Global Optimization Problems Research Articles

Solving higher dimensional expensive black box global optimization problems using sparse directional search on surrogates

AbstractWe present a new algorithm Directional Optimization Search with Surrogate (DOSS), for optimizing problems with box constraints and a computationally expensive black-box objective function. DOSS is a radial basis function (RBF) based method that mainly focuses on higher dimensional and computationally expensive objective functions that can be multimodal. DOSS introduces three new techniques not previously used in earlier RBF algorithms, including using a combination of the coordinates knowledge level, fewer initial sampling points, and the surrogate’s gradient information. Numerical results on a test set including 14 test problems with 36, 48, and 60 dimensions show that DOSS outperforms two recently published algorithms RBFOpt and TuRBO, and earlier RBF algorithms such as DYCORS. TuRBO is a Gaussian process based optimization algorithm, which outperformed earlier state-of-the-art methods. DOSS algorithm also has a good performance on real-world optimization problems, including robot pushing and rover trajectory planning problems. Almost sure convergence for the DOSS algorithm is also proven in this paper. An implementation of DOSS is available at https://doi.org/10.5281/zenodo.13731558.

A New Hybrid Improved Arithmetic Optimization Algorithm for Solving Global and Engineering Optimization Problems

The Arithmetic Optimization Algorithm (AOA) is a novel metaheuristic inspired by mathematical arithmetic operators. Due to its simple structure and flexible parameter adjustment, the AOA has been applied to solve various engineering problems. However, the AOA still faces challenges such as poor exploitation ability and a tendency to fall into local optima, especially in complex, high-dimensional problems. In this paper, we propose a Hybrid Improved Arithmetic Optimization Algorithm (HIAOA) to address the issues of susceptibility to local optima in AOAs. First, grey wolf optimization is incorporated into the AOAs, where the group hunting behavior of GWO allows multiple individuals to perform local searches at the same time, enabling the solution to be more finely tuned and avoiding over-concentration in a particular region, which can improve the exploitation capability of the AOA. Second, at the end of each AOA run, the follower mechanism and the Cauchy mutation operation of the Sparrow Search Algorithm are selected with the same probability and perturbed to enhance the ability of the AOA to escape from the local optimum. The overall performance of the improved algorithm is assessed by selecting 23 benchmark functions and using the Wilcoxon rank-sum test. The results of the HIAOA are compared with other intelligent optimization algorithms. Furthermore, the HIAOA can also solve three engineering design problems successfully, demonstrating its competitiveness. According to the experimental results, the HIAOA has better test results than the comparator.

Centroid opposition-based backtracking search algorithm for global optimization and engineering problems

Evolutionary algorithms (EAs) have a lot of potential to handle nonlinear and non-convex objective functions. Particularly, the backtracking search algorithm (BSA) is a popular nature-based evolutionary optimization method that has attracted many researchers due to its simple structure and efficiency in problem-solving across diverse fields. However, like other optimization algorithms, BSA is also prone to reduced diversity, local optima, and inadequate intensification capabilities. To overcome the flaws and increase the performance of BSA, this research proposes a centroid opposition-based backtracking search algorithm (CoBSA) for global optimization and engineering design problems. In CoBSA, specific individuals simultaneously acquire current and historical population knowledge to preserve population variety and improve exploration capability. On the other hand, other individuals execute the position from the current population's centroid opposition to progress convergence speed and exploitation potential. In addition, an elite process based on logistic chaotic local search was developed to improve the superiority of the current individuals. The suggested CoBSA was validated on a set of benchmark functions and then employed in a set of application examples. According to extensive numerical results and assessments, CoBSA outperformed the other state-of-the-art methods in terms of accurateness, reliability, and execution capability.

Global optimization: a machine learning approach

AbstractMany approaches for addressing global optimization problems typically rely on relaxations of nonlinear constraints over specific mathematical primitives. This is restricting in applications with constraints that are implicit or consist of more general primitives. Trying to address such limitations, Bertsimas and Ozturk (2023) proposed OCTHaGOn as a way of solving very general global optimization problems by approximating the nonlinear constraints using hyperplane-based decision-trees and then using those trees to construct a unified MIO approximation of the original problem. We provide extensions to this approach, by (i) approximating the original problem using other MIO-representable ML models besides decision trees, such as gradient boosted trees, multi layer perceptrons and suport vector machines (ii) proposing adaptive sampling procedures for more accurate ML-based constraint approximations, (iii) utilizing robust optimization to account for the uncertainty of the sample-dependent training of the ML models, (iv) leveraging a family of relaxations to address the infeasibilities of the final MIO approximation. We then test the enhanced framework in 81 global optimization instances. We show improvements in solution feasibility and optimality in the majority of instances. We also compare against BARON, showing improved optimality gaps and solution times in more than 9 instances.

