Standard Evolutionary Algorithms Research Articles

Machine learning and evolutionary optimization approach for solving the flexible job-shop scheduling problem

This paper proposes a method of using machine learning and an evolutionary algorithm to solve the flexible job shop problem (FJSP). Specifically, a back propagation (BP) neural network is used as the machine learning method, the most widely used genetic algorithm (GA) is employed as the optimized object to address the machine-selection sub-problem of the FJSP, and particle swarm optimization (PSO) is utilized to solve the operation-order sub-problem of the FJSP. At present, evolutionary algorithms such as the GA, PSO, ant colony algorithm, simulated annealing algorithm, and their optimization algorithms are widely used to solve the FJSP; however, none of them optimizes the initial solutions. Because each of these algorithms only focuses on solving a single FJSP, they can only use randomly generated initial solutions and cannot determine whether the initial solutions are good or bad. Based on these standard evolutionary algorithms and their optimized versions, the JSON object was introduced in this study to cluster and reconstruct FJSPs such that the machine learning strategies can be used to optimize the initial solutions. Specifically, the BP neural networks are trained so that the generalization of BP neural networks can be used to judge whether the initial solutions of the FJSPs are good or bad. This approach enables the bad solutions to be filtered out and the good solutions to be maintained as the initial solutions. Extensive experiments were performed to test the proposed algorithm. They demonstrated that it was feasible and effective. The contribution of this approach consists of reconstructing the mathematical model of the FJSP so that machine learning strategies can be introduced to optimize the algorithms for the FJSP. This approach seems to be a new direction for introducing more interesting machine learning methodologies to solve the FJSP.

Self-adjusting offspring population sizes outperform fixed parameters on the cliff function

In the discrete domain, self-adjusting parameters of evolutionary algorithms (EAs) have emerged as a fruitful research area with many runtime analyses showing that self-adjusting parameters can outperform the best fixed parameters. Most existing runtime analyses focus on elitist EAs on simple problems, for which moderate performance gains were shown. Here we consider a much more challenging scenario: the multimodal function Cliff, defined as an example where a (1,λ) EA is effective, and for which the best known upper runtime bound for standard EAs is O(n25).We prove that a (1,λ) EA self-adjusting the offspring population size λ using success-based rules optimises Cliff in O(n) expected generations and O(nlog⁡n) expected evaluations. Along the way, we prove tight upper and lower bounds on the runtime for fixed λ (up to a logarithmic factor) and identify the runtime for the best fixed λ as nη for η≈3.97677 (up to sub-polynomial factors). Hence, the self-adjusting (1,λ) EA outperforms the best fixed parameter by a factor of at least n2.9767.

Advances in teaching–learning-based optimization algorithm: A comprehensive survey(ICIC2022)

Teaching-learning-based optimization (TLBO) algorithm which imitates the teaching–learning process in a classroom, is one of population-based heuristic stochastic swarm intelligent algorithms. TLBO executes through similar iterative evolution processes as utilized by a standard evolutionary algorithm. Unlike traditional evolutionary algorithms and swarm intelligent algorithms, the iterative computation process of teaching–learning-based optimization is divided into two phases and each phase executes iterative learning operation. In this paper, we present a comprehensive survey on the recent advances in TLBO. A review of the current literature reveals intriguing challenges and suggests potential future research directions.

A Fast Multipoint Expected Improvement for Parallel Expensive Optimization

The multipoint expected improvement (EI) criterion is a well-defined parallel infill criterion for expensive optimization. However, the exact calculation of the classical multipoint EI involves evaluating a significant amount of multivariate normal cumulative distribution functions, which makes the inner optimization of this infill criterion very time consuming when the number of infill samples is large. To tackle this problem, we propose a novel fast multipoint EI criterion in this work. The proposed infill criterion is calculated using only univariate normal cumulative distributions; thus, it is easier to implement and cheaper to compute than the classical multipoint EI criterion. It is shown that the computational time of the proposed fast multipoint EI is several orders lower than the classical multipoint EI on the benchmark problems. In addition, we propose to use cooperative coevolutionary algorithms (CCEAs) to solve the inner optimization problem of the proposed fast multipoint EI by decomposing the optimization problem into multiple subproblems with each subproblem corresponding to one infill sample and solving these subproblems cooperatively. Numerical experiments show that using CCEAs can improve the performance of the proposed algorithm significantly compared with using standard evolutionary algorithms. This work provides a fast and efficient approach for parallel expensive optimization.

