Standard Benchmark Functions Research Articles

An improved sine–cosine algorithm for simultaneous network reconfiguration and DG allocation in power distribution systems

This paper presents a recently proposed meta-heuristic sine–cosine algorithm combined with levy flights to reconfigure the distribution network with simultaneous allocation (placement and size) of multiple distributed generators (DGs). The algorithm is proposed to be adaptive with an exponentially decreasing conversion parameter and a self-controlled levy mutation in order to explore the solution space more efficiently during the course of iterations. The effectiveness of the algorithm is verified on 10 standard benchmark functions. Later, it is used to address the issues of a real combinatorial optimization, such as network reconfiguration (NR) in the presence of DGs. In order to enhance the effectiveness of the system, a multi-objective function is developed considering total active power loss and overall voltage stability of the network with suitable weights without violating the system limitations. To evaluate the objective function, a depth fast search integrated forward–backward sweep based load flow technique that is capable of managing any topological alterations owing to the NR and DG integration is developed. In order to demonstrate the efficiency of the system, four distinct cases of NR and DG installation are investigated. The proposed algorithm is contrasted with other well-known algorithms that exist in the literature, namely, harmony search algorithm (HSA), fireworks algorithm (FWA), genetic algorithm (GA), refined genetic algorithm (RGA) and firefly (FF) algorithm considering 33 and 69-bus distribution systems at three different load levels and its superiority is established.

How the Duration of the Learning Period Affects the Performance of Random Gradient Selection Hyper-Heuristics

Recent analyses have shown that a random gradient hyper-heuristic (HH) using randomised local search (RLSk) low-level heuristics with different neighbourhood sizes k can optimise the unimodal benchmark function LeadingOnes in the best expected time achievable with the available heuristics, if sufficiently long learning periods τ are employed. In this paper, we examine the impact of the learning period on the performance of the hyper-heuristic for standard unimodal benchmark functions with different characteristics: Ridge, where the HH has to learn that RLS1 is always the best low-level heuristic, and OneMax, where different low-level heuristics are preferable in different areas of the search space. We rigorously prove that super-linear learning periods τ are required for the HH to achieve optimal expected runtime for Ridge. Conversely, a sub-logarithmic learning period is the best static choice for OneMax, while using super-linear values for τ increases the expected runtime above the asymptotic unary unbiased black box complexity of the problem. We prove that a random gradient HH which automatically adapts the learning period throughout the run has optimal asymptotic expected runtime for both OneMax and Ridge. Additionally, we show experimentally that it outperforms any static learning period for realistic problem sizes.

Swine Influenza Mimicked Optimization (SIMO)

In this paper, Swine Influenza Model based Optimization (SIMBO) is modified as Swine Influenza mimicked Optimization (SIMO) and explored through the application in the antenna design. Different researchers proposed different optimization techniques and algorithms so that the accuracy of optima will be improved. For fast convergence and better accuracy SIMBO with its variants such as treatment (SIMBOT), vaccination (SIMBOV) and quarantine (SIMBOQ). We have modified Swine Influenza model to propose new technique known as SIMO. In SIMO, health of individuals is improved by synchronizing vaccination, quarantine and treatment. Test 1 and Test 2 are used before vaccine and quarantine respectively to adjust antiviral dose dynamically during its treatment. The additional feature in SIMO such as infection factor control and improve the health of individuals gradually without checking the state/health at every day. SIMO changes solution indirectly during treatment and directly via vaccination and quarantine. The time varying treatment control the health of individuals in defined days such that individual will not feel illness for longer duration. An available closed form formula of equilateral triangular microstrip patch antenna resonant frequency has been used to form the fitness function in order to optimize the dimensional parameters. The proposed technique is used to determine the accurate resonant frequency of equilateral triangular microstrip patch antenna of different dimension. In order to optimize the technique with speedy convergence and effective precision of global optima, this method also used for the optimization of standard benchmark functions.

