Benchmark Optimization Problems Research Articles

Multi-objective modified heat transfer search for truss optimization

In this article, a modified version of heat transfer search (HTS) is proposed for multi-objective structural optimization. Contrary to the basic HTS optimizer which activates only one of the three phases of HTS at a time, multi-objective HTS simultaneously exploits the effect of all phases. The proposed modified optimizer is based on the principle of thermodynamics with design solutions being thought of molecules that interact with other molecules of the system itself, and simultaneously with the surrounding molecules through the three modes of heat transfer, namely conduction, convection, and radiation phases. To examine the effectiveness and feasibility of the proposed modification, five truss optimization benchmark problems are used for the performance test. Truss mass minimization and nodal displacement maximization are taken as objectives, while design variables are discrete. The new method along with several recent multi-objective meta-heuristics including ant system, ant colony system, symbiotic organism search, and HTS is used to solve the test problems and compared for the hypervolume and spacing-to-extent indicators. The results reveal that the improved version of HTS is superior to its previous version and the other optimizers. The statistical examination of this study has been performed by conducting Friedman’s rank. Results show the dominance of the proposed optimizer performance in comparison with the others.

Large-scale structural optimization using a fuzzy reinforced swarm intelligence algorithm

In contrast with conventional structural optimization benchmark problems real size structures mostly contain a large number of members and their optimal design provide a serious challenging area for optimization methods. In this regard, current study deals with assessing the search performance of the recently developed fuzzy reinforced metaheuristic technique so called Interactive Fuzzy Search Algorithm on the optimization of large-scale structures. This method is a self-adaptive and parameter-free algorithm which applies a dual-module fuzzy decision mechanism to adjust its search behavior during the optimization process. This mechanism employs two nine rule fuzzy modules which permanently monitor the agents updating process and based on the governing conditions of the problem emphasize their exploration or exploitation search behavior. Attained results show that proposed method can adopt itself with the extensive search space of the studied problems. Form both accuracy and stability aspects Interactive Fuzzy Search Algorithm provides promising results on solving large-scale structural optimization problems.

Island-based Crow Search Algorithm for solving optimal control problems

Crow Search Algorithm (CROW) is one of the members of recently developed swarm-based metaheuristic algorithms. Literature includes different applications of this algorithm on engineering design problems. However, this optimization method suffers from some drawbacks such as premature convergence and trapping into local optima at the early phase of iterations. In order to conquer this algorithm specific inabilities, many research studies have been conducted in the literature dealing with the improvements and enhancements on the search mechanism of CROW. Structured population mechanism plays a vital role in preserving and controlling diversity, and thus increases the solution efficiency in evolutionary algorithms. Among the different types of methods used in structured algorithms, the island model is one of the widely applied solution strategies, in which the population individuals are subdivided into a predefined number of subpopulations. Migration mechanism is the key factor increasing population diversity, which takes place between independently running subpopulations during iterations to exchange valuable and useful solution information. This study embeds the fundamentals of the island model concepts into the Crow Search Algorithm to improve its probing capabilities of the search domain, by means of the periodically interacting subpopulations on the course of iterations. In addition, four different hierarchical migration topologies have been proposed, and their search effectiveness have been evaluated and compared over 45 optimization test functions. The optimization function test set includes classic benchmark optimization problems and CEC 2015 benchmark functions. Furthermore, each hierarchical island model is applied for solving six different optimal control problems in order to investigate their efficiencies on multi-dimensional real world optimization problems. The investigated optimal control problems are parallel reaction, continuous stirred tank reactor, batch reactor consecutive reaction, nonlinear constrained mathematical system, nonlinear continuous stirred tank reactor and nonlinear crane container problems. It is found out that the island model concepts improved the optimization performance of CROW. The proposed island models outperformed or showed similar performance compared to the six selected literature optimizers for 27–29 classic benchmark optimization problems. Moreover, incorporating the master sub-population to the island model improved the optimization capability of the algorithm further in most cases. The island models that employ the master sub-population came up with more favorable results compared to their non-master sub-population peers in all optimal control problems. The island model that includes the master sub-population and has the migration topology entitled “82” found the most desirable solutions for 4–6 optimal control problems.