Combining Lipschitz and RBF surrogate models for high-dimensional computationally expensive problems

Standard evolutionary optimization algorithms assume that the evaluation of the objective and constraint functions is straightforward and computationally cheap. However, in many real-world optimization problems, these evaluations involve computationally expensive numerical simulations or physical experiments. Surrogate-assisted evolutionary algorithms (SAEAs) have recently gained increased attention for their performance in solving these types of problems. The main idea of SAEAs is the integration of an evolutionary algorithm with a selected surrogate model that approximates the computationally expensive function. In this paper, we propose a surrogate model based on a Lipschitz underestimation and use it to develop a differential evolution-based algorithm. The algorithm, called Lipschitz Surrogate-assisted Differential Evolution (LSADE), utilizes the Lipschitz-based surrogate model, along with a standard radial basis function surrogate model and a local search procedure. The experimental results on seven benchmark functions of dimensions 30, 50, 100, and 200 show that the proposed LSADE algorithm is competitive compared with the state-of-the-art algorithms under a limited computational budget, being especially effective for the very complicated benchmark functions in high dimensions.

A comprehensive survey on the sine–cosine optimization algorithm

Metaheuristic algorithms based on intelligent rules have been successfully developed and applied to solve many optimization areas over the past few decades. The sine–cosine algorithm (SCA) imitates the behaviour of transcendental functions while the sine and cosine functions are presented to explore and exploit the search space. SCA starts by random population and executes iterative evolution processes to update the standard evolutionary algorithm’s destination or the best location. SCA used linear transition rules to balance the exploration and exploitation searches while searching for the best or optimal solutions. Since Mirjalili proposed it in 2016, SCA has attracted many researchers’ attention to deal with several optimization problems in many fields due to its strengths in solving optimization tasks that include the simple concept, easiness of implementation, and rapid convergence. This paper aims to provide researchers with a relatively comprehensive and extensive overview of the Sine–Cosine optimization algorithm in the literature to inspire further research. It examines the available publications, including improvements, binary, chaotic, hybridizations, multi-objective variants, and different applications. Some optimization formulations regarding single-objective optimization problems, multi-objective optimization problems, binary-objective optimization problems, and more classifications regarding the optimization types are discussed. An extensive bibliography is also included.

Dual adaption based evolutionary algorithm for optimized the smart healthcare communication service of the Internet of Things in smart city

The Internet of Things (IoT) is a revolutionary technique of sharing data for smart devices that generates huge amounts of data from smart healthcare systems. Therefore, healthcare systems utilize the convergence power and traffic analysis of sensors that cannot be satisfactorily handled by the IoT. In this article, a novel mutation operator is devised and incorporated with the differential evolution (DE) algorithm. Two tests have been conducted in the validation process. Firstly, the newly dual adaption-based operators incorporated with the differential evolution algorithm are being proposed. The proposed approach provides sufficient diversity and enhances the search speed of nature’s local and global search environments in the problem. The proposed method incorporates the application of IoT-based smart healthcare. Second, an application-based test has been conducted, in which the proposed approach is applied to the application in the smart healthcare system. Therefore, IoT sensor deployment is an optimization problem to minimize service time, delay, and energy loss by considering the communication constraint between sensors(objects). The proposed algorithm is applied in this article to solve this optimization problem. Further, in the experimentation and comparative study, the proposed method is superior to the standard evolutionary algorithms in IoT applications concerning the minimum number of function evaluations and minimization of traffic services. The proposed approach also achieves efficiency in the minimum loss of energy in each service and reduces load and delay.

