Approach to Discrete Optimization Under Uncertainty: The Population-Based Sampling Genetic Algorithm

This paper presents the Generalized PopulationBased Sampling (GPBS) approach, which is a generalized version of the Population-Based Sampling (PBS) approach that was developed by the authors of this paper in earlier work. PBS is a Genetic Algorithm (GA) based approach that allows for discrete design optimization under uncertainty and requires a computational cost that is two orders of magnitude lower than the state-of-the-art method that couples the GA with Monte Carlo Sampling (MCS). The PBS approach uses the population-based search of the GA to provide samples that are used in the statistical evaluation of aggregate, uncertain fitness functions. In PBS, while large numbers of samples are accumulated to evaluate the fitness values of “good” designs, the computational cost spent on designs with “poor” fitness is minimal. The main assumption in PBS is that the uncertain parameters associated with the design variables all have Gaussian probability distributions; hence, the probability distributions of aggregate fitness functions are assumed to be Gaussian themselves. This valid assumption is used to impose constraints on estimated probabilities of success of expected values of aggregate fitness functions even when the number of samples accumulated is small, which is usually the case at the beginning of the optimization run. The suggested GPBS approach generalizes the PBS approach by allowing design variables’ uncertain parameters with non-Gaussian probability distributions and by eliminating the normality assumption on the probability distributions of aggregate fitness functions. The GPBS approach combines the concepts of MCS and PBS and imposes constraints on calculated, rather than estimated, probabilities of success of expected values of aggregate fitness functions. In this paper, the probabilistic approaches described above are implemented for reliability-based design of a communication satellite with uncertain component failure rates. NOMENCLATURE c penalty multiplier ( ) E expected value f fitness function g inequality constraint function G uncertain inequality constraint function samples N number of samples ( ) P probability of payload R total payload reliability spacecraft R total spacecraft reliability m std measured standard deviation of aggregate probabilistic function

In response to the problems of traditional genetic algorithms in evaluating English compositions, the stability of automatic grading of English compositions has been further enhanced. This article evaluates the teaching effectiveness of automatic grading of English compositions using an optimization fusion algorithm combined with genetic optimization algorithm and CNN model. By analyzing genetic content and optimization algorithms, a corresponding fusion optimization model was obtained, and the automatic evaluation of English compositions was analyzed and predicted through experimental verification. The results indicate that the curves corresponding to different parameters exhibit typical segmentation features through the variation curves of individual numbers under different scale factors. And through quantitative description and analysis of the curve, it can be seen that the change in proportion factor has an absolute advantage in the impact of genetic algorithm on the number of children. As the number of samples increases, the performance of genetic optimization algorithms under the f function shows an upward trend. Research has shown that the writing content index has the greatest impact on English writing, while the corresponding grammar errors have the smallest impact on English writing. Finally, the accuracy of the optimized model was verified by comparing the model curve with experimental data. This study provides theoretical support for the use of genetic optimization algorithms and CNN models in English, and provides ideas for the use of optimization algorithms in other fields.

In this paper, the application of a population-based sampling algorithm, i.e., differential evolution, in the geological well testing of a multi-layered faulted reservoir model is discussed. In this sense, the available multiple well test datasets are used to calibrate the geological model parameters rather than fitting simplified analytical models. In the exercise studied in this paper, the parameter space includes a range of geostatistical, petrophysical, and structural parameters. The differential evolution algorithm starts with an initial random population from the ranges of input variables and progresses with successive evaluation of the static models’ transient tests. The static models’ input parameters are perturbed to generate new populations, which can finally match the truth model well test derivative with lower misfits. The ensemble of population models (samples) along with the misfit values are used to highlight the value of well test data in reducing the uncertainty in the parameter space. A Bayesian framework is employed to implement the Markov chain Monte Carlo (McMC) methods to estimate the posterior distributions of the parameters. The results are confirmed by the sample-based Sobol sensitivity indices, which rank the influential parameters. To reduce the computational cost of the McMC and sensitivity indices, a cross-validated proxy model (i.e., Multivariate Adaptive Regression Spline) is constructed. The effect of different variants of differential evolution algorithm on the geological well test matching is also discussed. This paper provides a workflow for quantitative integration of well test data into the reservoir characterization workflow.