A New Approach to the Solution of Facility Layout Problems with Filled Function Method

Facility layout problems are generally solved by stochastic methods in the literature. The large number of iterations used in these methods is quite costly in terms of solution time. In this study, in order to get rid of this disadvantage, the facility layout problem was solved using the filled function method, which is known to be very successful in solving global optimization problems. In order to demonstrate the effectiveness of the filled function method, the classical linear facility layout problem was handled in a non-linear manner and the problem was deliberately made more difficult. In order to use the filled function method, the facility layout problem was transformed into an unconstrained and multimodal (including more than one local minima) global optimization problem by using the hyperbolic smoothing technique and the penalty function method. Thus, in this first study in the literature where a deterministic method is combined with the solution of the facility layout problem, it is shown that the non-convex facility layout problem can be solved with the filled function method with very few iterations and short solution times.

A new improved convex underestimator for univariate functions in global optimization

ABSTRACT In this paper, we consider convex underestimators for univariate nonconvex functions over an interval in R . We propose a new convex underestimator that can be used for computing the lower bound of the range of nonconvex functions, or for solving global optimization problems. We show that the new underestimator is tighter than other underestimators which are developed in the literature.

Tighter convex underestimator for general twice differentiable function for global optimization

In this paper, we propose a new convex underestimator for a general C 2 nonconvex function. The new underestimator can be used in branch and bound algorithm for solving global optimization problems. We show that the new underestimator is tighter than the classical underestimator in the α BB method.

An improved sand cat swarm optimization with lens opposition-based learning and sparrow search algorithm

The sand cat swarm optimization (SCSO) is a recently proposed meta-heuristic algorithm. It inspires hunting behavior with sand cats based on hearing ability. However, in the later stage of SCSO, it is easy to fall into local optimality and cannot find a better position. In order to improve the search ability of SCSO and avoid falling into local optimal, an improved algorithm is proposed - Improved sand cat swarm optimization based on lens opposition-based learning and sparrow search algorithm (LSSCSO). A dynamic spiral search is introduced in the exploitation stage to make the algorithm search for better positions in the search space and improve the convergence accuracy of the algorithm. The lens opposition-based learning and the sparrow search algorithm are introduced in the later stages of the algorithm to make the algorithm jump out of the local optimum and improve the global search capability of the algorithm. To verify the effectiveness of LSSCSO in solving global optimization problems, CEC2005 and CEC2022 test functions are used to test the optimization performance of LSSCSO in different dimensions. The data results, convergence curve and Wilcoxon rank sum test are analyzed, and the results show that it has a strong optimization ability and can reach the optimal in most cases. Finally, LSSCSO is used to verify the effectiveness of the algorithm in solving engineering optimization problems.

A new filled function method for solving constrained global optimization problems

ABSTRACT Filled function methods have been considered as effective algorithms for solving global optimization problems. However, their effectiveness is greatly affected by the selection of parameters, the noncontinuous or non-differentiable properties of the constructed filled function. In addition, many of the constructed filled functions are only for unconstrained optimization problems, and they are unable to solve constrained optimization problems. In this paper, a new filled function is constructed for solving constrained global optimization problems. The new filled function has only one parameter which needs to be adjusted, and, when the objective functions and constrained functions are all continuously differentiable functions, the constructed filled function is also a continuously differentiable function. Then, the classical local optimization methods can be used to find a better minimum of the proposed filled function and a few parameter adjustments are needed. At last, a new filled function algorithm for constrained global optimization is developed based on the proposed filled function. The new algorithm is applied to several test examples. The results of the numerical experiments show that the new filled function algorithm is effective and efficient.

Metaheuristics for Solving Global and Engineering Optimization Problems: Review, Applications, Open Issues and Challenges

Metaheuristics for Solving Global and Engineering Optimization Problems: Review, Applications, Open Issues and Challenges

Optimization Techniques in the Localization Problem: A Survey on Recent Advances

Optimization is a mathematical discipline or tool suitable for minimizing or maximizing a function. It has been largely used in every scientific field to solve problems where it is necessary to find a local or global optimum. In the engineering field of localization, optimization has been adopted too, and in the literature, there are several proposals and applications that have been presented. In the first part of this article, the optimization problem is presented by considering the subject from a purely theoretical point of view and both single objective (SO) optimization and multi-objective (MO) optimization problems are defined. Additionally, it is reported how local and global optimization problems can be tackled differently, and the main characteristics of the related algorithms are outlined. In the second part of the article, extensive research about local and global localization algorithms is reported and some optimization methods for local and global optimum algorithms, such as the Gauss–Newton method, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), and so on, are presented; for each of them, the main concept on which the algorithm is based, the mathematical model, and an example of the application proposed in the literature for localization purposes are reported. Among all investigated methods, the metaheuristic algorithms, which do not exploit gradient information, are the most suitable to solve localization problems due to their flexibility and capability in solving non-convex and non-linear optimization functions.