Real-Time Maintenance Policy Optimization in Manufacturing Systems: An Energy Efficiency and Emission-Based Approach

Within the frame of the Fourth Industrial Revolution, the application of Internet of Things technologies makes it possible to convert conventional manufacturing systems into cyber-physical systems, where the used new technologies enable the improvement of maintenance and operation processes. The aim of this work is to develop and validate a new real-time maintenance policy model and optimization algorithm based on digital twin simulation. The maintenance policy model is based on the conventional failure and operation data from ERP (enterprise resource planning) and the real-time and forecasted failure and operation data from digital twin simulation. The described maintenance policy model and its optimization algorithm represent an innovative way to manage predictive, preventive, corrective, and opportunistic maintenance strategies. The novelty of the presented method is that the real-time data generated by the digital twin solution allow the definition of a more accurate maintenance strategy. The optimization algorithm is characterized by a standard evolutionary algorithm. The impact of maintenance policy optimization on the energy efficiency and emission was analyzed in the case of both conventional and cyber-physical manufacturing systems with and without digital-twin-based simulation. The results showed that the energy consumption and the greenhouse gas emission in the real-time maintenance policy optimization scenario decreased by 21%, depending on the electricity generation source.

Enhanced Teaching Learning-Based Algorithm for Fuel Costs and Losses Minimization in AC-DC Systems

The Teaching Learning-Based Algorithm (TLBA) is a powerful and effective optimization approach. TLBA mimics the teaching-learning process in a classroom, where TLBA’s iterative computing process is separated into two phases, unlike standard evolutionary algorithms and swarm intelligence algorithms, and each phase conducts an iterative learning operation. Advanced technologies of Voltage Source Converters (VSCs) enable greater active and reactive power regulation in these networks. Various objectives are addressed for optimal energy management, with the goal of attaining economic and technical advantages by decreasing overall production fuel costs and transmission power losses in AC-DC transmission networks. In this paper, the TLBA is applied for various sorts of nonlinear and multimodal functioning of hybrid alternating current (AC) and multi-terminal direct current (DC) power grids. The proposed TLBA is evaluated on modified IEEE 30-bus and IEEE 57-bus AC-DC networks and compared to other published methods in the literature. Numerical results demonstrate that the proposed TLBA has great effectiveness and robustness indices over the others. Economically, the reduction percentages of 13.84 and 21.94% are achieved for the IEEE 30-bus and IEEE 57-bus test systems when the fuel costs are minimized. Technically, significant improvement in the transmission power losses with reduction 28.01% and 69.83%, are found for the IEEE 30-bus and IEEE 57-bus test system compared to the initial case. Nevertheless, TLBA has faster convergence, higher quality for the final optimal solution, and more power for escaping from convergence to local optima compared to other published methods in the literature.

Muscle-Effort-Minimization-Inspired Kinematic Redundancy Resolution for Replicating Natural Posture of Human Arm.

Replicating natural postures of human arms is essential to generate human-like behaviors in robotic applications for humans nearby. However, how to realize this requirement in interactive scenarios remains a challenge due to the kinematic redundancy and unknown postural control strategy of human arms. Inspired by the physiological characteristics that the musculoskeletal system is coordinated to minimize muscle effort in human behaviors, this paper aims to address the issue by solving a muscle effort minimization problem. It adopts a high-fidelity human arm musculoskeletal model (HAMM) and considers the implicit constraint (desired hand pose) and the inequality constraints (range of joint motion). The constrained minimization is in general nonconvex, consequently sensitive to initial guesses in iterative procedures. So, it is impracticable to solve it directly with existing gradient-based deterministic approaches or standard evolutionary algorithms. As the main contribution, a hybrid inverse kinematics algorithm was proposed for the HAMM with 7 independent and 13 mimic joints to obtain the feasible arm postures satisfying the minimization constraints. Using the arm swivel angle that parametrizes the kinematic redundancy of the HAMM, geometrically equidistant initial guess candidates can be generated over the 1-dimension feasible posture manifold. As another contribution, we present a two-phase global minimization algorithm to handle the nonconvexity of the constrained minimization. It consists of a local-search phase on the null-space of the geometric Jacobian matrix and a global-search phase with an initial guess resampling strategy. The proposed approach was validated by replicating the natural arm postures of 5 right-handed subjects in daily tasks.