The main concern of all economic companies is the resources equipping and allocating them in different economic sectors with the aim of maximizing profit and minimizing risk. Decentralization is one of the important factors that reduce investment risk. The investors plan to create investment by carefully planning and collecting sufficient information on the economic situation and analyzing the situation of various industries. As an economic enterprise, banks are looking for short- and long-term investments in a types of loans ,such as bailment of a capital , civil participation, reward, etc, which guarantees the return of their capital. In this paper, considering the condition of a bank as an economic enterprise, a model is presented which not only increases profit but also reduces risk. Two objective functions have been defined that the first objective is to minimize the risk and the second objective function is to maximize the of the bank profit, which is used by robust programming and Malvi Sim model. In this paper, we have investigated the Risky and non-Risky Partfolio and the optimal portfolio of bank assets from scenario based solution of the model and by using PSO and Genetic Optimization Algorithm. At all levels of confidence and optimal values of risk based on the estimation of SPP-CVAR method by Particle Swarm Algorithm (PSA) is less than genetic algorithm, which indicates better performance of Particle Swarm Algorithm (PSA) than Genetic Algorithm (GA). Also, the optimum wealth obtained from PSA solution is higher at all levels of confidence than the corresponding value of Genetic Algorithm (GA), and this is another reason to confirm the performance of PSO algorithm compared to the Genetic Algorithm (GA). The values of the first goal function, obtained from the PSO algorithm, for all confidence levels are lower than those of the genetic algorithm. The optimum wealth obtained from PSA is higher than genetic algorithm. At 0.9 level, the value of LR of kupiec statistics for the SPP-CVAR method was less than the Chi-square statistics (Critical value) which was assumed to be acceptable.

ABSTRACTThis article introduces a method of mistuned parameter identification which consists of static frequency testing of blades, dichotomy and finite element analysis. A lumped parameter model of an engine bladed-disc system is then set up. A bladed arrangement optimization method, namely the genetic particle swarm optimization algorithm, is presented. It consists of a discrete particle swarm optimization and a genetic algorithm. From this, the local and global search ability is introduced. CUDA-based co-evolution particle swarm optimization, using a graphics processing unit, is presented and its performance is analysed. The results show that using optimization results can reduce the amplitude and localization of the forced vibration response of a bladed-disc system, while optimization based on the CUDA framework can improve the computing speed. This method could provide support for engineering applications in terms of effectiveness and efficiency.

DOA and Power Estimation Using Genetic Algorithm and Fuzzy Discrete Particle Swarm Optimization

This paper firstly proposes an improved genetic algorithm (GA) for optimization in adaptive bus signal priority control at signalized intersections. Unlike conventional genetic algorithms with slow convergence speed, this algorithm can increase the convergence speed by utilizing the compensation rule between consecutive signal cycles to narrow new possible generated population spaces. Secondly, the paper would like to present a way to apply the algorithm to a simple adaptive bus signal priority control as well as compare how much the computation time is saved when applying the improved algorithm. Then the research thirdly investigates the efficiency of the proposed algorithm under various flow rate situations. The results show that the improved genetic algorithm can reduce the computation time considerably, by up to 48.39% for the studied case. With high saturation degrees on the cross street, the convergence rate performance of the improved genetic algorithm is significantly good. The figure can be up to 36.2% when compared with the convergence rate of the conventional GA.

The Darwinian Theory serves as the authentic inspiration behind several mathematical techniques known as metaheuristic methods and evolutionary algorithms, which emulate aspects of biological species' development. Among these methods, Genetic Algorithms have emerged at the forefront and have become the most practical technique. Previous studies have highlighted their capabilities in solving complex problems and their wide utilization across numerous disciplines, particularly optimization. This paper focuses on implementing Genetic Algorithms for structural optimization within the context of reliability assessment and safety. The proposed methodology, termed Reliability Genetic Algorithms Optimization (RGAO), combines Genetic Algorithms with reliability constraints. These constraints are defined by the probability of violating safety criteria within the structural problem's limit state function. To convey the idea, the proposed approach is applied to two case studies: The first case involves the reliability optimization of a bridge pier subjected to seismic loading, utilizing response spectrum analysis. Formulating the reliability optimization problem involves considering minimal design requirements, buckling conditions, and allowable stress constraints to determine the optimal and reliable dimensions for the studied structural component. The second case involves the optimization of the height of a prestressed bridge deck slab, while ensuring reliability by considering prestress geometrical conditions according to the French standard BPEL 91 revised 99. This work contributes to enhancing the use of bio-inspired techniques in structural optimization and reliability analysis, offering valuable perspectives for researchers and engineers.

