Constrained Benchmark Functions Research Articles

Unmanned Aerial Vehicle 3D Path Planning Based on an Improved Artificial Fish Swarm Algorithm

A well-organized path can assist unmanned aerial vehicles (UAVs) in performing tasks efficiently. The artificial fish swarm algorithm (AFSA) is a widely used intelligent optimization algorithm. However, the traditional AFSA exhibits issues of non-uniform population distribution and susceptibility to local optimization. Despite the numerous AFSA variants introduced in recent years, many of them still grapple with challenges like slow convergence rates. To tackle the UAV path planning problem more effectively, we present an improved AFSA algorithm (IAFSA), which is primarily rooted in the following considerations: (1) The prevailing AFSA variants have not entirely resolved concerns related to population distribution disparities and a predisposition for local optimization. (2) Recognizing the specific demands of the UAV path planning problem, an algorithm that can combine global search capabilities with swift convergence becomes imperative. To evaluate the performance of IAFSA, it was tested on 10 constrained benchmark functions from CEC2020; the effectiveness of the proposed strategy is verified on the UAV 3D path planning problem; and comparative algorithmic experiments of IAFSA are conducted in different maps. The results of the comparison experiments show that IAFSA has high global convergence ability and speed.

An enhanced surrogate-assisted differential evolution for constrained optimization problems

The application of evolutionary algorithms (EAs) to complex engineering optimization problems may present difficulties as they require many evaluations of the objective functions by computationally expensive simulation procedures. To deal with this issue, surrogate models have been employed to replace those expensive simulations. In this work, a surrogate-assisted evolutionary optimization procedure is proposed. The procedure combines the differential evolution method with a $$k$$ -nearest neighbors (k-NN) similarity-based surrogate model. In this approach, the database that stores the solutions evaluated by the exact model, which are used to approximate new solutions, is managed according to a merit scheme. Constraints are handled by a rank-based technique that builds multiple separate queues based on the values of the objective function and the violation of each constraint. Also, to avoid premature convergence of the method, a strategy that triggers a random reinitialization of the population is considered. The performance of the proposed method is assessed by numerical experiments using 24 constrained benchmark functions and 5 mechanical engineering problems. The results show that the method achieves optimal solutions with a remarkably reduction in the number of function evaluations compared to the literature.

MaOMFO: Many-objective moth flame optimizer using reference-point based non-dominated sorting mechanism for global optimization problems

Many-objective optimization (MaO) deals with a large number of conflicting objectives in optimization problems to acquire a reliable set of appropriate non-dominated solutions near the true Pareto front, and for the same, a unique mechanism is essential. Numerous papers have reported multi-objective evolutionary algorithms to explain the absence of convergence and diversity variety in many-objective optimization problems. One of the most encouraging methodologies utilizes many reference points to segregate the solutions and guide the search procedure. The above-said methodology is integrated into the basic version of the Moth Flame Optimization (MFO) algorithm for the first time in this paper. The proposed Many-Objective Moth Flame Optimization (MaOMFO) utilizes a set of reference points progressively decided by the hunt procedure of the moth flame. It permits the calculation to combine with the Pareto front yet synchronize the decent variety of the Pareto front. MaOMFO is employed to solve a wide range of unconstrained and constrained benchmark functions and compared with other competitive algorithms, such as non-dominated sorting genetic algorithm, multi-objective evolutionary algorithm based on dominance and decomposition, and novel multi-objective particle swarm optimization using different performance metrics. The results demonstrate the superiority of the algorithm as a new many-objective algorithm for complex many-objective optimization problems.

Hybrid teaching-learning with comprehensive learning capability for electromagnetic device design problems

Many optimal design problems in the engineering field are nonlinear, multivariate, mixed integer, multimodal, and constrained. Meta-heuristic approaches have been widely used to solve these complex problems, but most of them are often sensitive to the settings of tuning parameters for different optimization problems, and suffer from premature convergence during the evolution process. This article proposes a novel hybrid teaching-learning-based optimization (HTLBO) algorithm to tackle this problem. A comprehensive teaching-learning mechanism with no adjustable parameters is introduced to improve the global optimal solution while in the meantime maintaining the solution diversity. The performance of the proposed HTLBO is tested on nine unconstrained benchmark functions and two nonlinear constrained benchmark functions with integer variables. Then the algorithm is applied to solve two significant electromagnetic design problems, that is, optimal brushless direct-current (BLDC) motor design and electromagnetic actuator geometric construction design. Simulation results on both the benchmark functions and practical engineering design problems confirm the efficiency and robustness of the proposed algorithm.

