Continuous Global Optimization Research Articles

Improving quality of service for Internet of Things(IoT) in real life application: A novel adaptation based Hybrid Evolutionary Algorithm

In this paper, we address critical challenges in IoT sensor lifespan, service latency, and coverage area, all impacting energy consumption in smart agriculture applications. To enhance the quality of service (QoS) while prolonging the energy efficiency of smart sensors, a novel optimization algorithm is introduced. Referred to as the ”Adaptation-Based Hybrid Evolutionary Algorithm,” this innovative approach combines the strengths of Grey Wolf Optimizers (GWO) and Differential Evolution (DE) algorithms. The methodology involves a new adaptation-based strategy and incorporates a hybrid algorithm that synergizes the exploratory and exploitative capabilities of both GWO and DE algorithms. This hybrid approach is leveraged to meticulously select optimal mutation new adaptation services, drawing from the GWO and DE algorithm frameworks. Notably, the algorithm’s control parameters autonomously adjust through insights gained from prior evolutionary searches. Furthermore, we enhance the DE-based crossover technique by integrating the proficient search capabilities of the GWO algorithm, renowned for tackling continuous global optimization problems. To validate our approach, we apply it to IoT scenarios and optimize QoS through a fitness function that comprehensively accounts for energy consumption, coverage rate, lifespan, and latency. Comparative evaluations against standard algorithms underscore the superior performance of our proposed methodology, particularly evident in its application to IoT-smart agriculture settings.

Chaotic opposition learning with mirror reflection and worst individual disturbance grey wolf optimizer for continuous global numerical optimization

The effective meta-heuristic technique known as the grey wolf optimizer (GWO) has shown its proficiency. However, due to its reliance on the alpha wolf for guiding the position updates of search agents, the risk of being trapped in a local optimal solution is notable. Furthermore, during stagnation, the convergence of other search wolves towards this alpha wolf results in a lack of diversity within the population. Hence, this research introduces an enhanced version of the GWO algorithm designed to tackle numerical optimization challenges. The enhanced GWO incorporates innovative approaches such as Chaotic Opposition Learning (COL), Mirror Reflection Strategy (MRS), and Worst Individual Disturbance (WID), and it’s called CMWGWO. MRS, in particular, empowers certain wolves to extend their exploration range, thus enhancing the global search capability. By employing COL, diversification is intensified, leading to reduced solution stagnation, improved search precision, and an overall boost in accuracy. The integration of WID fosters more effective information exchange between the least and most successful wolves, facilitating a successful exit from local optima and significantly enhancing exploration potential. To validate the superiority of CMWGWO, a comprehensive evaluation is conducted. A wide array of 23 benchmark functions, spanning dimensions from 30 to 500, ten CEC19 functions, and three engineering problems are used for experimentation. The empirical findings vividly demonstrate that CMWGWO surpasses the original GWO in terms of convergence accuracy and robust optimization capabilities.

Continuous global optimization on fractals through $$\alpha $$-dense curves

Continuous global optimization on fractals through $$\alpha $$-dense curves

Fitness-Distance-Constraint (FDC) based guide selection method for constrained optimization problems

In the optimization of constrained type problems, the main difficulty is the elimination of the constraint violations in the evolutionary search process. Evolutionary algorithms are designed by default according to the requirements of unconstrained and continuous global optimization problems. Since there are no constraint functions in these type of problems, the constraint violations are not considered in the design of the guiding mechanism of evolutionary algorithms. In this study, two new methods were introduced to redesign the evolutionary algorithms in accordance with the requirements of constrained optimization problems. These were (i) constraint space-based, called Fitness-Distance-Constraint (FDC), selection method and (ii) dynamic guiding mechanism. Firstly, thanks to the FDC guide selection method, the constraint violation values of the individuals in the population were converted into score values and the individuals who increase the diversity in the search process were selected as guide. On the other hand, in dynamic guiding mechanism, the FDC method was applied in case of constraint violation, otherwise the default guide selection method was used The proposed methods were used to redesign the guiding mechanism of adaptive guided differential evolution (AGDE), a current evolutionary algorithm, and the FDC-AGDE algorithm was designed. The performance of the FDC-AGDE was tested on eleven different constrained real-world optimization problems. The results of the FDC-AGDE and AGDE were evaluated using the Friedman and Wilcoxon test methods. According to Wilcoxon pairwise results, the FDC-AGDE showed better performance than the AGDE in nine of the eleven problems and equal performance in two of the eleven problems. Moreover, the proposed algorithm was compared with the competitive and up-to-date MHS algorithms in terms of the results of Friedman test, Wilcoxon test, feasibility rate, and success rate. According to Friedman test results, the first three algorithms were the FDC-AGDE, LSHADE-SPACMA, and AGDE algorithms with the score of 2.69, 4.05, and 4.34, respectively. According to the mean values of the success rates obtained from the eleven problems, the FDC-AGDE, LSHADE-SPACMA, and AGDE algorithms ranked in the first three with the success rates of 67%, 48% and 28%, respectively. Consequently, the FDC-AGDE algorithm showed a superior performance comparing with the competing MHS algorithms. According to the results, it is expected that the proposed methods will be widely used in the constrained optimization problems in the future.