Scalable and customizable benchmark problems for many-objective optimization

Solving many-objective problems (MaOPs) is still a significant challenge in the multi-objective optimization (MOO) field. One way to measure algorithm performance is through the use of benchmark functions (also called test functions or test suites), which are artificial problems with a well-defined mathematical formulation, known solutions and a variety of features and difficulties. In this paper we propose a parameterized generator of scalable and customizable benchmark problems for MaOPs. It is able to generate problems that reproduce features present in other benchmarks and also problems with some new features. We propose here the concept of generative benchmarking, in which one can generate an infinite number of MOO problems, by varying parameters that control specific features that the problem should have: scalability in the number of variables and objectives, bias, deceptiveness, multimodality, robust and non-robust solutions, shape of the Pareto front, and constraints. The proposed Generalized Position-Distance (GPD) tunable benchmark generator uses the position-distance paradigm, a basic approach to building test functions, used in other benchmarks such as Deb, Thiele, Laumanns and Zitzler (DTLZ), Walking Fish Group (WFG) and others. It includes scalable problems in any number of variables and objectives and it presents Pareto fronts with different characteristics. The resulting functions are easy to understand and visualize, easy to implement, fast to compute and their Pareto optimal solutions are known.

Multiple scale self-adaptive cooperation mutation strategy-based particle swarm optimization

Particle Swarm Optimization (PSO) algorithm has lately received great attention due to its powerful search capacity and simplicity in implementation. However, previous studies have demonstrated that PSO still suffers from two key drawbacks of premature convergence and slow convergence, especially when dealing with multi-modal optimization problems. In order to address these two issues, we propose a multiple scale self-adaptive cooperative mutation strategy-based particle swarm optimization algorithm (MSCPSO) in this paper. In the proposed approach, we adopt multi-scale Gaussian mutations with different standard deviations to promote the capacity of sufficiently searching the whole solution space. In the adopted multi-scale mutation strategy, large-scale mutation can make populations explore the global solution space and rapidly locate the better solution area at the early stage, thus avoiding the premature convergence and simultaneously speeding up the convergence, while small-scale mutation can allow the populations to more accurately exploit the local best solution area during the later stage, thus improving the accuracy of final solution. In order to guarantee the convergence speed while avoiding premature convergence, the standard deviations for multi-scale Gaussian mutations would be reduced with the increase of iterations, which can make populations pay more attention to local accurate solution exploitation during the later evolution stage and consequently speed up the convergence. In addition, the threshold for each dimension to execute mutation is also dynamically adjusted according to its previous mutation frequency, which can allow MSCPSO to better balance the global and local search capacities, thus avoiding premature convergence without reducing convergence speed. The extensive experimental results on various benchmark optimization problems demonstrate that the proposed approach is superior to other existing PSO techniques with good robustness.

Adaptive Global WASF-GA to handle many-objective optimization problems

Abstract In this paper, a new version of the aggregation-based evolutionary algorithm Global WASF-GA (GWASF-GA) for many-objective optimization is proposed, called Adaptive Global WASF-GA (A-GWASF-GA). The fitness function of GWASF-GA is defined by an achievement scalarizing function (ASF) based on the Tchebychev distance, which considers two reference points (the nadir and utopian points) and a set of weight vectors. Despite of the benefits of using these two reference points simultaneously and a well-distributed set of weight vectors, it is necessary to go a step further to get better approximations in problems with complicated Pareto optimal fronts. For this, in A-GWASF-GA, some of the weight vectors are re-calculated during the optimization process based on the sparsity of the solutions found so far, and taking into account some theoretical results demonstrated in this paper regarding the ASF considered. Different strategies are carried out to accelerate the convergence and to maintain the diversity. The computational results, carried out in comparison with RVEA, NSGA-III, and different versions of MOEA/D, show the potential of A-GWASF-GA in well-known but also in novel many-objective optimization benchmark problems.