Optimal foraging algorithm with direction prediction and Gaussian oscillation for constrained optimization problems

Optimal foraging algorithm (OFA) is a newly stochastic optimization technique and is famous for its computational accuracy. However, the high computational accuracy leads to slow convergence speed. Experimental results demonstrate that OFA is good at unimodal functions but poor at multimodal functions. To improve these drawbacks, in this paper a novel modified OFA with direction prediction and Gaussian oscillation, named OFA/P&G is introduced. In OFA/P&G, a transition matrix is constructed when a new global optimum is found to generate the candidate individuals. If the current global optimum does not change, the Gaussian oscillation is employed in a low probability and OFA update method is used in a high probability to generate the candidate individuals. The superior performance of OFA/P&G is verified on the 12 CEC2017 benchmark functions, 13 constrained benchmark functions and 5 engineering problems. Experimental results demonstrate that OFA/P&G outperforms other comparative algorithms. Finally, a real-world problem, drilling path optimization, is solved by OFA/P&G.

A Tandem Running Strategy-Based Heat Transfer Search Algorithm and Its Application to Chemical Constrained Process Optimization

Constrained optimization problems (COPs) are widely encountered in chemical engineering processes, and are normally defined by complex objective functions with a large number of constraints. Classical optimization methods often fail to solve such problems. In this paper, to solve COPs efficiently, a two-phase search method based on a heat transfer search (HTS) algorithm and a tandem running (TR) strategy is proposed. The main framework of the MHTS–TR method aims to alternate between a feasible search phase that only examines feasible solutions, using the HTS algorithm, and an infeasible search phase where the treatment of infeasible solutions is relaxed in a controlled manner, using the TR strategy. These two phases play different roles in the search process; the former ensures an intensified optimum in a relevant feasible region, whereas the latter is used to introduce more diversity into the former. Thus, the ensemble of these two complementary phases can provide an effective method to solve a wide variety of COPs. The proposed variant was investigated over 24 well-known constrained benchmark functions, and then compared with various well-established metaheuristic approaches. Furthermore, it was applied for solving a chemical COP. The promising results demonstrate that the MHTS–TR approach is applicable for solving real-world COPs.

An advanced hybrid algorithm for nonlinear function optimization with real world applications

SummaryThis article presents an advanced hybrid algorithm (haDEPSO) for nonlinear constrained function optimization problem. It consists of the advised advanced differential evolution, that is, aDE (wherein a novel mutation, crossover, and selection strategy is introduced, to avoid premature convergence) and particle swarm optimization, namely, aPSO (in which novel gradually varying parameters is utilized, to escape stagnation). The proposed haDEPSO achieve better results as aDE and aPSO provides diverse convergence characteristic to the solution space. Moreover, in haDEPSO distinct population is merged with other in a predefined way, to balance between exploration and exploitation. Efficiency of the proposed hybrid haDEPSO along with its integrating component aDE and aPSO are inspected on IEEE CEC'2006 constrained benchmark functions and IEEE CEC'2011 real world problems. According to the comparison results, the proposed methods achieved better results than traditional DE and PSO with their hybrids as well as over many state‐of‐the‐art algorithms.

A Multiswarm Intelligence Algorithm for Expensive Bound Constrained Optimization Problems

Constrained optimization plays an important role in many decision-making problems and various real-world applications. In the last two decades, various evolutionary algorithms (EAs) were developed and still are developing under the umbrella of evolutionary computation. In general, EAs are mainly categorized into nature-inspired and swarm-intelligence- (SI-) based paradigms. All these developed algorithms have some merits and also demerits. Particle swarm optimization (PSO), firefly algorithm, ant colony optimization (ACO), and bat algorithm (BA) have gained much popularity and they have successfully tackled various test suites of benchmark functions and real-world problems. These SI-based algorithms follow the social and interactive principles to perform their search process while approximating solution for the given problems. In this paper, a multiswarm-intelligence-based algorithm (MSIA) is developed to cope with bound constrained functions. The suggested algorithm integrates the SI-based algorithms to evolve population and handle exploration versus exploitation issues. Thirty bound constrained benchmark functions are used to evaluate the performance of the proposed algorithm. The test suite of benchmark function is recently designed for the special session of EAs competition in IEEE Congress on Evolutionary Computation (IEEE-CEC′13). The suggested algorithm has approximated promising solutions with good convergence and diversity maintenance for most of the used bound constrained single optimization problems.