Enhanced Multi-Strategy Slime Mould Algorithm for Global Optimization Problems.

In order to further improve performance of the Slime Mould Algorithm, the Enhanced Multi-Strategy Slime Mould Algorithm (EMSMA) is proposed in this paper. There are three main modifications to SMA. Firstly, a leader covariance learning strategy is proposed to replace the anisotropic search operator in SMA to ensure that the agents can evolve in a better direction during the optimization process. Secondly, the best agent is further modified with an improved non-monopoly search mechanism to boost the algorithm's exploitation and exploration capabilities. Finally, a random differential restart mechanism is developed to assist SMA in escaping from local optimality and increasing population diversity when it is stalled. The impacts of three strategies are discussed, and the performance of EMSMA is evaluated on the CEC2017 suite and CEC2022 test suite. The numerical and statistical results show that EMSMA has excellent performance on both test suites and is superior to the SMA variants such as DTSMA, ISMA, AOSMA, LSMA, ESMA, and MSMA in terms of convergence accuracy, convergence speed, and stability.

A class of one-parameter filled functions with the same local minima as the objective function for global optimization problems

As an effective global optimization method, the filled function algorithm obtains the optimal solution of optimization problems by alternately minimizing the objective function and filled function. One development direction of the filled function method is to construct the filled function with good properties, which directly affects the efficiency of the algorithm and has attracted the attention of scholars. This paper presents a class of one-parameter filled function that is easy to adjust. It is proved theoretically that the filled function is continuously differentiable and has the same local minimizers as the objective function, and these minimizers are all better than the current local minimizer of the objective function. Meanwhile, some natures of the constructed filled function are conducted as followed by a new algorithm is presented. The new filled function algorithm optimizes the iterative framework of the conventional filled function method, improving the efficiency and decreasing the computational cost. The numerical experiments of the new algorithm on several optimization issues are reported with satisfactory computational results, verifying the feasibility and efficiency of the algorithm.

Improved Osprey Optimization Algorithm Based on Two-Color Complementary Mechanism for Global Optimization and Engineering Problems.

Aiming at the problem that the Osprey Optimization Algorithm (OOA) does not have high optimization accuracy and is prone to falling into local optimum, an Improved Osprey Optimization Algorithm Based on a Two-Color Complementary Mechanism for Global Optimization (IOOA) is proposed. The core of the IOOA algorithm lies in its unique two-color complementary mechanism, which significantly improves the algorithm's global search capability and optimization performance. Firstly, in the initialization stage, the population is created by combining logistic chaos mapping and the good point set method, and the population is divided into four different color groups by drawing on the four-color theory to enhance the population diversity. Secondly, a two-color complementary mechanism is introduced, where the blue population maintains the OOA core exploration strategy to ensure the stability and efficiency of the algorithm; the red population incorporates the Harris Hawk heuristic strategy in the development phase to strengthen the ability of local minima avoidance; the green group adopts the strolling and wandering strategy in the searching phase to add stochasticity and maintain the diversity; and the orange population implements the optimized spiral search and firefly perturbation strategies to deepen the exploration and effectively perturb the local optimums, respectively, to improve the overall population diversity, effectively perturbing the local optimum to improve the performance of the algorithm and the exploration ability of the solution space as a whole. Finally, to validate the performance of IOOA, classical benchmark functions and CEC2020 and CEC2022 test sets are selected for simulation, and ANOVA is used, as well as Wilcoxon and Friedman tests. The results show that IOOA significantly improves convergence accuracy and speed and demonstrates high practical value and advantages in engineering optimization applications.

Piranha predation optimization algorithm (PPOA) for global optimization and engineering design problems

A new nature-inspired optimization algorithm, Piranha predation optimization algorithm (PPOA), is proposed based on the unique foraging and predation behaviors of piranhas. Briefly, PPOA consists of three optimization operations, i.e., narrowing down to tear prey, swimming in a straight line, and swimming in a spiral. In this paper, various mathematical models for simulating the behavioral operators are presented in detail to solve different optimization challenges effectively. In this paper, the performance of PPOA is rigorously tested on 23 benchmark optimization functions, CEC2017 competition test set, CEC2020 real-world engineering optimization problems and four engineering design applications to show the applicability of the algorithm in different applications. Comparison experiments with other good and advanced competitive algorithms are conducted to reveal the advantages and performance of PPOA by using performance metrics such as Wilcoxon rank sum test and Friedman mean rank. The comparative results of this paper demonstrate the effectiveness of the proposed algorithmic strategy and its potential in applying it to solving optimization real-world engineering optimization problems.

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.