Adaptive differential evolution algorithm with a pheromone-based learning strategy for global continuous optimization

Abstract Differential evolution algorithm (DE) is a well-known population-based method for solving continuous optimization problems. It has a simple structure and is easy to adapt to a wide range of applications. However, with suitable population sizes, its performance depends on the two main control parameters: scaling factor (F ) and crossover rate (CR). The classical DE method can achieve high performance by a time-consuming tunning process or a sophisticated adaptive control implementation. We propose in this paper an adaptive differential evolution algorithm with a pheromone-based learning strategy (ADE-PS) inspired by ant colony optimization (ACO). The ADE-PS embeds a pheromone-based mechanism that manages the probabilities associated with the partition values of F and CR. It also introduces a resetting strategy to reset the pheromone at a specific time to unlearn and relearn the progressing search. The preliminary experiments find a suitable number of subintervals (ns) for partitioning the control parameter ranges and the reset period (rs) for resetting the pheromone. Then the comparison experiments evaluate ADE-PS using the suitable ns and rs against some adaptive DE methods in the literature. The results show that ADE-PS is more reliable and outperforms several well-known methods in the literature.

Continuous global optimization of multivariable functions based on Sergeev and Kvasov diagonal approach

Abstract. One of modern global optimization algorithms is method of Strongin and Piyavskii modified by Sergeev and Kvasov diagonal approach. In recent paper we propose an extension of this approach to continuous multivariable functions defined on the multidimensional parallelepiped. It is known that Sergeev and Kvasov method applies only to a Lipschitz continuous function though it effectively extends one-dimensional algorithm to multidimensional case. So authors modify We modify mentioned method to a continuous functions using introduced by Vanderbei ε-Lipschitz property that generalizes conventional Lipschitz inequality. Vanderbei proved that a real valued function is uniformly continuous on a convex domain if and only if it is ε-Lipschitz. Because multidimensional parallelepiped is a convex compact set, we demand objective function to be only continuous on a search domain. We describe extended Strongin’s and Piyavskii’s methods in the Sergeev and Kvasov modification and prove the sufficient conditions for the convergence. As an example of proposed method’s application, at the end of this article we show numerical optimization results of different continuous but not Lipschitz functions using three known partition strategies: “partition on 2”, “partition on 2N” and “effective”. For the first two of them we present formulas for computing a new iteration point and for recalculating the ε-Lipschitz constant estimate. We also show algorithm modification that allows to find a new search point on any algorithm’s step.

Spherical search algorithm with adaptive population control for global continuous optimization problems

Spherical search algorithm (SSA) calculates the spherical boundary and generates new solutions on it by two sub-populations jointly. Many researches have shown that SSA is a promising algorithm, but in some cases, the fixed sub-population size causes it to be prone to search inadequately and easily falling into local optimum. In this paper, a new improved algorithm, named SSAP, is proposed to alleviate these problems. In SSAP, we propose a novel population control strategy to efficiently balance exploration and exploitation. This strategy adaptively adjusts the number of individuals in both sub-populations to improve the search performance of the algorithm. It is realized by adjusting the frequency of search patterns through a cumulative index. Comparative experiments conducted on a large number of benchmark functions show that SSAP significantly outperforms other state-of-the-art algorithms. Additionally, SSAP is used to solve real-world problems to further verify its validity. Finally, the search characteristics and population diversity of SSAP are analyzed.

Limit sets in global multiobjective optimization

ABSTRACT Inspired by the recently introduced branch-and-bound method for continuous multiobjective optimization problems from G. Eichfelder, P. Kirst, L. Meng, O. Stein [A general branch-and-bound framework for continuous global multiobjective optimization. J Glob Optim. 2021;80:195–227], we study for a general class of branch-and-bound methods in which sense the generated terminal enclosure and the terminal provisional nondominated set approximate the nondominated set when the termination accuracy is driven to zero. Our convergence analysis of the enclosures relies on constructions from the above paper, but is self-contained and also covers the mixed-integer case. The analysis for the provisional nondominated set is based on general convergence properties of the epsilon-nondominated set, and hence it is also applicable to other algorithms which generate such points. Furthermore, we discuss post-processing steps for the terminal enclosure and provide numerical illustrations for the cases of two and three objective functions.