Plasma generation optimization: a new physically-based metaheuristic algorithm for solving constrained optimization problems

Purpose This paper aims to present a new physically inspired meta-heuristic algorithm, which is called Plasma Generation Optimization (PGO). To evaluate the performance and capability of the proposed method in comparison to other optimization methods, two sets of test problems consisting of 13 constrained benchmark functions and 6 benchmark trusses are investigated numerically. The results indicate that the performance of the proposed method is competitive with other considered state-of-the-art optimization methods. Design/methodology/approach In this paper, a new physically-based metaheuristic algorithm called plasma generation optimization (PGO) algorithm is developed for solving constrained optimization problems. PGO is a population-based optimizer inspired by the process of plasma generation. In the proposed algorithm, each agent is considered as an electron. Movement of electrons and changing their energy levels are based on simulating excitation, de-excitation and ionization processes occurring through the plasma generation. In the proposed PGO, the global optimum is obtained when plasma is generated with the highest degree of ionization. Findings A new physically-based metaheuristic algorithm called the PGO algorithm is developed that is inspired from the process of plasma generation. Originality/value The results indicate that the performance of the proposed method is competitive with other state-of-the-art methods.

The Performance of Penalty Methods on Tree-Seed Algorithm for Numerical Constrained Optimization Problems

The constraints are the most important part of many optimization problems. The metaheuristic algorithms are designed for solving continuous unconstrained optimization problems initially. The constraint handling methods are integrated into these algorithms for solving constrained optimization problems. Penalty approaches are not only the simplest way but also as effective as other constraint handling techniques. In literature, there are many penalty approaches and these are grouped as static, dynamic and adaptive. In this study, we collect them and discuss the key benefits and drawbacks of these techniques. Tree-Seed Algorithm (TSA) is a recently developed metaheuristic algorithm, and in this study, nine different penalty approaches are integrated with the TSA. The performance of these approaches is analyzed on well-known thirteen constrained benchmark functions. The obtained results are compared with state-of-art algorithms like Differential Evolution (DE), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), and Genetic Algorithm (GA). The experimental results and comparisons show that TSA outperformed all of them on these benchmark functions

Best-Worst-Play (BWP): A metaphor-less Optimization Algorithm

A novel algorithm which is an ensemble of two metaphor-less algorithms is presented in this paper. The algorithm is inspired by Rao-1 and Jaya algorithms. Since the algorithm always plays around with the best and worst solutions; the algorithm is named as Best-Worst-Play (BWP) algorithm. The algorithm does not require any algorithm specific parameters, however, algorithm control parameters are required. To test the effectiveness and performance of the proposed algorithm, a number of unconstrained and constrained benchmark functions are considered. It is found that proposed algorithm has outperformed several well-established metaphor based algorithms. The proposed BWP algorithm may be used by researchers to solve the unconstrained and constrained optimization problems

A hybrid optimization algorithm based on cuckoo search and differential evolution for solving constrained engineering problems

Based on Cuckoo Search (CS) and Differential Evolution (DE), a novel hybrid optimization algorithm, called CSDE, is proposed in this paper to solve constrained engineering problems. CS has strong ability on global search and less control parameters, but easy to suffer from premature convergence and lower the density of population. DE specializes in local search and good robustness, however, its convergence rate is too late to find the satisfied solution. Furthermore, these two algorithms are both proved to be especially suitable for engineering problems. This work divides population into two subgroups and adopts CS and DE for these two subgroups independently. By division, these two subgroups can exchange useful information and these two algorithms can utilize each other’s advantages to complement their shortcoming, thus avoid premature convergence, balance the quality of solution and the computation consumption, and find satisfactory global optima. Due to the tremendous design variables and constrained conditions of engineering problems, single optimizer failed to meet the requirement of precision, so hybrid optimization algorithms (such like CSDE) is the most promising mean to complete this job. Simulation results reveal that CSDE has more ability to find promising results than other 12 algorithms (including traditional algorithms and state-of-the-art algorithm) on 30 unconstrained benchmark functions, 10 constrained benchmark functions and 6 constrained engineering problems.

