Continuous Optimization Algorithm Research Articles

Continuous optimization by quantum adaptive distribution search

We introduce the quantum adaptive distribution search (QuADS), a quantum continuous optimization algorithm that integrates Grover adaptive search (GAS) with the covariance matrix adaptation evolution strategy (CMA-ES), a classical technique for continuous optimization. QuADS utilizes the quantum-based search capabilities of GAS and enhances them with the principles of CMA-ES for more efficient optimization. It employs a multivariate normal distribution for the initial state of the quantum search and repeatedly updates it throughout the optimization process. Our numerical simulations show that QuADS outperforms both GAS and CMA-ES. This is achieved through adaptive refinement of the initial state distribution rather than consistently using a uniform state, resulting in fewer oracle calls. This study presents an important step toward exploiting the potential of quantum computing for continuous optimization. Published by the American Physical Society 2024

Retraction Note: A-COA: an adaptive cuckoo optimization algorithm for continuous and combinatorial optimization

Retraction Note: A-COA: an adaptive cuckoo optimization algorithm for continuous and combinatorial optimization

Image denoising method of HV insulator damage based on U-Net neural network

The noise of the image will lead to large errors in the image processing of high-voltage insulator damage. In order to reduce the impact of noise, a denoising method for high-voltage insulator damage image is designed based on U-Net neural network. The specific method is to define the perception features of the real domain of the HV insulator damage image, to obtain the input and output values in the convolution layer, to construct the excitation function of the convolution layer, to calculate the average value in the selected region, and to obtain the network image feature mapping results. Based on this, displacement changes were acquired by calculating the mean and variance of image data, and multi-scale image features were extracted combined with U-Net neural network. Thus, the image denoising model of high voltage insulator damage is established. Through the continuous optimization algorithm, the value of loss function reaches the predetermined standard, and the denoising of high voltage insulator damage image is finally realized. The experimental results show that as the noise level increases, the peak signal-to-noise(PSNR) ratio obtained by this denoising method shows a decreasing trend. When the noise level is 5 dB and 75 dB, the PSNR values of this denoising method on the color dataset are 27.6 dB and 26.8 dB, respectively. In the grayscale dataset, when the noise level is 75 dB, the PSNR value is 26.9 dB. From the experimental data, it can be seen that the proposed U-Net neural network denoising method is better.

A Resampling Ant Colony Optimization with Elite Exploration and Convergence Mechanism for Multithreshold Segmentation of Breast Cancer Images

Previous studies have emphasized the potential of threshold image segmentation for early breast cancer detection. However, traditional methods encounter challenges regarding low segmentation efficiency and accuracy. Addressing this, the ant colony optimization algorithm for continuous optimization (ACOR) shows promise. Yet, existing ACOR variants still grapple with poor initial population quality, affecting convergence speed and avoiding local optimization. These issues impact segmentation efficiency and accuracy. To tackle them, this study introduces RESACO, an enhanced ACOR version integrating three novel optimization strategies: resampling initialization (RIS), elite exploration (EES), and strengthened convergence mechanism (SCM). RIS enhances initial population quality by resampling regions with individuals demonstrating superior fitness and segmentation efficiency. EES promotes exploration across the search space, preventing local optima entrapment and enhancing model stability. SCM expediting convergence, segmentation efficiency, and precision. RESACO's performance is assessed through extensive experiments using IEEE CEC 2014 and IEEE CEC 2022 benchmark functions, including ablation experiments and comparisons with basic and improved algorithms and ACOR variants. Subsequently, the threshold image segmentation model based on RESACO is compared with other models using metaheuristic algorithms for segmenting realistic breast cancer medical images. Results demonstrate the proposed model's faster convergence and higher segmentation accuracy, preserving more lesion tissue details.

Convergence Rate of the (1+1)-ES on Locally Strongly Convex and Lipschitz Smooth Functions

Evolution strategy (ES) is one of promising classes of algorithms for black-box continuous optimization. Despite its broad successes in applications, theoretical analysis on the speed of its convergence is limited on convex quadratic functions and their monotonic transformation. In this study, an upper bound and a lower bound of the rate of linear convergence of the (1+1)-ES on locally $L$-strongly convex functions with $U$-Lipschitz continuous gradient are derived as $\exp\left(-\Omega_{d\to\infty}\left(\frac{L}{d\cdot U}\right)\right)$ and $\exp\left(-\frac1d\right)$, respectively. Notably, any prior knowledge on the mathematical properties of the objective function such as Lipschitz constant is not given to the algorithm, whereas the existing analyses of derivative-free optimization algorithms require them.