Optimizing Convolutional Neural Network Hyperparameters by Enhanced Swarm Intelligence Metaheuristics

Computer vision is one of the most frontier technologies in computer science. It is used to build artificial systems to extract valuable information from images and has a broad range of applications in various areas such as agriculture, business, and healthcare. Convolutional neural networks represent the key algorithms in computer vision, and in recent years, they have attained notable advances in many real-world problems. The accuracy of the network for a particular task profoundly relies on the hyperparameters’ configuration. Obtaining the right set of hyperparameters is a time-consuming process and requires expertise. To approach this concern, we propose an automatic method for hyperparameters’ optimization and structure design by implementing enhanced metaheuristic algorithms. The aim of this paper is twofold. First, we propose enhanced versions of the tree growth and firefly algorithms that improve the original implementations. Second, we adopt the proposed enhanced algorithms for hyperparameters’ optimization. First, the modified metaheuristics are evaluated on standard unconstrained benchmark functions and compared to the original algorithms. Afterward, the improved algorithms are employed for the network design. The experiments are carried out on the famous image classification benchmark dataset, the MNIST dataset, and comparative analysis with other outstanding approaches that were tested on the same problem is conducted. The experimental results show that both proposed improved methods establish higher performance than the other existing techniques in terms of classification accuracy and the use of computational resources.

ATLA: A novel metaheuristic optimization algorithm inspired by the mating search behavior of longicorn beetles in the nature

Compared with the traditional optimization algorithms, metaheuristic optimization algorithm has more powerful performance in the optimization problem, which has attracted more and more scholars’ attention. In this paper, a novel metaheuristic optimization algorithm, named artificial transgender longicorn algorithm (ATLA), is proposed, which is inspired by the mating search behavior of longicorn in the nature. ATLA simulates the mechanism of sex pheromone emission and attraction between female and male longicorn beetles, and realizes the process of local search and global search of an optimization problem. Simulation results based on three standard benchmark functions show the good search performance of optimal solution and the effectiveness of the proposed ATLA.

Emended salp swarm algorithm for multiobjective electric power dispatch problem

This paper presents an emended salp swarm algorithm (ESSA) which is basically the extension of the basic salp swarm algorithm (SSA) to solve multiobjective electric power load dispatch problem. The main inspiration behind ESSA is the swarming behavior and reproduction cycle of salps. Salps, in the chain, move across a multi-dimensional search space to aim for the food source (global solution). Owing to the searching behavior of SSA that makes the algorithm prone to premature convergence, the solitary and colonial reproduction phase of salp has been introduced to improve the convergence behavior along with their swarming behavior The multiobjective optimization problem is firstly converted into scalar objective exploiting fuzzy set theory and the conflicting nature of objectives is resolved by cardinal priority ranking. The variable elimination method with exterior penalty is used to handle the physical and operational constraints of generating units. The validation of the proposed ESSA has been examined on the standard benchmark functions and seven EcLD test systems including both scalar and multiple objectives. The statistical analysis based on Wilcoxon sign rank test, supports that results achieved by the algorithm are superior to the other competing algorithms. So, the proposed algorithm (ESSA) is found a promising algorithm.

A hybrid memory-based dragonfly algorithm with differential evolution for engineering application

The dragonfly algorithm (DA) is a swarm-based stochastic algorithm which possesses static and dynamic behavior of swarm and is gaining meaningful popularity due to its low computational cost and fast convergence in solving complex optimization problems. However, it lacks internal memory and is thereby not able to keep track of its best solutions in previous generations. Furthermore, the solution also lacks in diversity and thereby has a propensity of getting trapped in the local optimal solution. In this paper, an iterative-level hybridization of dragonfly algorithm (DA) with differential evolution (DE) is proposed and named as hybrid memory-based dragonfly algorithm with differential evolution (DADE). The reason behind selecting DE is for its computational ability, fast convergence and capability in exploring the solution space through the use of crossover and mutation techniques. Unlike DA, in DADE the best solution in a particular iteration is stored in memory and proceeded with DE which enhances population diversity with improved mutation and accordingly increases the probability of reaching global optima efficiently. The efficiency of the proposed algorithm is measured based on its response to standard set of 74 benchmark functions including 23 standard mathematical benchmark functions, 6 composite benchmark function of CEC2005, 15 benchmark functions of CEC2015 and 30 benchmark function of CEC2017. The DADE algorithm is applied to engineering design problems such as welded beam deign, pressure vessel design, and tension/compression spring design. The algorithm is also applied to the emerging problem of secondary user throughput maximization in an energy-harvesting cognitive radio network. A comparative performance analysis between DADE and other most popular state-of-the-art optimization algorithms is carried out and significance of the results is deliberated. The result demonstrates significant improvement and prominent advantages of DADE compared to conventional DE, PSO and DA in terms of various performance measuring parameters. The results of the DADE algorithm applied on some important engineering design problems are encouraging and validate its appropriateness in the context of solving interesting practical engineering challenges. Lastly, the statistical analysis of the algorithm is also performed and is compared with other powerful optimization algorithms to establish its superiority.