A combined Monte Carlo (MC) simulation and Genetic Algorithm (GA) method was proposed by other researchers for the optimisation of spare parts allocation. From case studies, it was found that the number of simulation trials of the existing method tended to be either excessive or inadequate. Thus, a simulation replication number control method making full use of the advance simulation effort is proposed and implemented into the existing method. A numerical example shows significant improvement on overall simulation efficiency and that at the same time the required accuracy is guaranteed. Furthermore, it is argued that application-specific knowledge should be embedded into the general GA procedure so that the evolution process can be more efficient. Heuristic methods for initial population preparation for GA with and without considering component cost difference are proposed and illustrated for spare parts allocation. A computing experiment was designed and performed to examine the influence of parameters for replication number control and initial population preparation. The generation of availability–cost curve further indicates the necessity to adopt heuristic methods to improve searching efficiency in GA.

Genetic algorithm-based optimization of testing and maintenance under uncertain unavailability and cost estimation: A survey of strategies for harmonizing evolution and accuracy

This paper presents a comparative performance assessment for loss minimization of vector controlled induction motor (IM) drive based on two different efficient optimization algorithms, namely Genetic Algorithm (GA) and Golden Search (GS). Here the features of GA and GS both for estimation and recalculation of optimized flux component of current ( ), have been utilized for a better optimal efficiency operation of the IM drive. In this context, a comparative performance of IM drive based on GA and GS optimization algorithms is carried out. Both the GA and GS based algorithms greatly improve the efficiency by reducing the core loss of the drive system. Moreover, both the approaches have no effect on parameter variation and also need no additional hardware for hardware implementation. However, GA based loss minimization scheme proves its edge over GS based scheme for the IM drive. The simulation results for various speed patterns and operating conditions are presented here. Stability study of the whole drive system is also carried out utilizing both the optimizing schemes. The performance of the proposed drive is validated experimentally on dSPACE-1104 based laboratory prototype.

This paper presents a new multi-objective optimization method, which is inspired from the idea of non-dominated sorting genetic algorithm (NSGA) and genetic quantum algorithm (GQA). The GQA has been tested on well known test beds in single objective optimization and compared with the genetic algorithm (GA) in the lead author’s previous work [22]. This paper aims to apply the idea of GQA to multi-objective optimization (MOO). The developed method is called non-dominated sorting genetic quantum algorithm (NSGQA). The developed method is tested with benchmark problems collected from literature, which have characteristics representing various aspects of a MOO problem. Test results show that NSGQA has better performance on most benchmark problems than currently popular MOO methods such as the NSGA. The integration of GQA with MOO, and the systematic comparison with other MOO methods on benchmark problems, should be of general interest to researchers on MOO and to practitioners using MOO methods in design.

This paper addresses a distributed permutation flowshop scheduling problem with an order acceptance strategy in heterogeneous factories. Each order has a related revenue and due date, and several flowshop machines are operated in each factory, and they have a distinct sequence-dependent setup time. We select/reject production orders, assign the selected orders to the factories, and determine the permutation manufacturing sequence in each factory to maximize the total profit. To optimally solve the scheduling problem, we formulate the scheduling problem as a mixed integer linear programming model to find an optimal solution for small-sized experiments. Then, we propose two population-based algorithms, a genetic algorithm and particle swarm optimization for large-sized experiments. We proved that the proposed genetic algorithm effectively and efficiently solves the problem to guarantee a near optimal solution through computational experiments. Finally, we conduct a sensitivity analysis of the genetic algorithm to observe the relationship between order selection, revenue, and order tardiness cost.

Study of Thermal Sensitive Point Simulation and Cutting Trial of Five Axis Machine Tool Based on Genetic Algorithm

Vortex beams (VBs) generated by plasmonic metasurfaces hold great potential in the field of information transmission due to their unique helical phase wavefronts and infinite eigenstates. However, achieving perfect multiplexing and superposition of VBs with different orders remains a challenging issue in nanophotonics research. In this paper, based on a single-layer metallic porous metasurface structure applicable to the infrared spectrum, VBs with orders 2, 4, 6, and 8 are realized through the arrangement of annular elliptical apertures. Moreover, perfect VBs are achieved by optimizing key structural parameters using a genetic algorithm. The optimization of key structural parameters via genetic-based optimization algorithms to attain the desired effects can significantly reduce the workload of manual parameter adjustment. In addition, leveraging the orthogonality between VBs of different orders, concentric circular multi-channel VBs array (l = 2, 6) and (l = 4, 8) are realized. High-purity multiplexing architectures (>90%) are achieved via rational optimization of critical structural parameters using a genetic optimization algorithm, which further mitigates information crosstalk in optical communication transmission. The introduction of the genetic algorithm not only reduces the workload of manual arrangement of unit arrays but also enables the generation of more perfect VBs, providing a new research direction for optical communication transmission and optical communication encryption.