Automatic calibration of SWMM parameters based on multi-objective optimisation model

Abstract To address the issue of low accuracy and inefficiency in the traditional parameter calibration methods for the SWMM model, this paper constructs an automatic parameter calibration model based on multi-objective optimisation algorithms. Firstly, the Sobol method and GLUE method are utilised to determine sensitive parameters and their ranges, aiming to narrow down the solution space and expedite the model-solving speed. Secondly, the NSGA-3 multi-objective optimisation algorithm based on the Pareto theory is applied for the optimisation and calibration of sensitive parameter sets. The model is validated in the rainwater drainage system with independent runoff in a residential area in a northwestern city in China. The results show that parameters such as N-Imperv and KSlope are highly sensitive to the model output under the land-use conditions of the study area. The simulation accuracy of the multi-objective continuous optimisation algorithm is significantly better than that of the single-objective genetic algorithm. The simulation results of the SWMM model under multi-objective optimisation demonstrate a certain level of reliability and stability. The research findings can provide technical support for the automatic calibration of SWMM model parameters, accurate model simulation, and application.

Identifying Influential Spatial Drivers of Forest Fires through Geographically and Temporally Weighted Regression Coupled with a Continuous Invasive Weed Optimization Algorithm

Identifying the underlying factors derived from geospatial and remote sensing data that contribute to forest fires is of paramount importance. It aids experts in pinpointing areas and periods most susceptible to these incidents. In this study, we employ the geographically and temporally weighted regression (GTWR) method in conjunction with a refined continuous invasive weed optimization (CIWO) algorithm to assess certain spatially relevant drivers of forest fires, encompassing both biophysical and anthropogenic influences. Our proposed approach demonstrates theoretical utility in addressing the spatial regression problem by meticulously accounting for the autocorrelation and non-stationarity inherent in spatial data. We leverage tricube and Gaussian kernels to weight the GTWR for two distinct temporal datasets, yielding coefficients of determination (R2) amounting to 0.99 and 0.97, respectively. In contrast, traditional geographically weighted regression (GWR) using the tricube kernel achieved R2 values of 0.87 and 0.88, while the Gaussian kernel yielded R2 values of 0.8138 and 0.82 for the same datasets. This investigation underscores the substantial impact of both biophysical and anthropogenic factors on forest fires within the study areas.

Semiparametric Estimation of Distribution Algorithms for Continuous Optimization

Semiparametric Estimation of Distribution Algorithms for Continuous Optimization

The first hitting time analysis of evolutionary algorithms based on renewal process

<abstract> <p>Running time analysis of evolutionary algorithms for continuous optimization is one research challenge in the field of evolutionary algorithms (EAs). However, the theoretical analysis results have rarely been applied to evolutionary algorithms for continuous optimization in practice, let alone their variants for evolution strategy. In this paper, we regarded the first hitting time of evolution strategy as the stopping time of the renewal process on the basis of the renewal process and in combination with Wald's inequality and stopping time theory. Afterwards, to demonstrate the application of the proposed model in the first hitting time analysis of (1 + 1) ES, we analyzed it with different mutation operators on the sphere function. First, we significantly improved the lower bound on the first hitting time of (1 + 1) ES with a uniform mutation operator, i.e., from $\Omega(n)$ to $\Omega\left(e^{c n}\right)$. Next, $O\left(n^{2} \sqrt{n}\right)$ was the upper bound on the first hitting time of (1 + 1) ES with a Gaussian mutation operator from the initial distance <italic>R</italic> to half of the initial distance <italic>R</italic>/2. The numerical experimental results showed that the theoretical calculation was consistent with the actual running time, which provides a novel method for analyzing the first hitting time of EAs.</p> </abstract>

Design of a novel multimodal optimization algorithm and its application in logistics optimization

<abstract> <p>This study was purposed to design a multimodal continuous optimization algorithm based on a scheme agent to address the multidimensional complexity of optimization. An evolutionary sampling method of subarea exploration and multiple exploitations was developed by employing the scheme with variable population size so as to obtain higher optimization speed and accuracy. Second, the distribution plan was quantified into high-dimensional variable parameters based on the characteristics of logistics distribution optimization problems, and a high-dimensional discrete optimization model was constructed. Then, we identified and addressed the prominent issues and malignant virtual changes in the application of continuous algorithms to discrete problems. We have introduced a reasonable mutation mechanism during the optimization sampling process to mitigate this issue. Continuous real coordinate points were transformed across the neighborhood to standard discrete integer coordinate points by normalizing and logicizing the optimization sampling coordinates; also, the discretization of the continuous algorithm was realized. This approach could effectively prevent the algorithm from searching for targets in continuous optimization space, thereby fully reducing the complexity of the objective function distribution after conversion. The experiments showed that the transformed multimodal discrete optimization algorithm effectively addressed the optimization design problem of logistics distribution.</p> </abstract>