An improved firefly algorithm with distance-guided selection strategy and its application

In this paper, to reduce the redundant attractions and incorrect directions of firefly algorithm (FA), a distance-guided selection approach (DSFA) is proposed, which consists of a distance-guided mechanism and selection strategy. Where the designed distance-guided mechanism reduces the attractions and plays as a classifier for global search and local search, the suggested selection strategy can avoid local search falling into traps, thereby increasing the probability of correct direction. With the good cooperation of these two approaches, DSFA obtains a good balance of exploration and exploitation. To confirm the performance of the proposed algorithm, excessive experiments are conducted on CEC2013 benchmark functions, large-scale optimization problems CEC2008, and software defect prediction (SDP). In the comparison with the 5 advanced FA variants, DSFA provides the optimal solutions to most CEC2013 problems. Besides, when facing the problems of class imbalance and the dimensional explosion of datasets, DSFA greatly improves the performance of machine learning classifiers employed by SDP. It can be concluded that DSFA is an effective method for global continuous optimization problems.

An opposition learning and spiral modelling based arithmetic optimization algorithm for global continuous optimization problems

In engineering applications, many real-world optimization problems are nonlinear with multiple local optimums. Traditional algorithms that require gradients are not suitable for these problems. Meta-heuristic algorithms are popularly employed to deal with these problems because they can promisingly jump out of local optima and do not need any gradient information. The arithmetic optimization algorithm (AOA), a recently developed meta-heuristic algorithm, uses arithmetic operators (multiplication, division, subtraction, and addition) to solve optimization problems including nonlinear ones. However, the exploration and exploitation of AOA are not effective to handle some complex optimization problems. In this paper, an opposition learning and spiral modelling based AOA, namely OSAOA, is proposed for enhancing the optimization performance. It improves AOA from two perspectives. In the first perspective, the opposition-based learning (OBL) is committed to taking both candidate solutions and their opposite solutions into consideration for improving the global search with a high probability of jumping out of local minima. Then, the spiral modelling is introduced as the second perspective, which is particularly useful in getting the solutions gathering faster and accelerating the convergence speed in the later stage. In addition, OSAOA is compared with other existing advanced meta-heuristic algorithms based on 23 benchmark functions and four engineering problems: the three-bar truss design, the cantilever beam design, the pressure vessel design, and the tubular column design. From our simulations and engineering applications, the proposed OSAOA can provide better optimization results in dealing with these real-world optimization problems.

A novel enhanced global exploration whale optimization algorithm based on Lévy flights and judgment mechanism for global continuous optimization problems

A novel enhanced global exploration whale optimization algorithm based on Lévy flights and judgment mechanism for global continuous optimization problems

Giant Trevally Optimizer (GTO): A Novel Metaheuristic Algorithm for Global Optimization and Challenging Engineering Problems

Metaheuristic algorithms are becoming powerful methods for solving continuous global optimization and engineering problems due to their flexible implementation on the given problem. Most of these algorithms draw their inspiration from the collective intelligence and hunting behavior of animals in nature. This paper proposes a novel metaheuristic algorithm called the Giant Trevally Optimizer (GTO). In nature, giant trevally feeds on many animals, including fish, cephalopods, and seabirds (sooty terns). In this work, the unique strategies of giant trevally when hunting seabirds are mathematically modeled and are divided into three main steps. In the first step, the foraging movement patterns of giant trevallies are simulated. In the second step, the giant trevallies choose the appropriate area in terms of food where they can hunt for prey. In the last step, the trevally starts to chase the seabird (prey). When the prey is close enough to the trevally, the trevally jumps out of the water and attacks the prey in the air or even snatches the prey from the water surface. The performance of GTO is compared against state-of-the-art metaheuristics for global optimization on a set of forty benchmark functions with different characteristics and five complex engineering problems. The comparative study, scalability analysis, statistical analysis based on the Wilcoxon rank sum test, and the findings suggest that the proposed GTO is an efficient optimizer for global optimization. Note that the MATLAB source codes for GTO will be publicly available after the acceptance of the paper.

