP. In this framework, auxiliary tasks are created to optimize the local processing overhead and the edge processing overhead of task offloading. On this basis, we propose an effective multitask evolutionary algorithm that includes segmented knowledge transfer and auxiliary task update. Specifically, source and extended decision variables are considered as different knowledge to be utilized, while the auxiliary tasks are allowed to be updated dynamically. Related knowledge that is learned from cheap and simple auxiliary tasks promotes the evolutionary search for CTOP. Experimental results verify the effectiveness of knowledge transfer. Compared to existing multitasking and single-tasking algorithms, the proposed algorithm shows competitive performance in CTOP instances and achieves better comprehensive performance in terms of energy consumption and processing latency.

A parallel chimp optimization algorithm based on tracking-learning and fuzzy opposition-learning behaviors for data classification

Chimp optimization algorithm (ChOA), which simulates the social behaviors of chimps, is a novel swarm intelligence algorithm for solving global optimization problems. ChOA has the advantages of fast convergence and avoiding falling into local optimum. However, the global search capability is weakened and the time overhead is too large when solving complex optimization problems. In order to improve the overall performance of ChOA, a parallel chimp optimization algorithm based on tracking-learning and fuzzy opposition-learning behaviors (PChOA) is proposed in this paper. First, a tracking-learning behavior is designed to improve the search accuracy. Second, a fuzzy opposition-learning behavior is adopted to enhance the global search capability. Third, a parallel computing architecture is developed to accelerate computational speed. Moreover, the convergence of our proposed PChOA has been analyzed theoretically. To validate the effectiveness of PChOA, it is applied to solve classification problem. The experimental results demonstrate that the classification performance of our proposed algorithm outperforms six other state of the art algorithms on most used datasets. Meanwhile, the time overhead of PChOA is significantly reduced in the environment of parallel computing. When the number of processors is increased to 16, PChOA costs less time than NBTree which is the fastest comparison algorithm in the experiment.

Intelligent Scheduling Technology of Swarm Intelligence Algorithm for Drone Path Planning

Different kinds of swarm intelligence algorithm obtain superior performances in solving complex optimization problems and have been widely used in path planning of drones. Due to their own characteristics, the optimization results may vary greatly in different dynamic environments. In this paper, a scheduling technology for swarm intelligence algorithms based on deep Q-learning is proposed to intelligently select algorithms to realize 3D path planning. It builds a unique path point database and two basic principles are proposed to guide model training. Path planning and network learning are separated by the proposed separation principle and the optimal selection principle ensures convergence of the model. Aiming at the problem of reward sparsity, the comprehensive cost of each path point in the whole track sequence is regarded as a dynamic reward. Through the investigation of dynamic environment conditions such as different distances and threats, the effectiveness of the proposed method is validated.

Design of Runge-Kutta optimization for fractional input nonlinear autoregressive exogenous system identification with key-term separation

Population-based metaheuristic algorithms have gained significant attention in research community due to its effectiveness in solving complex optimization problems in diverse fields. In this study, knacks of population-based Runge-Kutta optimizer (RUN) are exploited for the identification of fractional input non-linear exogenous auto-regressive (FINARX) system with key term separation. The fractional order calculus operator of the Grünwald-Letnikov derivative is exploited to develop FINARX from a conventional non-linear auto-regressive exogenous system. The identification scheme for FINARX model is implemented through a mean-square-error-based fitness function. RUN utilizes the slope variations calculated by the well-known Runge-Kutta method for an effective search mechanism in the exploration and exploitation phases. Moreover, an enhanced solution quality mechanism is employed for speedy convergence and keeping the movement toward the best solution by escaping the local optima. The robustness of the algorithm is analyzed by multiple variations of non-linearity as well as different noise scenarios. The performance of the RUN to identify the FINARX system is validated in terms of convergence rate, fitness value, robustness, and accuracy in weight estimation. The effectiveness of the RUN is further assessed through exhaustive simulations with their statistics as well as comparison with the standard recent counterparts, including the Whale optimization algorithm, Reptile Search algorithm, and Aquila optimizer on different performance indices for the FINARX system.