Improving artificial algae algorithm performance by predicting candidate solution quality

The success of optimization algorithms is most of the time directly proportional to the number of fitness evaluations. However, not all fitness evaluations lead to successful fitness updates. Besides, the maximum number of fitness evaluations is limited and also balance of exploration and exploitation is still challenging. Best possible solution should be found in a reasonable time. Surely it can be said more fitness evaluation takes more time. Since methods are tested under fixed numbers of maximum fitness evaluation and the duration of each fitness evaluation of a problem may vary depending on the characteristic of the problem, finding best result with fewer fitness evaluations is challenging in optimization algorithms. For that reason in this study, we proposed a new method that predicts the quality of a candidate solution before evaluation of its fitness employing Gaussian-based Naïve Bayes probabilistic model. If the candidate solution is predicted to generate good result then that solution is evaluated by the objective function. Otherwise new candidate solution is created as usual. The primary purpose of the proposed method is improving the performance of AAA and at the same time preventing unnecessary fitness evaluation. The proposed method is evaluated using standard benchmark functions and CEC’05 test suite. The obtained results suggests that the new method outperformed the basic AAA and other state-of-the-art meta-heuristic algorithms with fewer fitness evaluations. Thus, the new method can be extended to cost sensitive industrial problems.

Extension of Bat Algorithm on Standard Benchmark Functions

Meta heuristics are superior methods of finding, producing and even modifying heuristics that are able to solve various optimization problems. All Meta-heuristic algorithms are influenced by the nature. These types of algorithms tend to mimic the behaviour of biotic components in nature and are emerging as an effective way of solving global optimization algorithms. We have reviewed that no any algorithm is best for all applications due to lack of generality (no. of parameters), non-dynamic input values. So, this paper studied BAT algorithm deeply and found weakness in terms of non-dynamic pulse rate and loudness. In order to avoid being trapped into local optima these inputs are made dynamic with inclusion of levy Flight too. Performance of this proposed Modified BAT approach is evaluated using few standard benchmark functions. For justifying the superiority of Modified BAT, its performance has been compared with standard Bat algorithm too. From simulation it is found that dynamic pulse rate and dynamic loudness improve the performance of Bat algorithm in terms of results without being stuck at local optima and is more general.

A hybrid multi‐objective tour route optimization algorithm based on particle swarm optimization and artificial bee colony optimization

SummaryComputational intelligence techniques have widespread applications in the field of engineering process optimization, which typically comprises of multiple conflicting objectives. An efficient hybrid algorithm for solving multi‐objective optimization, based on particle swarm optimization (PSO) and artificial bee colony optimization (ABCO) has been proposed in this paper. The novelty of this algorithm lies in allocating random initial solutions to the scout bees in the ABCO phase which are subsequently optimized in the PSO phase with respect to the velocity vector. The last phase involves loyalty decision‐making for the uncommitted bees based on the waggle dance phase of ABCO. This procedure continues for multiple generations yielding optimum results. The algorithm is applied to a real life problem of intercity route optimization comprising of conflicting objectives like minimization of travel cost, maximization of the number of tourist spots visited and minimization of the deviation from desired tour duration. Solutions have been obtained using both pareto optimality and the classical weighted sum technique. The proposed algorithm, when compared analytically and graphically with the existing ABCO algorithm, has displayed consistently better performance for fitness values as well as for standard benchmark functions and performance metrics for convergence and coverage.

A new randomness approach based on sine waves to improve performance in metaheuristic algorithms

The main goal of this paper is to outline a new approach to represent the randomness that we can find in different metaheuristics as a stochastic process which helps in the performance of the analyzed metaheuristic. This new way of viewing randomness is based on the behavior of sine waves that we can find in many situations in nature or in physics laws. In this paper, we evaluate this proposed randomness with three metaheuristics: the grey wolf optimizer, firefly algorithm and flower pollination algorithm, with the goal of studying the performance of the proposed randomness method in different types of metaheuristics. A set of standard benchmark functions were used to test the proposed randomness method, which are classified as unimodal and multimodal benchmark functions. In addition, the benchmark functions of the CEC 2015 Competition are used. Finally, we present tests with functions that were presented in the CEC 2017 competition for constrained real-parameter optimization. We also present a comparative study of the analyzed metaheuristics, and this comparison is between their original randomness method and the proposed randomness method for each algorithm. Finally, we present the performance and results of the methods with different number of dimensions to complete the study.