A NOVEL APPROACH BASED ON ELEPHANT HERDING OPTIMIZATION FOR CONSTRAINED OPTIMIZATION PROBLEMS

Many real-world problems can be formulated as an optimization problem and they have some constraints generally. To overcome these constraints, bio-inspired algorithms are adapted to constrained optimization using constraint handling methods and some modifications. In this study, a new approach is developed to solve constrained optimization problems with elephant herding optimization algorithm which is a newly-emerging optimization technique. Besides the basic EHO, two EHO variants (EHO-NoB and GL-EHO) are adapted to constrained optimization with this approach. The well-known thirteen constrained benchmark functions are used to analysis the performances of algorithms. Experimental results show that the GL-EHO has a better performance than the basic EHO and other algorithms. In addition, the results of GL-EHO are comparable level with the result of another EHO variant in the literature.

Nuclear Reaction Optimization: A Novel and Powerful Physics-Based Algorithm for Global Optimization

Meta-heuristic algorithms have gained substantial popularity in recent decades and have focused on applications in a wide spectrum of fields. In this paper, a new and powerful physics-based algorithm named nuclear reaction optimization (NRO) is presented. Meanwhile, NRO imitates the nuclear reaction process and consists of two phases, namely, a nuclear fission (NFi) phase and a nuclear fusion (NFu) phase. The Gaussian walk and differential evolution operators between nucleus and neutron are employed for exploitation and appropriate exploration in the (NFi) phase, respectively. Meanwhile, the variants of differential evolution operator are utilized for exploration in the NFu phase, which consists of the ionization and fusion stages. Additionally, the variants of Levy flight are used for random searching to escape from the local optima in each stage of the NFu phase. The exploration and exploitation abilities of NRO can be balanced due to a combination of the two phases. Both constrained and unconstrained benchmark functions are employed for testing the performance of NRO. To make comparisons between NRO and the state-of-the-art algorithms, 23 classic benchmark functions and twenty-night modern benchmark functions are performed. Moreover, three engineering design optimization problems are solved as constrained benchmark functions by using NRO and the compared algorithms. The results illustrate that the proposed nuclear reaction optimization algorithm is a potential and powerful approach for global optimization.

GPGPU based Multi-hive ABC Algorithm for Constrained Global Optimization Problems

INTRODUCTION: The artificial bee colony (ABC) algorithm is a nature-inspired technique used for solving different optimization problems. This paper presents a multi-hive ABC algorithm for solving constrained benchmark functions of CEC2006. The CEC2006 data set contains the global benchmark functions with different design variables, number and type of constraints. OBJECTIVES: The objective of the proposed work is to design and apply the GPGPU based multi-hive ABC algorithm to solve constrained optimization problems. METHODS: The proposed approach is a multi-population coarse-grained system implemented using General Purpose Graphics Processing Unit (GPGPU). The performance of the proposed approach is compared with the serial ABC algorithm for eleven benchmark functions and results in the literature. The multi-hive ABC algorithm has multiple hives, each running separate ABC algorithm on different cores of GPGPU. RESULTS: The proposed approach provides global best solutions in significantly reduced time for all benchmark functions. The speed-up obtained is approximately 7X to 9X. The GPGPU device utilization is approximately 57% to 91%. CONCLUSION: The GPGPU based multi-hive ABC algorithm is a found good with respect to best results, speed up factor and GPU utilization to solve constrained optimization problems.

An optimization method: hummingbirds optimization algorithm

This paper introduces an optimization algorithm, the hummingbirds optimization algorithm (HOA), which is inspired by the foraging process of hummingbirds. The proposed algorithm includes two phases: a self-searching phase and a guide-searching phase. With these two phases, the exploration and exploitation abilities of the algorithm can be balanced. Both the constrained and unconstrained benchmark functions are employed to test the performance of HOA. Ten classic benchmark functions are considered as unconstrained benchmark functions. Meanwhile, two engineering design optimization problems are employed as constrained benchmark functions. The results of these experiments demonstrate HOA is efficient and capable of global optimization.