History-Guided Hill Exploration for Evolutionary Computation

Although evolutionary computing (EC) methods are stochastic optimization methods, it is usually difficult to find the global optimum by restarting the methods when the population converges to a local optimum. A major reason is that many optimization problems have basins of attraction (BoAs) that differ widely in shape and size, and the population always prefers to converge toward basins of attraction that are easy to search. Although heuristic restart based on tabu search is a theoretically feasible idea to solve this problem, existing EC methods with heuristic restart are difficult to avoid repetitive search results while maintaining search efficiency. This paper tries to overcome the dilemma by online learning the BoAs and proposes a search mode called history-guided hill exploration (HGHE). In the search mode, evaluated solutions are used to help separate the search space into hill regions which correspond to the BoAs, and a classical EC method is used to locate the optimum in each hill region. An instance algorithm for continuous optimization named HGHE differential evolution (HGHE-DE) is proposed to verify the effectiveness of HGHE. Experimental results prove that HGHE-DE can continuously discover unidentified BoAs and locate optima in identified BoAs.

A user-friendly Bees Algorithm for continuous and combinatorial optimisation

A user-friendly Bees Algorithm for continuous and combinatorial optimisation

Dual-mutation mechanism-driven snake optimizer for scheduling multiple budget constrained workflows in the cloud

Scheduling workflows in cloud computing is to find the most appropriate mapping from a series of dependent tasks to a set of available virtual resources so as to minimize or maximize some user concerned objectives, which is very significant to a sustainable and high-efficient cloud data center. However, it still faces challenges since its NP-hardness and the diversified requirements of both the cloud service consumers and cloud service providers need to be satisfied at the same time, especially in addressing multiple applications requested simultaneously. This work proposes a dual-mutation mechanism-driven snake optimizer for scheduling multiple workflows in the cloud for minimizing the makespan of each workflow under user pre-defined budget constraints. Firstly, a continuous optimization algorithm, namely Snake Optimizer (SO) is adopted into discrete optimization, i.e., workflow scheduling. Secondly, a task execution order aware fitness function is designed to reduce the gaps or waiting time between parent and child tasks within a workflow and thus reduce the total execution time of the workflow. Besides, we analyze the existing snake optimizer and adjust the parameters corresponding to different evolutionary stages to adapt to our considered problem. Finally, a dual-mutation mechanism is developed by introducing a non-improvement iteration number for each snake and applying a standard bit mutation operation to prematurely converging snakes and the individuals randomly selected from the remaining snakes so that the population diversity can be enhanced and more potential solutions can be explored. Experimental results on a set of real-world scientific workflows show that our proposed algorithm is of great superiority in constraint satisfiability, meaning that compared with its peers, it is always the first to find feasible solutions.

An Improved Mayfly Optimization Algorithm for Type-2 Multi-Objective Integrated Process Planning and Scheduling

The type-2 multi-objective integrated process planning and scheduling problem, as an NP-hard problem, is required to deal with both process planning and job shop scheduling, and to generate optimal schedules while planning optimal machining paths for the workpieces. For the type-2 multi-objective integrated process planning and scheduling problem, a mathematical model with the minimization objectives of makespan, total machine load, and critical machine load is developed. A multi-objective mayfly optimization algorithm with decomposition and adaptive neighborhood search is designed to solve this problem. The algorithm uses two forms of encoding, a transformation scheme designed to allow the two codes to switch between each other during evolution, and a hybrid population initialization strategy designed to improve the quality of the initial solution while taking into account diversity. In addition, an adaptive neighborhood search cycle based on the average distance of the Pareto optimal set to the ideal point is designed to improve the algorithm’s merit-seeking ability while maintaining the diversity of the population. The proposed encoding and decoding scheme can better transform the continuous optimization algorithm to apply to the combinatorial optimization problem. Finally, it is experimentally verified that the proposed algorithm achieves better experimental results and can effectively deal with type-2 MOIPPS.