A Cauchy-Gaussian Quantum-Behaved Bat Algorithm Applied to Solve the Economic Load Dispatch Problem

In this paper, a novel Cauchy-Gaussian quantum-behaved bat algorithm (CGQBA) is applied to solve the economic load dispatch (ELD) problem. The bat algorithm (BA) is an acknowledged metaheuristic optimization algorithm owing to its performance. However, the classical BA presents some weaknesses, such as premature convergence. To withstand the drawbacks of the BA, quantum mechanics theories and Gaussian and Cauchy operators are integrated into the standard BA to enhance its effectiveness. Since the economic load dispatch is a nonlinear, complex and constrained optimization problem, its main objective is to reduce the total generation cost while matching the equality and inequality constraints of the system. The validity of the CGQBA is tested on six standard benchmark functions with different characteristics. The numerical results indicate that the CGQBA is effective and superior to many other algorithms. Moreover, the CGQBA is applied to solve the ELD problems on various test systems including 3,6,20, 40,110 and 160 implemented generating units. The simulation results illustrate the strength of the CGQBA compared with other algorithms recently reported in the literature.

Performance Analysis of Weighted Cat Swarm Optimization with Sobol Mutation

Abstract This paper introduces an analysis by suggesting three types of modification to an existing well known algorithm for optimization i.e. Cat swarm optimization. The motivation behind the proposed modification is to provide a superior convergence along with the production of finer results in diverse real world applications. The first modification introduces a modified weight factor by the replacement of traditional weight factor in the original algorithm. In the second proposed modification, a versatile mutation process i.e. sobol mutation operator is embedded in the execution process of cat swarm optimization for further enhancement in the performance of the optimization technique. The third proposed modification uses the sobol mutation operator with the modified version weighted cat swarm optimization algorithm. This paper provides a detailed analysis of the three proposed techniques for establishing the superiority over the traditional algorithm. Standard benchmark functions are used in this paper for analysing the effectiveness of the modification proposals. The third proposed modification combines the best feature of both the first and second modifications and compensates the disadvantages to some extent. This third modified version provides the best results in almost all categories of functions along with higher precision. Moreover, all the modifications are providing superior results in comparison to the standard cat swarm algorithm, but the weighted cat swarm optimization algorithm with sobol mutation is dominating in all the cases.

A variant of EAM to uncover community structure in complex networks

Environmental adaptation method (EAM) was developed to solve single-objective optimisation problems. After the first proposal, other variants have been suggested to speed up the convergence rate and to maintain the diversity of the solutions. Among those variants, IEAM-RP works with real numbers. In this paper, a variant of IEAM-RP has been suggested with major changes in adaptation operator to improve the overall performance of the algorithm. In the proposed method, significant attention has been given for balancing exploration and exploitation of individuals in the population. The performance of the proposed algorithm is compared against 14 state-of-the-art algorithms using standard benchmark functions of the comparing continuous optimisers (COCO) framework. Further, to check the effectiveness of the proposed approach, it has been applied to a real-world problem of community detection in complex networks. Again, the experimental results are found very promising and competitive compared to other algorithms.

Numerical function optimization by conditionalized PSO algorithm

A lot of research has been directed to the new optimizers that can find a suboptimal solution for any optimization problem named as heuristic black-box optimizers. They can find the suboptimal solutions of an optimization problem much faster than the mathematical programming methods (if they find them at all). Particle swarm optimization (PSO) is an example of this type. In this paper, a new modified PSO has been proposed. The proposed PSO incorporates conditional learning behavior among birds into the PSO algorithm. Indeed, the particles, little by little, learn how they should behave in some similar conditions. The proposed method is named Conditionalized Particle Swarm Optimization (CoPSO). The problem space is first divided into a set of subspaces in CoPSO. In CoPSO, any particle inside a subspace will be inclined towards its best experienced location if the particles in its subspace have low diversity; otherwise, it will be inclined towards the global best location. The particles also learn to speed-up in the non-valuable subspaces and to speed-down in the valuable subspaces. The performance of CoPSO has been compared with the state-of-the-art methods on a set of standard benchmark functions.

