Optimization Problems In Continuous Space Research Articles

HAPI-DE: Differential evolution with hierarchical archive based mutation strategy and promising information

Differential Evolution (DE), as a population-based meta-heuristic global optimization technique, has shown excellent performance in handling optimization problems in continuous spaces. Despite its effectiveness, the DE algorithm suffers from shortcomings such as complexity of parameter selection and limitations of the mutation strategy. Therefore, this paper presents a new strategy for generating trial vectors based on a hierarchical archive, which integrates promising information during evolution with current populations to obtain a good perception of the objective landscape. Moreover, to mitigate mis-scaling by scale factor, an adaptive parameter generation mechanism with hierarchical selection (APSH) is proposed. Furthermore, a novel population diversity metric technique and a restart mechanism based on wavelet functions is introduced in this paper. Comparative experiments were conducted to evaluate the performance of the proposed algorithm using 100 benchmark functions from the CEC2013, CEC2014, CEC2017, and CEC2022 test suites. The results demonstrate that the HAPI-DE algorithm outperforms or is on par with 6 recent powerful DE variants. Additionally, HAPI-DE was utilized in parameter extraction for the photovoltaic model STP6-120/36. The findings suggest that our algorithm, HAPI-DE, demonstrates competitiveness when compared to the 6 other DE variants.

Collaborative resource allocation-based differential evolution for solving numerical optimization problems

Differential evolution (DE) is an efficient and powerful population-based search algorithm for solving numerical optimization problems in continuous spaces. It has been proven that multi-strategy DE algorithms are more effective than single-strategy DE algorithms in addressing benchmark and real-world problems. However, most multi-strategy DE variants focus on maintaining population diversity and balancing exploitation and exploration, ignoring the dynamic allocation of computational resources. Moreover, the success of these algorithms often depends on additional designed techniques, leading to increased computational complexity. In this paper, the Collaborative Resource Allocation-based Differential Evolution (CRADE) is introduced. It involves a collaborative resource allocation mechanism that utilizes the historical performance ranking of three mutation strategies to automatically allocate computational resources to various subpopulations during the search process. The parameter adaptation technique is used to adjust the associated control parameters of different mutation strategies. As a result, the most efficient mutation strategy consumes the majority of computational resources at different search stages to mitigate inefficient search under constrained resources. The performance of CRADE is evaluated on the well-known CEC2013 benchmark function set. The paper also investigates its application in the parameter identification of photovoltaic solar cells and modules. The overall results show that CRADE exhibits superior and competitive performance compared to other state-of-the-art algorithms. Consequently, CRADE has emerged as a novel and effective approach for addressing numerical optimization problems, distinguished by its excellence, practicality, and unwavering reliability.

Martial Art Learning Optimization: A Novel Metaheuristic Algorithm for Night Image Enhancement

<p>This paper proposes a human behavior-based optimization algorithm, Martial Arts Learning Optimization (MALO), for optimization problems in continuous spaces. The algorithm simulates the process of characters in martial arts learning so as to apply it to optimization problems. Characters in martial arts stories usually go through multiple stages of learning martial arts, such as self-study and leader teaching. Multiple learning stages of characters are modeled in this paper, utilizing the wisdom of the characters learning martial arts in the novel, enabling the optimization process. To verify and analyze the performance of the proposed algorithm, the algorithm is numerically tested on 30 benchmark functions, and it is found that its performance was better than the state-of-the-art nine algorithms. In addition, the algorithm is also used to solve the problem of nighttime image brightness enhancement. Compared with other image enhancement methods, the proposed MALO algorithm has superior results in both visual effects and quantitative image quality assessments.</p> <p> </p>

Feature selection using differential evolution for microarray data classification