Cooperative coevolutionary instance selection for multilabel problems

Multilabel classification as a data mining task has recently attracted greater research interest. Many current data mining applications address problems having instances that belong to more than one class, which requires the development of new efficient methods. Advantageously using the correlation among different labels can provide better performance than methods that deal with each label separately. Instance-based classification models, such as k-nearest neighbors for multilabel datasets, ML-kNN, are among the best performing methods on any classification task and have also shown very goog performance in multilabel problems. Despite their simplicity, they achieve comparable performance to considerably more complex methods. One of the challenges associated with instance-based classification models is their requirement for storing all the training instances in memory. To ameliorate this problem, instance selection methods have been proposed. However, their application to multilabel problems is problematic because the adaptation of most of their concepts to multilabel problems is difficult. In this paper, we propose a cooperative coevolutionary algorithm for instance selection for multilabel problems. Two different populations evolve together cooperatively. One of the populations is devoted to obtaining solutions for each label, whereas the other population combines these results into solutions for the instance selection for multilabel dataset tasks. On a large set of 70 real-world problems, our approach improves the results of both the ML-kNN method with the whole dataset and an instance selection method using a standard evolutionary algorithm.

An exploitation-enhanced multi-objective efficient global optimization algorithm for expensive aerodynamic shape optimizations

The traditional multi-objective efficient global optimization (EGO) algorithms have been hybridized and adapted to solving the expensive aerodynamic shape optimization problems based on high-fidelity numerical simulations. Although the traditional EGO algorithms are highly efficient in solving some of the optimization problems with very complex landscape, it is not preferred to solve most of the aerodynamic shape optimization problems with relatively low-degree multi-modal design spaces. A new infill criterion encouraging more local exploitation has been proposed by hybridizing two traditional multi-objective expected improvements (EIs), namely, statistical multi-objective EI and expected hypervolume improvement, in order to improve their robustness and efficiency in aerodynamic shape optimization. Different analytical test problems and aerodynamic shape optimization problems have been investigated. In comparison with traditional multi-objective EI algorithms and a standard evolutionary multi-objective optimization algorithm, the proposed method is shown to be more robust and efficient in the tests due to its hybrid characteristics, easier handling of sub-optimization problems, and enhanced exploitation capability.

A global optima search field division method for evolutionary algorithms

This study aims to investigate the deployment of a proposed search field division method (SFDM) within evolutionary algorithms (EAs) to enhance the capability of searching for the global optima in nonlinear problems. The proposed technique is benchmarked against the following eight widely-used single-modal, multi-modal, and unimodal benchmark functions: Sphere, Rosenbrock, Rastringin, Griewank, Ackley, Fletcher, Quartic, and Schwefel functions, and the outcome is compared to their standard EAs counterparts to validate the effectiveness of the deployed approach in EAs. In the proposed method, we apply three low, medium, high field divisions (1, 2, and 5) dimensions on nine different EAs simultaneously with two different scenarios, 10 and 100 variables, to reach the optimal solution. Then for the validity of our proposed SFDM technique, we examined the exploration-exploitation search space rates and diversity behavior. The results of the implementation of SFDM on eight benchmark test functions show that the consideration of dimensions using SFDM for EAs improves the outcomes of all nine tested EAs. In our proposed method, we find better compatibility with the integration of SFDM in the Particle Swarm Optimization Algorithm concerning searching for the optimum solution relative to the other EAs. Highlights A novel Search Field Division Method (SFDM) for evolutionary algorithms. Applying three field divisions (1, 2, and 5) dimensions on nine different Evolutionary Algorithms (EAs) simultaneously to reach the optimal global solution. The implementation of SFDM on eight benchmark functions shows significant improvement in all nine tested EAs. In our proposed method, we find the Particle Swarm Optimization Algorithm has better compatibility with respect to the other EAs.

Resampled Efficient Frontier Integration for MOEAs.