Global-best brain storm optimization algorithm based on chaotic difference step and opposition-based learning

Recently, the following global-best strategy and discussion mechanism have been prevailing to solve the slow convergence and the low optimization accuracy in the brain storm optimization (BSO) algorithm. However, the traditional BSO algorithm also suffers from the problem that it is easy to fall into local optimum. Therefore, this work innovatively designed the chaotic difference step strategy. This strategy introduced four commonly used chaotic maps and difference step to expand the population search space to improve the situation. Moreover, opposition-based learning thought was innovatively adopted into the BSO algorithm. The thought aims to generate the opposition-based population, increase the search density, and make the algorithm out of the local optimum as soon as possible. In summary, this work proposed a global-best brain storm optimization algorithm based on the chaotic difference step and opposition-based learning (COGBSO). According to the CEC2013 benchmark test suit, 15 typical benchmark functions were selected, and multiple sets of simulation experiments were conducted on MATLAB. The COGBSO algorithm was also compared to recent competitive algorithms based on the complete CEC2018 benchmark test suit. The results demonstrate that the COGBSO outperforms BSO and other improved algorithms in solving complex optimization problems.

Improving precision and robustness in level control of coupled tank systems: A tree seed optimization and [formula omitted]-analysis approach

Background:Efficient control of liquid levels in interconnected tank systems is a fundamental challenge in various industries, including chemical processes, wastewater treatment, and manufacturing. The traditional approach to achieving precise control has relied on Proportional-Integral-Derivative (PID) controllers, whose performance largely depends on tuned parameters. However, tuning PID controllers for complex and nonlinear systems like coupled tanks remains a challenging task. In recent years, nature-inspired optimization algorithms have gained prominence in control system design. The tree seed optimization (TSO), inspired by the dispersion of tree seeds in search of optimal growth conditions, has shown promise in solving complex optimization problems. This study seeks to explore the application of TSO in tuning PID controllers for coupled tank systems.Methodology:This research employs the TSO to optimize PID controller parameters for enhanced liquid-level control in coupled tank systems. The optimization process involves integrating performance metrics and closed-loop gain constraints to achieve optimal control of coupled tank systems. The imposed constraints aim to ensure robustness and system stability in the face of uncertainties and disturbances. Besides, μ analysis quantifies the robustness of the system by assessing its ability to tolerate uncertainties.Findings:Simulation studies conducted in this research verify the efficacy of the proposed TSO-based approach for tuning PID controllers in coupled tank systems. Compared with various methods, the TSO consistently yields better control performance, reduces settling time, and minimizes overshoot. The robustness of the optimized controllers is also evaluated, showing the ability to handle varying operating conditions effectively.

Quasi-dynamic opposite learning enhanced Runge-Kutta optimizer for solving complex optimization problems

Quasi-dynamic opposite learning enhanced Runge-Kutta optimizer for solving complex optimization problems

Disassembly line optimization with reinforcement learning

AbstractAs the environmental aspects become increasingly important, the disassembly problems have become the researcher’s focus. Multiple criteria do not enable finding a general optimization method for the topic, but some heuristics and classical formulations provide effective solutions. By highlighting that disassembly problems are not the straight inverses of assembly problems and the conditions are not standard, disassembly optimization solutions require human control and supervision. Considering that Reinforcement learning (RL) methods can successfully solve complex optimization problems, we developed an RL-based solution for a fully formalized disassembly problem. There were known successful implementations of RL-based optimizers. But we integrated a novel heuristic to target a dynamically pre-filtered action space for the RL agent (dlOptRL algorithm) and hence significantly raise the efficiency of the learning path. Our algorithm belongs to the Heuristically Accelerated Reinforcement Learning (HARL) method class. We demonstrated its applicability in two use cases, but our approach can also be easily adapted for other problem types. Our article gives a detailed overview of disassembly problems and their formulation, the general RL framework and especially Q-learning techniques, and a perfect example of extending RL learning with a built-in heuristic.

Balancing exploration and exploitation: Unleashing the adaptive power of automatic cuckoo search for meta-heuristic optimization