The dimensions of microarray datasets are very large, containing noise and redundancy. The problem with microarray datasets is the presence of more features compared to the number of samples, which adversely affects algorithm performance. In other words, the number of columns exceeds the number of rows. Therefore, to extract precise information from microarray datasets, a robust technique is required. Microarray datasets play a critical role in detecting various diseases, including cancer and tumors. This is where feature selection techniques come into play. In recent times, feature selection (FS) has gained significant importance as a data preparation method, particularly for high-dimensional data. It is preferable to address classification problems with fewer features while maintaining high accuracy, as not all features are necessary to achieve this goal. The primary objective of feature selection is to identify the optimal subset of features. In this context, we will employ the Differential Evolution (DE) algorithm. DE is a population-based stochastic search approach that has found widespread use in various scientific and technical domains to solve optimization problems in continuous spaces. In our approach, we will combine DE with three different classification algorithms: Random Forest (RF), Decision Tree (DT), and Logistic Regression (LR). Our analysis will include a comparison of the accuracy achieved by each algorithmic model on each dataset, as well as the fitness error for each model. The results indicate that when feature selection was used the results were better compared to the results where the feature selection was not used.

Two-level parameter cooperation-based population regeneration framework for differential evolution

Differential evolution (DE) has shown excellent performance in dealing with optimization problems in continuous space, but it still faces the problems of population stagnation and premature convergence. To address these difficulties and enhance the performance of existing DE algorithms, this paper proposes a two-level parameter cooperation-based population regeneration (TPPR) framework that can easily be integrated with various DE algorithms without increasing the time consumption. In the TPPR framework, whether an individual executes the regeneration operation depends on a specific cooperation strategy for a macroparameter and a microparameter, and the regeneration operation updates the positions of the selected individuals using a dynamic coordination strategy for the Cauchy and Gaussian distributions, that are constructed using those two parameters. Comparative experiments of ten representative DE algorithms with and without the TPPR framework on thirty functions with different dimensions from the IEEE CEC 2014 test platform and four real-life problems are conducted to verify the effectiveness of the TPPR framework. The comparative results based on the improvement rate and deterioration rate indicate that using the TPPR framework, the performance of the adopted DE algorithms can be significantly improved with a very high probability, and the possibility of deterioration is very low.

Novel binary differential evolution algorithm for knapsack problems

The capability of the conventional differential evolution algorithm to solve optimization problems in continuous spaces has been well demonstrated and documented in the literature. However, differential evolution has been commonly considered inapplicable for several binary/permutation-based real-world problems because of its arithmetic reproduction operator. Moreover, many limitations of the standard differential evolution algorithm, such as slow convergence and becoming trapped in local optima, have been defined. In this paper, a novel technique which makes a simple differential evolution algorithm suitable and very effective for solving binary-based problems, such as binary knapsack ones, is proposed. It incorporates new components, such as representations of solutions, a mapping method and a diversity technique. Also, a new efficient fitness evaluation approach for calculating and, at the same time, repairing knapsack candidate solutions, is introduced. To assess the performance of this new algorithm, four datasets with a total of 44 instances of binary knapsack problems are considered. Its performance and those of 22 state-of-the-art algorithms are compared, with the experimental results demonstrating its superiority in terms of both the quality of solutions and computational times. It is also capable of finding new solutions which are better than the current best ones for five large knapsack problems.

The Buttressed Walls Problem: An Application of a Hybrid Clustering Particle Swarm Optimization Algorithm

The design of reinforced earth retaining walls is a combinatorial optimization problem of interest due to practical applications regarding the cost savings involved in the design and the optimization in the amount of CO 2 emissions generated in its construction. On the other hand, this problem presents important challenges in computational complexity since it involves 32 design variables; therefore we have in the order of 10 20 possible combinations. In this article, we propose a hybrid algorithm in which the particle swarm optimization method is integrated that solves optimization problems in continuous spaces with the db-scan clustering technique, with the aim of addressing the combinatorial problem of the design of reinforced earth retaining walls. This algorithm optimizes two objective functions: the carbon emissions embedded and the economic cost of reinforced concrete walls. To assess the contribution of the db-scan operator in the optimization process, a random operator was designed. The best solutions, the averages, and the interquartile ranges of the obtained distributions are compared. The db-scan algorithm was then compared with a hybrid version that uses k-means as the discretization method and with a discrete implementation of the harmony search algorithm. The results indicate that the db-scan operator significantly improves the quality of the solutions and that the proposed metaheuristic shows competitive results with respect to the harmony search algorithm.