Improved multi-strategy artificial rabbits optimization for solving global optimization problems

Artificial rabbits optimization (ARO) is a metaheuristic algorithm based on the survival strategy of rabbits proposed in 2022. ARO has favorable optimization performance, but it still has some shortcomings, such as weak exploitation capacity, easy to fall into local optima, and serious decline of population diversity at the later stage. In order to solve these problems, we propose an improved multi-strategy artificial rabbits optimization, called IMARO, based on ARO algorithm. In this paper, a roulette fitness distance balanced hiding strategy is proposed so that rabbits can find better locations to hide more reasonably. Meanwhile, in order to improve the deficiency of ARO which is easy to fall into local optimum, an improved non-monopoly search strategy based on Gaussian and Cauchy operators is designed to improve the ability of the algorithm to obtain the global optimal solution. Finally, a covariance restart strategy is designed to improve population diversity when the exploitation is stagnant and to improve the convergence accuracy and convergence speed of ARO. The performance of IMARO is verified by comparing original ARO algorithm with six basic algorithms and seven improved algorithms. The results of CEC2014, CEC2017, CEC2022 show that IMARO has a good exploitation and exploration ability and can effectively get rid of local optimum. Moreover, IMARO produces optimal results on six real-world engineering problems, further demonstrating its efficiency in solving real-world optimization challenges.

An improved Genghis Khan optimizer based on enhanced solution quality strategy for global optimization and feature selection problems

Feature selection (FS) is the activity of defining the most contributing feature subset among all used features to improve the superiority of datasets with a large number of dimensions by selecting significant features and eliminating redundant and irrelevant ones. Therefore, this process can be seen as an optimization process. The primary goals of feature selection are to decrease the number of dimensions and enhance classification accuracy in many domains, such as text classification, large-scale data analysis, and pattern recognition. Several metaheuristics, such as the Genghis Khan Shark Optimizer Algorithm (GKSO), can assist in optimizing the FS issue. However, these methods tend to converge towards local solutions with a low convergence rate. In order to address this issue in GKSO, a more refined version called I-GKSO is implemented. The I-GKSO suggested introducing a new approach to modify solutions that have low fitness values. In addition, it employs the Enhanced Solution Quality (ESQ) strategy to enhance the exploration phase. It utilizes Quasi-opposite-based learning (QOBL) to enhance the best solution obtained and, consequently, the entire population. The algorithm presented aims to solve the FS problem and has been assessed using benchmark optimization problems from the CEC’2017 and CEC’2022. To assess the efficacy of the I-GKSO, it has been subjected to comparisons with multiple different algorithms. The trials conducted using FS datasets yield a quantitative consideration of the I-GKSO's capacity to attain the most optimal subset of features. Furthermore, Wilcoxon and Friedman's non-parametric tests were accomplished to support the performance of the proposed method.

Metaheuristic algorithm inspired by enterprise development for global optimization and structural engineering problems with frequency constraints

In this study, a novel metaheuristic optimization algorithm inspired by the enterprise development (ED) process was developed. This process encompasses tasks, structure, technology, and human interactions. A mechanism for switching activities was utilized to determine each step by updating the searched solutions. The ED optimizer underwent evaluation against 50 mathematical functions and 54 IEEE Congress on Evolutionary Computation (CEC) functions, and it was compared with six up-to-date algorithms, three winners of CEC 2020 in real-world single-objective constrained optimization, and ten well-known algorithms. The evaluation results revealed that the ED optimizer outperformed the algorithms in mathematical tests. Using finite element simulation, this novel method was applied to minimize steel structure component weights under various frequency constraints. The engineering designs included a 37-bar planar truss, a 52-bar dome, a 72-bar space truss, a 600-bar dome, and a 1,410-bar dome. Optimization results for these structures showed that the developed ED optimizer yielded the optimal solution and required fewer function evaluations. In conclusion, the ED optimizer is a superior metaheuristic algorithm that can effectively solve complex structural design problems.

EOFA: An Extended Version of the Optimal Foraging Algorithm for Global Optimization Problems

The problem of finding the global minimum of a function is applicable to a multitude of real-world problems and, hence, a variety of computational techniques have been developed to efficiently locate it. Among these techniques, evolutionary techniques, which seek, through the imitation of natural processes, to efficiently obtain the global minimum of multidimensional functions, play a central role. An evolutionary technique that has recently been introduced is the Optimal Foraging Algorithm, which is a swarm-based algorithm, and it is notable for its reliability in locating the global minimum. In this work, a series of modifications are proposed that aim to improve the reliability and speed of the above technique, such as a termination technique based on stochastic observations, an innovative sampling method and a technique to improve the generation of offspring. The new method was tested on a series of problems from the relevant literature and a comparative study was conducted against other global optimization techniques with promising results.