Meta-heuristic optimization algorithms are versatile and efficient techniques for solving complex optimization problems. When applied to clustering algorithms, these algorithms offer numerous advantages over traditional optimization methods, including global search capabilities, iterative refinement processes, robustness to initial conditions, and flexibility in handling diverse clustering objectives and constraints. Employing meta-heuristic optimization in clustering algorithms leads to improved accuracy, scalability, robustness, and flexibility in finding optimal or near-optimal clustering solutions. These algorithms generate new individuals iteratively using nature-inspired operations to obtain high-quality results. However, they often suffer from slower convergence and lack guarantees of finding the best solution for every problem, posing ongoing challenges in algorithm development. This study focuses on addressing the issue of premature convergence in metaheuristic algorithms by introducing an automatic cuckoo search (AuCS) algorithm. The AuCS algorithm aims to strike a balance between exploration and exploitation by dynamically updating the step size in each generation, thereby avoiding premature convergence. To evaluate the effectiveness of the proposed algorithm, experiments were conducted on 13 standard benchmark functions and 14 CEC 2005 benchmark functions. In overall performance, AuCS has the best optimum value in 72.22% of cases. This demonstrates the efficacy of the proposed algorithm in achieving improved clustering accuracy and minimizing intra-cluster distance. The proposed AuCS algorithm was applied to data clustering and compared with four swarm optimization algorithms. Here, AuCS outperforms these well-known algorithms in 5 out of 7 datasets. The experimental evaluations in both benchmark functions and clustering problems confirm the promising results of the proposed algorithm, suggesting that AuCS could be considered as a potential improvement over the cuckoo search algorithm.

A Review of Genetic Algorithm: Operations and Applications

This article presents a review of the Genetic Algorithm (GA), a prominent optimization technique inspired by natural selection and genetics. In the context of rapidly evolving computational methodologies, GA have gained considerable attention for their efficacy in solving complex optimization problems across various domains. The background highlights the growing significance of optimization techniques in addressing real-world challenges. However, the inherent complexity and diversity of problems necessitate versatile approaches like GA. The problem statement underscores the need to explore the underlying operations and applications of GA to provide a nuanced understanding of their capabilities and limitations. The objectives of this review encompass delving into the fundamental genetic operators, such as selection, crossover, and mutation, while examining their role in maintaining diversity and converging toward optimal solutions. Methodology-wise, a systematic analysis of existing literature is undertaken to distil key insights and trends in GA applications. The main findings show the adaptability of GA in tackling problems spanning engineering, economics, bioinformatics, and beyond. By facilitating the discovery of optimal or near-optimal solutions within large solution spaces, GA proves its mettle in scenarios where traditional methods fall short. The conclusion underscores the enduring relevance of GA in the optimization landscape, emphasizing their potential to remain a pivotal tool for addressing intricate real-world challenges, provided their parameters are fine-tuned judiciously to balance exploration and exploitation.

The Pine Cone Optimization Algorithm (PCOA).

The present study introduces a novel nature-inspired optimizer called the Pine Cone Optimization algorithm (PCOA) for solving science and engineering problems. PCOA is designed based on the different mechanisms of pine tree reproduction, including pollination and pine cone dispersal by gravity and animals. It employs new and powerful operators to simulate the mentioned mechanisms. The performance of PCOA is analyzed using classic benchmark functions, CEC017 and CEC2019 as mathematical problems and CEC2006 and CEC2011 as engineering design problems. In terms of accuracy, the results show the superiority of PCOA to well-known algorithms (PSO, DE, and WOA) and new algorithms (AVOA, RW_GWO, HHO, and GBO). The results of PCOA are competitive with state-of-the-art algorithms (LSHADE and EBOwithCMAR). In terms of convergence speed and time complexity, the results of PCOA are reasonable. According to the Friedman test, PCOA's rank is 1.68 and 9.42 percent better than EBOwithCMAR (second-best algorithm) and LSHADE (third-best algorithm), respectively. The authors recommend PCOA for science, engineering, and industrial societies for solving complex optimization problems.

Optimization of Nursing Scheduling in Emergency by Using Genetic Algorithm

Scheduling nurse duty is one of the problems in health organizations that is quite complicated to solve. Starting from the uncertain number of patients, serious patient illnesses, characteristics of organizational groups, requests for nurses to take time off, and the qualifications and specialization of the nurses themselves are why scheduling in the ER is difficult to optimize. The same thing is being experienced by one of the health institutions, RSUD Dr. Pirngadi. Preparing schedules or determining the number of nurses on duty is still done manually, resulting in a lack of optimization in scheduling and the number of nurses who must be on duty, especially in the emergency department. In solving this problem, an appropriate method is needed so that the process of scheduling and optimizing the number of nurses can be formed properly. This research applies the Genetic Algorithm in optimal emergency department (IGD) nurse duty scheduling. Genetic algorithms, also called search algorithms, are based on the mechanisms of natural selection and genetics. Genetic algorithms are one of the appropriate methods for solving complex optimization problems. This method is good enough to optimize shift scheduling for the Emergency Room Nursing Service in a Hospital. This Genetic Algorithm can be a solution to multi-criteria and multi-objective problems modeled using biological and evolutionary processes. So, the concept of this method can be applied in optimizing the Nursing Service schedule. The results of calculations using the Genetic Algorithm show quite significant comparisons, including several nurses losing their positions and being eliminated by mutation because they could not compete with several other strong individuals.