Multi-Strategy Adaptive Cuckoo Search Algorithm

Cuckoo search algorithm (CS) is a powerful biological-inspired search algorithm, which is widely used in continuous space optimization problems. However, a single search strategy in CS makes all cuckoos have similar search behavior, and it is liable to plunges into local optimal. In addition, whether CS can successfully solve a problem largely depends on the value of control parameters. Using the trial and error method to determine the value of parameters will cost a lot of computational expense frequently. In order to solve these problems, a multi-strategy adaptive cuckoo algorithm (MSACS) is proposed in this paper. Firstly, five search strategies are adapted to cooperate with each other, and the use of various previous strategies and control parameters are studied. The probability of each strategy being used and the value of control parameters are changed adaptively. Then, the performance of MSACS is tested and evaluated on 24 common benchmark functions. Finally, several advanced CS algorithms, particle swarm algorithm (PSO) and differential evolution algorithm (DE) variants will be compared with MSACS. The results show that the MSACS is better than the algorithms above.

Teaching–learning-based optimization with differential and repulsion learning for global optimization and nonlinear modeling

Teaching–learning-based optimization (TLBO) algorithm is one of the recently proposed optimization algorithms. It has been successfully used for solving optimization problems in continuous spaces. To improve the optimization performance of the TLBO algorithm, a modified TLBO algorithm with differential and repulsion learning (DRLTLBO) is presented in this paper. In the proposed algorithm, the differential evolution (DE) operators are introduced into the teacher phase of DRLTLBO to increase the diversity of the new population. In the learner phase of DRLLBO, local learning method or repulsion learning method are adopted according to a certain probability to make learners search knowledge from different directions. In the local learning method, learners learn knowledge not only from the best learner but also from another random learner of their neighbors. In the repulsion learning method, learners learn knowledge from the best learner and keep away from the worst learner of their neighbors. Moreover, self-learning method is adopted to improve the exploitation ability of learners when they are not changed in some continuous generations. To decrease the blindness of random self-learning method, the history information of the corresponding learners in some continuous generations is used in self-learning phase. Furthermore, all learners are regrouped after a certain iterations to improve the local diversity of the learners. In the end, DRLTLBO is tested on 32 benchmark functions with different characteristics and two typical nonlinear modeling problems, and the comparison results show that the proposed DRLTLBO algorithm has shown interesting outcomes in some aspects.

Exploratory Landscape Analysis of Continuous Space Optimization Problems Using Information Content

Data-driven analysis methods, such as the information content of a fitness sequence, characterize a discrete fitness landscape by quantifying its smoothness, ruggedness, or neutrality. However, enhancements to the information content method are required when dealing with continuous fitness landscapes. One typically employed adaptation is to sample the fitness landscape using random walks with variable step size. However, this adaptation has significant limitations: random walks may produce biased samples, and uncertainty is added because the distance between observations is not accounted for. In this paper, we introduce a robust information content-based method for continuous fitness landscapes, which addresses these limitations. Our method generates four measures related to the landscape features. Numerical simulations are used to evaluate the efficacy of the proposed method. We calculate the Pearson correlation coefficient between the new measures and other well-known exploratory landscape analysis measures. Significant differences on the measures between benchmark functions are subsequently identified. We then demonstrate the practical relevance of the new measures using them as class predictors on a machine learning model, which classifies the benchmark functions into five groups. Classification accuracy greater than 90% was obtained, with computational costs bounded between 1% and 10% of the maximum function evaluation budget. The results demonstrate that our method provides relevant information, at a low cost in terms of function evaluations.