Hybrid whale optimisation and β-hill climbing algorithm for continuous optimisation problems

The whale optimisation algorithm (WOA) is an efficient optimisation algorithm inspired by the bubble-net hunting strategy of humpback whale. As any optimisation algorithm, WOA may prematurely converge to suboptimal solutions. This paper introduces a new hybrid WOA algorithm (WOABHC) that efficiently combines the WOA algorithm with the β-hill climbing algorithm (BHC) to control the diversity of the search space. The β-hill climbing algorithm is called at each iteration of WOABHC based on the probability function used in simulated annealing to reduce the number of computations required to achieve a good solution. WOABHC was tested and compared to well-known optimisation algorithms using 25 standard benchmark functions. The experimental results confirm the efficiency of the proposed method in improving the accuracy of the results compared to WOA and other well-known optimisation algorithms.

Bat algorithm with Weibull walk for solving global optimisation and classification problems

Bat algorithm (BA) becomes the most widely employed meta-heuristic algorithm to interpret the diverse kind of optimisation and real-world classification problems. BA suffers from one of the influential challenges called local minima. In this study, we carry out two modifications in the original BA and proposed a modified variant of BA called bat algorithm with Weibull walk (WW-BA) to solve the premature convergence issue. The first modification involves the introduction of Weibull descending inertia weight for updating the velocity of bats. The second modification approach updates the local search strategy of BA by replacing the Random walk with the Weibull Walk. The simulation performed on 19 standard benchmark functions represent the competence and effectiveness of WW-BA compared to the state of the art techniques. The proposed WWBA is also examined for classification problem. The empirical results reveal that the proposed technique outperformed the classical techniques.

Application and development of improved meta-heuristic for making profitable bidding strategy in a day-ahead energy market under step-wise bidding scenario

In this paper, a hybrid model of whale optimisation algorithm (WOA) and sine-cosine algorithm (SCA), i.e., HWOASCA is proposed to solve optimal bidding problem of restructured power system with the aim of profit maximisation of generating company. First, HWOASCA algorithm is validated on 22 standard benchmark functions. After getting it supremacy over benchmark functions, it is verified on bidding problem of 7 GENCO's participating in an electricity market. By suggested approach, the optimal solution for market clearing price (MCP), load dispatch and tender cost under different capacity and price blocks are calculated. After meaningful comparison from other state of the art approaches, it is observed that the profit obtained by the proposed approach is significantly higher for single-hourly and multi-hourly trading trends. The mathematical and experimental results confirm the supremacy of proposed hybrid version of algorithm which is extremely useful for framing the bidding strategies for a generation company.

Hybrid Nature-Inspired Optimization Algorithm: Hydrozoan and Sea Turtle Foraging Algorithms for Solving Continuous Optimization Problems

In this paper, we develop a hybrid optimization algorithm inspired by the reproduction processes of hydrozoans and the foraging behavior of sea turtles for solving continuous optimization problems. Our hybrid algorithm combines the exploration capability of the hydrozoan algorithm with the exploitation capability of the sea turtle foraging algorithm. Moreover, a new adaptive crossover operator was introduced and integrated into the hybrid algorithm to further enhance exploration capability. Our hybrid algorithm was evaluated and compared to the individual algorithms and 12 state-of-the-art algorithms. Results on 21 standard benchmark functions showed that our algorithm was very effective and was among the best of the group, specifically it converged faster than the individual algorithms on most functions and reached optimal or near-optimal results on all functions.

A Novel Quantum Inspired Particle Swarm Optimization Algorithm for Electromagnetic Applications

Quantum inspired particle swarm optimization (QPSO) stimulated by perceptions from particle swarm optimization and quantum mechanics is a stochastic optimization method. Although, it has shown good performance in finding the optimal solution to many electromagnetic problems. However, sometimes it falls to local optima when dealing with hard optimization problems. Thus, to preserve a good balance between local and global searches to avoid premature convergence in quantum particle swarm optimization, this paper proposed three enhancements to the original QPSO method, the proposed method is called modified quantum particle swarm optimization (MQPSO) algorithm. Firstly, a novel selection technique is introduced that will choose the best particle among the population within the search domain to achieve a high-performance exploration. Secondly, a new mutation method is used to preserve the easiness of available QPSOs. Also, a dynamic parameter strategy is proposed for further facilitating the algorithm and tradeoff between exploration and exploitation searches. The experimental results obtained by solving standard benchmark functions and an electromagnetic design problem which is the superconducting magnetic energy storage (SMES) system available in both three parameters and eight parameters problems are reported to showcase the usefulness of the proposed approach.