A novel enhanced exploration firefly algorithm for global continuous optimization problems

A novel enhanced exploration firefly algorithm for global continuous optimization problems

Correction to: A general branch-and-bound framework for continuous global multiobjective optimization

The publisher introduced an error in the last sentence of the proof for Lemma 3.2.

A general branch-and-bound framework for continuous global multiobjective optimization

Current generalizations of the central ideas of single-objective branch-and-bound to the multiobjective setting do not seem to follow their train of thought all the way. The present paper complements the various suggestions for generalizations of partial lower bounds and of overall upper bounds by general constructions for overall lower bounds from partial lower bounds, and by the corresponding termination criteria and node selection steps. In particular, our branch-and-bound concept employs a new enclosure of the set of nondominated points by a union of boxes. On this occasion we also suggest a new discarding test based on a linearization technique. We provide a convergence proof for our general branch-and-bound framework and illustrate the results with numerical examples.

Binocular camera calibration based on dual update strategy weighted differential evolution particle swarm optimization

Aiming at the problem of camera calibration with multi-parameters in space target pose measurement, a novel calibration method based on dual update strategy weighted differential evolution particle swarm optimization was proposed . An adaptive judgment factor was constructed to control the usage proportion of weighted differential evolution (WDE) algorithm and particle swarm optimization (PSO) algorithm in each iteration process, which allowed the PSO or WDE algorithm to update individuals according to the probability laws. Moreover, through the information exchange mechanism, the individual obtained by the WDE operation was adopted to guide the individual evolution process operated by PSO algorithm. The proposed WDEPSO algorithm could ensure the diversity and effectiveness of the individual evolution of the population, and it was coupled with the camera nonlinear calibration model and parameters. Consequently, the proposed method could simultaneously realize the combined nonlinear and global continuous optimization, which overcomed the local convergence problem caused by the limited feature points arise from the saturated light intensity of the target space ambient. Experiments suggest that the objective function value optimized by the WDEPSO method is smaller, and the proposed method obtains the higher calibration accuracy. The standard gague measurement error obtained by the calibration parameters is less than 0.40 mm, the reconstruction attitude accuracy of the target under large angular motion is better than 0.30°, as well as the repeatability measurement results are stable.

An Adaptive Multi-Population Optimization Algorithm for Global Continuous Optimization

Nowadays, there are various optimization problems that exact mathematical methods are not applicable. Metaheuristics are considered as efficient approaches for finding the solutions. Yet there are many real-world problems that consist of different properties. For instance, financial portfolio optimization may contain many dimensions for different sets of assets, which suggests the need of a more adaptive metaheuristic method for tackling such problems. However, few existing metaheuristics can achieve robust performance across these variable problems even though they may obtain impressive results in specific benchmark problems. In this paper, a metaheuristic named the Adaptive Multi-Population Optimization (AMPO) is proposed for continuous optimization. The algorithm hybridizes yet modifies several useful operations like mutation and memory retention from evolutionary algorithms and swarm intelligence (SI) techniques in a multi-population manner. Furthermore, the diverse control on multiple populations, solution cloning and reset operation are designed. Compared with other metaheuristics, the AMPO can attain an adaptive balance between the capabilities of exploration and exploitation for various optimization problems. To demonstrate its effectiveness, the AMPO is evaluated on 28 well-known benchmark functions. Also, the parameter sensitivity analysis and search behavior study are conducted. Finally, the AMPO is validated on its applicability through a portfolio optimization problem as a challenging example of real-world applications. The benchmark results show that the AMPO achieves a better performance than those of nine state-of-the-art metaheuristics including the IEEE CEC winning algorithms, recent SI and multi-population/hybrid metaheuristics. Besides, the AMPO can consistently produce a good performance in portfolio optimization.

A covering method for continuous global optimisation

In this paper, we improve the reducing transformation method for solving a large class of global optimisation problems. The reducing transformation method allows us to transform a multidimensional ...

A covering method for continuous global optimisation

A covering method for continuous global optimisation

Проблемно-ориентированный программный комплекс для численного решения и исследования задач структурной биоинформатики с использованием методов стохастической оптимизации

In this paper presented problem-oriented software package for performing computational experiments in structural bioinformatics problems: protein structure prediction and peptide-protein docking. These problemsare formulated as continuous global optimization tasks. The primary purpose of the presented software package is to provide functionality for performing computational experiments using various stochastic optimization methods. To perform experiments for the selected task the objective function and search space are provided for user. In this work the software packagefunctionality, implementation features and the results of various experimentsare presented. The software is written in C++ and provides the possibility ofusing parallel computing using OpenMP technology. The presented package is open source software that stored in the GitHub repositories.