Adaptive neighbourhood for locally and globally tuned biogeography based optimization algorithm

Biogeography Based Optimization (BBO) is a population based metaheuristic algorithm using the idea of migration and mutation operation of species for solving complex optimization problems. BBO has demonstrated good performance on various unconstrained and constrained benchmark functions. It has also been applied to real world optimization problems of type linear or nonlinear, nominal or ordinal as well as mixed variables. But, it is realized that adaptation of the intensification and diversification for solving complex optimization problems are challenging tasks. To cope with these challenges, we develop a novel migration model for BBO which inherits features of the nearest neighbour of the local best individual to be migrated along with a global best individual of the pool. Furthermore to select the local best individual for the habitat to be migrated an adaptive local topological structure has been used. We name it as “Adaptive Neighbourhood for Locally and Globally Tuned Biogeography Based Optimization algorithm (ANLGBBO)”. This maintains the balance between intensification and diversification i.e., improve solution by exploiting the accumulated search space and exploring the large space by identifying regions with high quality solutions. We have carried out an extensive numerical evaluation and comparisons for experimental tests using twenty benchmark functions with different features to measure the efficiency of the algorithm. The experimental study confirms ANLGBBO draws clear line of other variants of BBO algorithms in terms of population diversity and establish the accuracy of global optimal solution.

An Artificial Bee Colony Algorithm Based on Dynamic Penalty and Lévy Flight for Constrained Optimization Problems

Artificial bee colony (ABC) algorithm is one of the most popular intelligence algorithms, which has been widely applied to some unconstrained optimization problems. Many improved versions of ABC algorithm are also used for solving constrained optimization problems (COPs). An artificial bee colony algorithm based on dynamic penalty function and Levy flight (DPLABC) is presented for COPs in this paper. Based on the original ABC algorithm, four modifications are put forward in this newly proposed algorithm: The dynamic penalty method is used to handle the constraints; Levy flight with logistic map is applied in the employed bee phase; according to the selection probability, a further search mechanism which is learned from the best solution and two other neighbor food sources is adopted for onlooker bees; different from pulling back to the upper and lower limits, the new boundary handling mechanism inspired by the best solution is also given to repair the invalid solutions. To validate the performance of DPLABC algorithm, it is tested on 13 constrained benchmark functions from 2006 IEEE Congress on Evolution Computation (CEC2006) and four engineering design problems. The experimental results indicate that DPLABC is competitive with the state-of-the-art algorithms including dynamic difference search algorithm and several improved variants of ABC for solving COPs.

A new hybrid teaching–learning particle swarm optimization algorithm for synthesis of linkages to generate path

This paper proposes a novel hybrid teaching–learning particle swarm optimization (HTLPSO) algorithm, which merges two established nature-inspired algorithms, namely, optimization based on teaching–learning (TLBO) and particle swarm optimization (PSO). The HTLPSO merges the best half of population obtained after the teacher phase in TLBO with the best half of the population obtained after PSO. The population so obtained is used subsequently in learner phase of TLBO. To validate the proposed algorithm, five constrained benchmark functions are considered to prove its robustness and efficiency. The proposed algorithm is applied to synthesize four-bar linkage for prescribed path. It is found that the HTLPSO performs better than other single nature-inspired algorithms for path synthesis problem in mechanism theory. Hence, HTLPSO may prove to be an important tool for mechanism design to follow the prescribed path.

Chaotic grey wolf optimization algorithm for constrained optimization problems

AbstractThe Grey Wolf Optimizer (GWO) algorithm is a novel meta-heuristic, inspired from the social hunting behavior of grey wolves. This paper introduces the chaos theory into the GWO algorithm with the aim of accelerating its global convergence speed. Firstly, detailed studies are carried out on thirteen standard constrained benchmark problems with ten different chaotic maps to find out the most efficient one. Then, the chaotic GWO is compared with the traditional GWO and some other popular meta-heuristics viz. Firefly Algorithm, Flower Pollination Algorithm and Particle Swarm Optimization algorithm. The performance of the CGWO algorithm is also validated using five constrained engineering design problems. The results showed that with an appropriate chaotic map, CGWO can clearly outperform standard GWO, with very good performance in comparison with other algorithms and in application to constrained optimization problems.Highlights Chaos has been introduced to the GWO to develop Chaotic GWO for global optimization. Ten chaotic maps have been investigated to tune the key parameter ‘a’, of GWO. Effectiveness of the algorithm is tested on many constrained benchmark functions. Results show CGWO's better performance over other nature-inspired optimization methods. The proposed CGWO is also used for some engineering design applications.