A new hybrid algorithm to solve bound-constrained nonlinear optimization problems

The goal of this work is to propose a hybrid algorithm called real-coded self-organizing migrating genetic algorithm by combining real-coded genetic algorithm (RCGA) and self-organizing migrating algorithm (SOMA) for solving bound-constrained nonlinear optimization problems having multimodal continuous functions. In RCGA, exponential ranking selection, whole-arithmetic crossover and non-uniform mutation operations have been used as different operators where as in SOMA, a modification has been done. The performance of the proposed hybrid algorithm has been tested by solving a set of benchmark optimization problems taken from the existing literature. Then, the simulated results have been compared numerically and graphically with existing algorithms. In the graphical comparison, a modified performance index has been proposed. Finally, the proposed algorithm has been applied to solve two real-life problems.

Dung beetle inspired local search in artificial bee colony algorithm for unconstrained and constrained numerical optimisation

In recent times, swarm intelligence (SI) centred strategies are proving their efficacy in the arena of engineering optimisation problems. Artificial bee colony (ABC) algorithm is one of the efficient SI centred technique. To intensify exploitation concept of ABC, a local search strategy inspired by dung beetle orientation and foraging activities is developed and amalgamated with ABC. This developed local search strategy is termed as dung beetle local search (DBLS) strategy. The developed amended algorithm is titled as dung beetle inspired ABC (DBABC) algorithm. The developed DBABC is analysed using 32 unconstrained benchmark optimisation problems, 18 constrained benchmark optimisation problems, and 3 engineering design problems. The obtained outcomes validate the competitiveness of the proposed approach.

Dung beetle inspired local search in artificial bee colony algorithm for unconstrained and constrained numerical optimisation

In recent times, swarm intelligence (SI) centred strategies are proving their efficacy in the arena of engineering optimisation problems. Artificial bee colony (ABC) algorithm is one of the efficient SI centred technique. To intensify exploitation concept of ABC, a local search strategy inspired by dung beetle orientation and foraging activities is developed and amalgamated with ABC. This developed local search strategy is termed as dung beetle local search (DBLS) strategy. The developed amended algorithm is titled as dung beetle inspired ABC (DBABC) algorithm. The developed DBABC is analysed using 32 unconstrained benchmark optimisation problems, 18 constrained benchmark optimisation problems, and 3 engineering design problems. The obtained outcomes validate the competitiveness of the proposed approach.

A Review of Evolutionary Algorithms in Solving Large Scale Benchmark Optimization Problems

A Review of Evolutionary Algorithms in Solving Large Scale Benchmark Optimization Problems

Sensitivity Analysis for Multi-Objective Optimization of the Benchmark TEAM Problem

In this article, the design sensitivity is examined using the material derivative concept of the shape sensitivity analysis to use a gradient-based algorithm for the multi-objective benchmark testing electromagnetic analysis methods (TEAMs) problem. To calculate the shape sensitivity, the original objective functions are replaced with the definite integral form of the functionals, and the p-norm expression is used to handle the minimax problem. The computed sensitivities are validated using the finite-difference numerical sensitivities. The validity of the modified objectives is demonstrated using the results of the single-objective optimization. The results show that the analytical sensitivities agree well with the numerical ones, and the modified objective functions are valid for the benchmark optimization problem.

Wildebeest herd optimization: A new global optimization algorithm inspired by wildebeest herding behaviour

This paper proposes a new metaheuristic global optimization algorithm inspired by Wildebeest herding behavior called Wildebeest Herd Optimization (WHO) algorithm. WHO algorithm mimics the way nomadic Wildebeest herds search vast areas of grasslands efficiently for regions of high food density. The WHO algorithm models five principal Wildebeest behaviors: firstly Wildebeests have limited eyesight and can only search for food locally, secondly Wildebeests stick to the herd to escape predators, thirdly Wildebeest herd as a whole migrates to regions of high food availability based on historical knowledge of annual grass growth rates and rainfall patterns, fourthly Wildebeests move out of crowded overgrazed regions and finally Wildebeests move to avoid starvation. The WHO algorithm is compared to Physics inspired, Swarm based, Biologically inspired and Evolution inspired global optimization algorithms on an extended test suite of benchmark optimization problems including rotated, shifted, noisy and high dimensional problems. Extensive simulation results indicate that the WHO algorithm proposed in this paper significantly outperforms state-of-the-art popular metaheuristic optimization algorithms like Particle Swarm Optimization Algorithm (PSO), Genetic Algorithm (GA), Gravitational Search Algorithm (GSA), Artificial Bee Colony Algorithm (ABC) and Simulated Annealing (SA) on shifted, high dimensional and large search range problems.