Mean-variance portfolio optimization is subject to estimation errors for asset returns and covariances. The search for robust solutions has been traditionally tackled using resampling strategies that offer alternatives to reference sets of returns or risk aversion parameters, which are subsequently combined. The issue with the standard method of averaging the composition of the portfolios for the same risk aversion is that, under real-world conditions, the approach might result in unfeasible solutions. In case the efficient frontiers for the different scenarios are identified using multiobjective evolutionary algorithms, it is often the case that the approach to averaging the portfolio composition cannot be used, due to differences in the number of portfolios or their spacing along the Pareto front. In this study, we introduce three alternatives to solving this problem, making resampling with standard multiobjective evolutionary algorithms under real-world constraints possible. The robustness of these approaches is experimentally tested on 15 years of market data.

On Steady-State Evolutionary Algorithms and Selective Pressure: Why Inverse Rank-Based Allocation of Reproductive Trials Is Best

We analyse the impact of the selective pressure for the global optimisation capabilities of steady-state evolutionary algorithms (EAs). For the standard bimodal benchmark function TwoMax , we rigorously prove that using uniform parent selection leads to exponential runtimes with high probability to locate both optima for the standard ( +1) EA and ( +1) RLS with any polynomial population sizes. However, we prove that selecting the worst individual as parent leads to efficient global optimisation with overwhelming probability for reasonable population sizes. Since always selecting the worst individual may have detrimental effects for escaping from local optima, we consider the performance of stochastic parent selection operators with low selective pressure for a function class called TruncatedTwoMax, where one slope is shorter than the other. An experimental analysis shows that the EAs equipped with inverse tournament selection, where the loser is selected for reproduction and small tournament sizes, globally optimise TwoMax efficiently and effectively escape from local optima of TruncatedTwoMax with high probability. Thus, they identify both optima efficiently while uniform (or stronger) selection fails in theory and in practice. We then show the power of inverse selection on function classes from the literature where populations are essential by providing rigorous proofs or experimental evidence that it outperforms uniform selection equipped with or without a restart strategy. We conclude the article by confirming our theoretical insights with an empirical analysis of the different selective pressures on standard benchmarks of the classical MaxSat and multidimensional knapsack problems.

Fast Immune System-Inspired Hypermutation Operators for Combinatorial Optimization

Various studies have shown that immune system-inspired hypermutation operators can allow artificial immune systems (AIS) to be very efficient at escaping local optima of multimodal optimization problems. However, this efficiency comes at the expense of considerably slower runtimes during the exploitation phase compared to the standard evolutionary algorithms. We propose modifications to the traditional hypermutations with mutation potential (HMP) that allow them to be efficient at exploitation, as well as maintaining their effective explorative characteristics. Rather than deterministically evaluating fitness after each bit-flip of a hypermutation, we sample the fitness function stochastically with a “parabolic” distribution. This allows the stop at the first constructive mutation (FCM) variant of HMP to reduce the linear amount of wasted function evaluations when no improvement is found to a constant. The stochastic distribution also allows the removal of the FCM mechanism altogether as originally desired in the design of the HMP operators. We rigorously prove the effectiveness of the proposed operators for all the benchmark functions, where the performance of HMP is rigorously understood in the literature. We validate the gained insights to show linear speed-ups for the identification of high-quality approximate solutions to classical NP-Hard problems from combinatorial optimization. We then show the superiority of the HMP operators to the traditional ones in an analysis of the complete standard Opt-IA AIS, where the stochastic evaluation scheme allows HMP and aging operators to work in harmony. Through a comparative performance study of other “fast mutation” operators from the literature, we conclude that a power-law distribution for the parabolic evaluation scheme is the best compromise in black-box scenarios, where little problem knowledge is available.