Multi-strategy synthetized equilibrium optimizer and application.

Improvement on the updating equation of an algorithm is among the most improving techniques. Due to the lack of search ability, high computational complexity and poor operability of equilibrium optimizer (EO) in solving complex optimization problems, an improved EO is proposed in this article, namely the multi-strategy on updating synthetized EO (MS-EO). Firstly, a simplified updating strategy is adopted in EO to improve operability and reduce computational complexity. Secondly, an information sharing strategy updates the concentrations in the early iterative stage using a dynamic tuning strategy in the simplified EO to form a simplified sharing EO (SS-EO) and enhance the exploration ability. Thirdly, a migration strategy and a golden section strategy are used for a golden particle updating to construct a Golden SS-EO (GS-EO) and improve the search ability. Finally, an elite learning strategy is implemented for the worst particle updating in the late stage to form MS-EO and strengthen the exploitation ability. The strategies are embedded into EO to balance between exploration and exploitation by giving full play to their respective advantages. Experimental results on the complex functions from CEC2013 and CEC2017 test sets demonstrate that MS-EO outperforms EO and quite a few state-of-the-art algorithms in search ability, running speed and operability. The experimental results of feature selection on several datasets show that MS-EO also provides more advantages.

An enhanced Equilibrium Optimizer for solving complex optimization problems

Equilibrium Optimizer (EO), despite its acceptable performance in several complex problems, suffers from low exploitation ability with unbalanced exploration, stagnation in local optima and poor convergence rate. To enhance the performance of the EO, the authors infused the intelligence of quasi-opposite numbers and chaotic-maps into the EO and proposed a Quasi-Oppositional Chaotic Equilibrium Optimizer (QOCEO) that consists of Quasi-Opposition based learning for improving the scalability, Chaotic Time Parameter for ensuring a proper balance between exploration and exploitation, and Chaotic Local Search for reducing the local stagnation. The performance of QOCEO and several contemporary metaheuristics have been evaluated on 96 benchmark functions (including classical benchmark, CEC-2017, CEC-2019, CEC-2020 and CEC-2022) and six constrained engineering optimization problems employing several statistical tests. The average rank Friedman test confirms that for all 96 benchmark functions, QOCEO outperforms CMA-ES, OBTLEO, m-EO, EO, LSHADE-SPACMA, SPS_L_SHADE_EIG, SHADE by 88%, 83%, 49%, 35%, 27%, 18% and 5%, respectively. Comparing the results of Bonferroni-Dunn and Holm’s tests, QOCEO outperforms PSO, GWO, EO, HGSO, SSA, and GSA for classical benchmark functions with 30, 100, 300, and 500 dimensions. Further, QOCEO outperform CMA-ES, OBTLEO, m-EO, EO, LSHADE-SPACMA for all 96 benchmark functions and statistically similar to SPS_L_SHADE_EIG, SHADE and EBOwithCMAR.

AN INNOVATIVE APPROACH TO CALCULATE THE CRITICAL DEPTH IN A TRIANGULAR SHAPED-CHANNEL

This paper focuses on a procedure for the dimensioning of the triangular-shaped channel at critical flow, which is important in the practice of the hydraulic engineer. The proposed approach, which explores the potential offered by heuristic methods for solving complex optimization problems, is based on the use of an analytical method that is presented and applied for the calculation of the critical depth y<sub>c</sub>, which is governed by a cubic equation with no second-order term. The resolution of this equation is essentially based on Cardan's theorem. This method takes into account, in particular, the effect of the absolute roughness ε, the effect of the kinematic viscosity ν through the Reynolds number Re, and the effect of the channel bed slope S through the friction factor f. These parameters are easily measurable in practice. In this research, we relied mainly on the application of two universally accepted relations of Darcy-Weisbach and the Colebrook formula in a state of critical flow. Explicit relations are deduced that govern the critical depth, y<sub>c</sub>, by a particular examination of two cases; one is a turbulent flow over a smooth surface and the other is a flow over a rough surface.