A new QPSO based hybrid algorithm for constrained optimization problems via tournamenting process

The goal of this paper is to propose a new hybrid algorithm based on advanced quantum behaved particle swarm optimization (QPSO) technique and binary tournamenting for solving constrained optimization problems. In binary tournamenting, six different situations/options are considered and accordingly six variants of hybrid algorithms are proposed. Then to test the efficiency and performance of these algorithms and also to select the best algorithm among these, six benchmark optimization problems are selected and solved. Then the computational results are compared graphically as well as numerically. Finally, the best found algorithm is applied to solve three engineering design problems and the computational results are compared with the existing algorithms available in the literature.

A reference point-based evolutionary algorithm for approximating regions of interest in multiobjective problems

Most evolutionary multiobjective optimization algorithms are designed to approximate the entire Pareto front. During the last decade, a series of preference-based evolutionary algorithms have been developed, where a part of the Pareto front is approximated by incorporating the preferences of a Decision Maker. However, only a few such algorithms are able to obtain well-distributed solutions covering the complete “region of interest” that is determined by a reference point. In this paper, a preference-based evolutionary algorithm for approximating the region of interest is proposed. It is based on the state-of-the-art genetic algorithm NSGA-II and the CHIM approach introduced in the NBI method which is used to obtain uniformly distributed solutions in the region of interest. The efficiency of the proposed algorithm has been experimentally evaluated and compared to other state-of-the-art multiobjective preference-based evolutionary algorithms by solving a set of multiobjective optimization benchmark problems. It has been shown that the incorporation of the Decision Maker’s preferences and the CHIM approach into the NSGA-II algorithm allows approximating the whole region of interest accurately while maintaining a good distribution of the obtained solutions.

A novel life choice-based optimizer

This paper presents a novel metaheuristic algorithm named as life choice-based optimizer (LCBO) developed on the typical decision-making ability of humans to attain their goals while learning from fellow members. LCBO is investigated on 29 popular benchmark functions which included six CEC-2005 functions, and its performance has been benchmarked against seven optimization techniques including recent ones. Further, different abilities of LCBO optimization algorithm such as exploitation, exploration and local minima avoidance were also investigated and have been reported. In addition to this, scalability is tested for several benchmark functions where dimensions have been varied till 200. Furthermore, two engineering optimization benchmark problems, namely pressure vessel design and cantilever beam design, were also optimized using LCBO and the results have been compared with recently reported other algorithms. The obtained comparative results in all the above-mentioned experimentations revealed the clear superiority of LCBO over the other considered metaheuristic optimization algorithms. Therefore, based on the presented investigations, it is concluded that LCBO is a potential optimizer for engineering problems.

A honeybees-inspired heuristic algorithm for numerical optimisation

Swarm intelligence is all about developing collective behaviours to solve complex, ill-structured and large-scale problems. Efficiency in collective behaviours depends on how to harmonise the individual contributors so that a complementary collective effort can be achieved to offer a useful solution. The main points in organising the harmony remain as managing the diversification and intensification actions appropriately, where the efficiency of collective behaviours depends on blending these two actions appropriately. In this paper, a hybrid bee algorithm is presented, which harmonises bee operators of two mainstream well-known swarm intelligence algorithms inspired of natural honeybee colonies. The parent algorithms have been overviewed with many respects, strengths and weaknesses are identified, first, and the hybrid version has been proposed, next. The efficiency of the hybrid algorithm is demonstrated in comparison with the parent algorithms in solving two types of numerical optimisation problems; (1) a set of well-known functional optimisation benchmark problems and (2) optimising the weights of a set of artificial neural network models trained for medical classification benchmark problems. The experimental results demonstrate the outperforming success of the proposed hybrid algorithm in comparison with two original/parent bee algorithms in solving both types of numerical optimisation benchmarks.