Chaotic Search Based Equilibrium Optimizer for Dealing with Nonlinear Programming and Petrochemical Application

In this article, chaotic search based constrained equilibrium optimizer algorithm (CS-CEOA) is suggested by integrating a novel heuristic approach called equilibrium optimizer with a chaos theory-based local search algorithm for solving general non-linear programming. CS-CEOA is consists of two phases, the first one (phase I) aims to detect an approximate solution, avoiding being stuck in local minima. In phase II, the chaos-based search algorithm improves local search performance to obtain the best optimal solution. For every infeasible solution, repair function is implemented in a way such that, a new feasible solution is created on the line segment defined by a feasible reference point and the infeasible solution itself. Due to the fast globally converging of evolutionary algorithms and the chaotic search’s exhaustive search, CS-CEOA could locate the true optimal solution by applying an exhaustive local search for a limited area defined from Phase I. The efficiency of CS-CEOA is studied over multi-suites of benchmark problems including constrained, unconstrained, CEC’05 problems, and an application of blending four ingredients, three feed streams, one tank, and two products to create some certain products with specific chemical properties, also to satisfy the target costs. The results were compared with the standard evolutionary algorithms as PSO and GA, and many hybrid algorithms in the same simulation environment to approve its superiority of detecting the optimal solution over selected counterparts.

Path planning for the autonomous robots using modified grey wolf optimization approach

Path planning for robots plays a vital role to seek the most feasible path due to power requirement, environmental factors and other limitations. The path planning for the autonomous robots is tedious task as the robot needs to locate a suitable path to move between the source and destination points with multifaceted nature. In this paper, we introduced a new technique named modified grey wolf optimization (MGWO) algorithm to solve the path planning problem for multi-robots. MGWO is modified version of conventional grey wolf optimization (GWO) that belongs to the category of metaheuristic algorithms. This has gained wide popularity for an optimization of different parameters in the discrete search space to solve various problems. The prime goal of the proposed methodology is to determine the optimal path while maintaining a sufficient distance from other objects and moving robots. In MGWO method, omega wolves are treated equally as those of delta wolves in exploration process that helps in escalating the convergence speed and minimizing the execution time. The simulation results show that MGWO gives satisfactory performance than other state of art methods for path planning of multiple mobile robots. The performance of the proposed method is compared with the standard evolutionary algorithms viz., Particle Swarm Optimization (PSO), Intelligent BAT Algorithm (IBA), Grey Wolf Optimization (GWO), and Variable Weight Grey Wolf Optimization (VW-GWO) and yielded better results than all of these.

Development of Multiple Behaviors in Evolving Robots

We investigate whether standard evolutionary robotics methods can be extended to support the evolution of multiple behaviors by forcing the retention of variations that are adaptive with respect to all required behaviors. This is realized by selecting the individuals located in the first Pareto fronts of the multidimensional fitness space in the case of a standard evolutionary algorithms and by computing and using multiple gradients of the expected fitness in the case of a modern evolutionary strategies that move the population in the direction of the gradient of the fitness. The results collected on two extended versions of state-of-the-art benchmarking problems indicate that the latter method permits to evolve robots capable of producing the required multiple behaviors in the majority of the replications and produces significantly better results than all the other methods considered.

ALGA: Active Learning-Based Genetic Algorithm for Accelerating Structural Optimization

Optimization of complex structures using standard evolutionary algorithms, like genetic algorithm (GA), is known to be computationally expensive, because a very large number of finite element analysis (FEA) must be conducted for each possible structural design during the optimization. In the literature, different pretrained surrogate models have been used to replace the FEA for improving the computational performance of the structural optimization. However, the optimal solution found by the optimizer often depends on the accuracy of the pretrained surrogate model itself. Moreover, large datasets may be needed for getting the required accuracy of the surrogate model. An adaptive machine learning technique called active learning is used in this paper to accelerate the evolutionary optimization of complex structures. An active learner is a machine-learning-based model that can interactively query the outputs of certain data points, whenever the model would be uncertain about those outputs. In the presented approach, the active learner helps the GA by predicting if the possible design is going to be feasible or infeasible, meaning if it satisfies the required constraints or not. If the active learner is uncertain about the output, an actual FEA is conducted, and it improves its own accuracy for future evaluations. The approach does not need a trained surrogate model before the optimization. The active learner adaptively learns about the structure during the optimization to improve the computational performance. The approach is used to optimize the classic 10-bar truss problem, the Hesse function, curvilinearly stiffened panels under buckling and stress constraints, and some benchmark constrained test functions. The results show that the approach has the potential to reduce the total required constraint evaluations by more than 50%.