A Novel Probability Binary Particle Swarm Optimization Algorithm and Its Application

Particle swarm optimization (PSO), an intelligent optimization algorithm inspired by the flocking behavior of birds, has been shown to perform well and widely used to solve the continuous problem. But the traditional PSO and most of its variants are developed for optimization problems in continuous space, which are not able to solve the binary combinational optimization problem. To tackle this problem, Kennedy extended the PSO and proposed a discrete binary PSO. But its performance is not ideal and just few further works were conducted based on it. In this paper, we propose a novel probability binary particle swarm optimization (PBPSO) algorithm for discrete binary optimization problems. In PBPSO, a novel updating strategy is adopted to update the swarm and search the global solution, which further simplify the computations and improve the optimization ability. To investigate the performance of the proposed PBPSO, the multidimensional knapsack problems are used as the test benchmarks. The experimental results demonstrate that PBPSO has a better performance for solving the multidimensional knapsack problem in terms of convergent speed and global search ability.

Greedy 선택방법을 적용한 빠른 모의 담금질 방법

모의 담금질 방법은 널리 사용되는 최적화 알고리즘들 중의 하나로서, 그 해의 수렴성이 수학적으로 증명되어 있는 장점이 있다. 하지만 원래의 모의 담금질 방법은 수렴 속도가 매우 느리기 때문에 복잡한 문제에 적용하기 힘들고, 이를 해결하기 위해서 빠른 모의 담금질 방법과 같은 다양한 방법이 연구되고 있다. 본 논문에서는, greedy 선택방법을 적용한 모의 담금질 방법을 제안하고, 이 알고리즘이 연속적인 공간에서의 최적화 문제에 대해서 전역 최적점을 찾아낸다는 것을 확률적으로 증명한다. greedy 선택방법은 무조건 좋은 해를 선택하기 때문에, 확률적으로 좋지 않은 해를 선택할 가능성이 있는 Metropolis 선택방법에 비해 빠른 수렴속도를 얻을 수 있다. 컴퓨터 모의 실험 결과, greedy 선택방법을 사용한 모의 담금질 방법이 기존의 빠른 모의 담금질 방법과 비슷한 성능을 보이는 해를 더 빠른 속도로 찾을 수 있음을 보인다. 또한, greedy 선택방법에서는 선택 가능한 상태들의 비용함수 값의 우열관계만을 이용하여 선택하기 때문에 비용 함수의 크기 조정에 무관하게 적용할 수 있다는 장점이 있다. Due to the mathematical convergence property, Simulated Annealing (SA) has been one of the most popular optimization algorithms. However, because of its problem of slow convergence in the practical use, many variations of SA like Fast SA (FSA) have been developed for faster convergence. In this paper, we propose and prove that Greedy SA (GSA) also finds the global optimum in probability in the continuous space optimization problems. Because the greedy selection does not allow the cost to become worse, GSA is expected to have faster convergence than the conventional FSA that uses Metropolis selection. In the computer simulation, the proposed method is shown to have as good performance as FSA with Metropolis selection in the viewpoints of the convergence speed and the quality of the found solution. Furthermore, the greedy selection does not concern the cost value itself but uses only dominance of the costs of solutions, which makes GSA invariant to the problem scaling.

Convergence theorems for quantum annealing

We prove several theorems to give sufficient conditions for convergence of quantum annealing, which is a protocol to solve generic optimization problems by quantum dynamics. In particular, the property of strong ergodicity is proved for the path-integral Monte Carlo implementation of quantum annealing for the transverse Ising model under a power decay of the transverse field. This result is to be compared with the much slower inverse-log decay of temperature in the conventional simulated annealing. Similar results are proved for the Green's function Monte Carlo approach. Optimization problems in continuous space of particle configurations are also discussed.