Triangulation topology aggregation optimizer: A novel mathematics-based meta-heuristic algorithm for continuous optimization and engineering applications

In recent years, numerous meta-heuristic algorithms based on swarm intelligence have been proposed and widely popularized. Although algorithms are designed by some specific behaviors of organisms, their heuristic paradigms and constructed modules are similar, resulting in algorithms still suffer from imbalance between exploration and exploitation for complex optimization problems. Combining mathematical properties with a stochastic search process in meta-heuristic algorithms contributes to breaking the traditional single/dual population-based evolutionary paradigm and facilitating individuals forward optimization. Taking this as motivation, this article proposes a novel mathematics-based meta-heuristic algorithm, named Triangulation Topology Aggregation Optimizer (TTAO), for solving continuous optimization and engineering applications. The core of the proposed algorithm is based on similar triangular topology in mathematics. The TTAO algorithm contains two strategies, i.e., the generic aggregation and the local aggregation, which contributes to iteratively constructing multiple similar triangular topological units to balance the exploration and exploitation. The former generates new vertexes through positive information exchange between different triangular topological units. And the latter constructs new units at promising locations according to the local optimum vertex of each unit. The performance of the TTAO algorithm is evaluated in comparison with some competitive algorithms on CEC2017 functions for different dimensions and 8 real-world engineering problems. Moreover, the Wilcoxon rank sum test is used to verify the effectiveness of the proposed algorithm. The experimental results show that the TTAO algorithm, compared with 10 competitors, obtains 23, 23, and 22 best average results for 29 CEC2017 functions on 30, 50 and 100 dimensions, and its Wilcoxon rank sum test scores still rank first on three different dimensional cases. And more numerical results verify the outstanding optimization performance of the TTAO algorithm effectively. Source codes of TTAO are publicly available at https://www.mathworks.com/matlabcentral/fileexchange/136029-triangulation-topology-aggregation-optimizer.

Improved ant colony-based algorithm for solving traveling salesmen problem

The purpose of this research is to examine how well the Improved Memetic Continuous Pheromone-based Ant Colony Optimization (ICMPACO) algorithm solves standard Traveling Salesman Problem (TSP) instances in comparison to the basic Ant Colony Optimization (ACO) algorithm and the Improved Ant Colony Optimization (IACO) algorithm. The findings of the computer simulation show that the ICMPACO algorithm has higher optimization capabilities, particularly for the berlin52, eil51, and dantzig42 examples. This superiority is further emphasized through better mean values in comparison to traditional ACO methods. The study also proposes a novel approach, Genetic Ant Colony Optimization (GACO), which integrates ACO with genetic algorithms. Pheromone data is efficiently employed to direct the choice of genetic operation points and maintain the foundational elements within the genetic algorithm. Performance results for various TSP instances reveal the potential of GACO in generating high-quality solutions. These findings suggest that both ICMPACO and GACO methods hold significant promise in addressing complex optimization challenges and could pave the way for further advancements in enhancing optimization algorithm performance.

CO_2 footprint minimization of solar-powered HALE using MDO and eco-material selection

Multidisciplinary Design Optimization (MDO) enables one to reach a better solution than by optimizing each discipline independently. In particular, the optimal structure of a drone varies depending on the selected material. The CO_2 footprint of a solar-powered High Altitude Long Endurance (HALE) drone is optimized here, where the structural materials used is one of the design variables. Optimization is performed using a modified version of OpenAeroStruct, a framework based on OpenMDAO. Our EcoHale framework is validated on a classical HALE testcase in the MDO community (FBhale) constructed using high-fidelity codes compared to our low-fidelity approach. The originality of our work is to include two specific disciplines (energy and environment) to adapt to a new problem of CO_2 minimization. The choice of eco-materials is performed in the global MDO loop from a choice of discrete materials . This is achieved through a variable relaxation, enabling the use of continuous optimization algorithms inspired from multimaterial topology optimization. Our results show that, in our specific case of electric drone, the optimal material in terms of CO_2 footprint is also the optimal material in terms of weight. It opens the door to new researches on digital microarchitectured materials that will decrease the CO_2 footprint of the drone.

A multi-stage descent algorithm for discrete and continuous optimization applied to truss structures optimal design

A multi-stage descent algorithm for discrete and continuous optimization applied to truss structures optimal design

Benchmarking Procedures for Continuous Optimization Algorithms

Reliable comparison of optimization algorithms requires the use of specialized benchmarking procedures. This paper highlights motivations which influence their structure, discusses evaluation criteria of algorithms, typical ways of presenting and interpreting results as well as related statistical procedures. Discussions are based on examples from CEC and BBOB benchmarks. Moreover, attention is drawn to these features of comparison procedures, which make them susceptible to manipulation. In particular, novel application of the weak axiom of revealed preferences to the field of benchmarking shows why it may be misleading to assess algorithms on basis of their ranks for each of test problems. Additionally, an idea is presented of developing massively parallel implementation of benchmarks. Not only would this provide faster computation but also open the door to improving reliability of benchmarking procedures and promoting research into parallel implementations of optimization algorithms.

Laplacian Salp Swarm Algorithm for continuous optimization

Laplacian Salp Swarm Algorithm for continuous optimization