Design and optimization of a CMOS power amplifier using innovative fractional-order particle swarm optimization

In this paper, a new optimization algorithm is proposed to design and optimize a CMOS power amplifier at the frequency of 2.4 GHz for wireless applications in TSMC 0.18μm with respect to stability. In this new algorithm which is denoted as Hunter-Attack Fractional-order Particle Swarm Optimization (HAFPSO) algorithm, two main weaknesses of the classic Particle Swarm Optimization (PSO), i.e. trapping in local optima (stagnation) and the slow convergence rate are resolved. In the proposed algorithm, using the fractional-order derivatives, the particle convergence rates accelerate to the optimal solution. In addition, Hunter-attack strategy is used to avoid stagnation in classic PSO. In order to investigate the performance of the HAFPSO optimization algorithm, fifteen computationally expensive benchmark optimization problems are utilized. The results of experiments show the significant performance of the proposed algorithm in comparison with seven other well known optimization algorithms i.e GA, PSO, HFPSO, CLPSO, PSOGSA, GAPSO and FPSO. A statistical test procedure is also exploited to show significant difference performance of proposed algorithm from other optimization algorithms. The power amplifier is designed using HAFPSO, GA and two PSO-based optimization algorithms, i.e. classic PSO and Fractional-order PSO (FPSO). The results show the improvement of 50% of in PAE of the power amplifier.

Multifidelity and Multiscale Bayesian Framework for High-Dimensional Engineering Design and Calibration

AbstractThis paper proposes a machine learning–based multifidelity modeling (MFM) and information-theoretic Bayesian optimization approach where the associated models can have complex discrepancies among each other. Advantages of MFM-based optimization over a single-fidelity surrogate, specifically under complex constraints, are discussed with benchmark optimization problems involving noisy data. The MFM framework, based on modeling of the varied fidelity information sources via Gaussian processes, is augmented with information-theoretic active learning strategies that involve sequential selection of optimal points in a multiscale architecture. This framework is demonstrated to exhibit improved efficiency on practical engineering problems like high-dimensional design optimization of compressor rotor via implementing its multiscale architecture and calibration of expensive microstructure prediction model. From the perspective of the machine learning–assisted design of multiphysics systems, advantages of the proposed framework have been presented with respect to accelerating the search of optimal design conditions under budget constraints.

Predicting molten steel endpoint temperature using a feature-weighted model optimized by mutual learning cuckoo search

A feature-weighted neural network model for the prediction of the endpoint temperature of molten steel (MSET) in a ladle furnace (LF) is proposed in this paper. Accurate prediction of MSET is essential for promoting product quality, reducing production costs and enhancing productivity. Considering that different features have different impacts on the MSET during the process of LF refining, a weight is applied to each feature before feeding the feature to neural networks. A mutual learning cuckoo search (MLCS) algorithm is proposed to simultaneously determine the feature weights and network parameters of the proposed prediction model. The search of each cuckoo in the basic cuckoo search algorithm and many of its variants is performed independently, which may decrease the algorithms’ performance. The proposed MLCS algorithm introduces two new search strategies, the mutual learning-based search strategy and the bottom reinforcement learning-based search strategy. The superior performance of MLCS is first confirmed with 20 benchmark optimization problems. Then, MLCS is applied to optimize the feature weights and network parameters in the feature-weighted MSET prediction model. Application to modeling the production data from a 300 t LF in an iron & steel plant in China demonstrates the effectiveness of the proposed feature-weighted neural network model.

Empirical study on rotation and information exchange in particle swarm optimization

Abstract This paper investigates whether rotational variance and information exchange affect the performance of Particle Swarm Optimization (PSO) algorithms. Four PSO versions which include the presence or absence of rotational variance, and the fast or late information exchange among particles are under evaluation. The goal is to highlight the best approach and principal benefits of each PSO version based on numerical simulations. To accomplish the aforesaid, the algorithms were evaluated on CEC 2017 benchmark optimization problems. Additionally, a method to estimate a reliable number of algorithms executions was also proposed. Statistical measurements based on Clerc's rules were used to strengthen the analyses. The results indicated the rotationally variant PSO as the overall winner, and the fast information exchange was statistically significant better than the late one, according to Friedman's and Wilcoxon's tests.