Real-parameter Single Objective Optimization Research Articles

Parameter Combination Framework for the Differential Evolution Algorithm

The differential evolution (DE) algorithm is a popular and efficient evolutionary algorithm that can be used for single objective real-parameter optimization. Its performance is greatly affected by its parameters. Generally, parameter control strategies involve determining the most suitable value for the current state; there is only a little research on parameter combination and parameter distribution which is also useful for improving algorithm performance. This paper proposes an idea to use parameter region division and parameter strategy combination to flexibly adjust the parameter distribution. Based on the idea, a group-based two-level parameter combination framework is designed to support various modes of parameter combination, and enrich the parameter distribution characteristics. Under this framework, two customized parameter combination strategies are given for a single-operation DE algorithm and a multi-operation DE algorithm. The experiments verify the effectiveness of the two strategies and it also illustrates the meaning of the framework.

HARD-DE: Hierarchical ARchive Based Mutation Strategy With Depth Information of Evolution for the Enhancement of Differential Evolution on Numerical Optimization

Differential evolution is a famous and effective branch of evolutionary computation, which aims at tackling complex optimization problems. There are two aspects significantly affecting the overall performance of DE variants, one is trial vector generation strategy and the other is the control parameter adaptation scheme. Here in this paper, a new hierarchical archive-based trial vector generation strategy with depth information of evolution was proposed to get a better perception of landscapes of objective functions as well as to improve the candidate diversity of the trial vectors. Furthermore, novel adaptation schemes both for crossover rate $Cr$ and for population size $ps$ were also advanced in this paper, and consequently, an overall better optimization performance was obtained after these changes. The novel HARD-DE algorithm was verified under many benchmarks of the Congress on Evolutionary Computation (CEC) Competition test suites on real-parameter single-objective optimization as well as two benchmarks on real-world optimization from CEC2011 test suite, and the experiment results showed that the proposed HARD-DE algorithm was competitive with the other state-of-the-art DE variants.

Adaptive Differential Evolution Algorithm Based on Restart Mechanism and Direction Information

Differential evolution is a competent algorithm for solving single objective real-parameter optimization problems. In order to enhance the performance of adaptive DE algorithms based on successful parameters, in this paper, a new DE algorithm, called adaptive differential evolution restart and direction, abbreviated ADERD, is proposed for solving global numerical optimization problems over continuous space. In the proposed algorithm, a novel mutation strategy based on the feasible descent direction is introduced. Only individuals of the population top ranked with smaller errors adopt this novel strategy to mutate. Additionally, the variable coefficient is used in the restart mechanism first to avoid stagnation and/or jump out of the local optima. Modified mechanism of crossover probability sorting is also introduced. In order to better understand the effectiveness of our proposed strategies, those are integrated into two representative adaptive DE variants, i.e. JADE_ rcr and JADE_ sort. Experimental results demonstrate that the our proposed strategies are capable of enhancing the performance of JADE_ rcr and JADE_ sort. Improved JADE_ sort is denoted as ADERD_ sort. Experiments have been conducted on 30 functions presented in CEC 2017 competition. Moreover, compared with recent adaptive DE algorithms, ADERD_ sort obtains better, or at least comparable, results in terms of the quality of final solutions.

An automatic nuclei segmentation method using intelligent gravitational search algorithm based superpixel clustering

Abstract A reliable nuclei segmentation is still an open-ended problem, especially in the breast cancer histology images. For the same, this paper proposes an intelligent gravitational search algorithm based superpixel clustering method for automatic nuclei segmentation. In the proposed method, a novel variant of gravitational search algorithm, intelligent gravitational search algorithm, is employed to obtain the optimal cluster centroids. The experimental and statistical results evince that the proposed variant surpasses existing meta-heuristic algorithms on 47 benchmark functions belonging to different problem categories i.e., unimodal, multimodal, and real-parameter single objective optimization problems of CEC, 2013. Further, the segmentation accuracy of the proposed method is examined on H&E stained estrogen receptor positive (ER+) breast cancer images. Experiments affirm that the proposed method is comparatively an efficacious and accurate method for segmenting the nuclei within breast cancer histology images.

Distance based parameter adaptation for Success-History based Differential Evolution

Abstract This paper proposes a simple, yet effective, modification to scaling factor and crossover rate adaptation in Success-History based Adaptive Differential Evolution (SHADE), which can be used as a framework to all SHADE-based algorithms. The performance impact of the proposed method is shown on the real-parameter single objective optimization (CEC2015 and CEC2017) benchmark sets in 10, 30, 50, and 100 dimensions for all SHADE, L-SHADE (SHADE with linear decrease of population size), and jSO algorithms. The proposed distance based parameter adaptation is designed to address the premature convergence of SHADE–based algorithms in higher dimensional search spaces to maintain a longer exploration phase. This design effectiveness is supported by presenting a population clustering analysis, along with a population diversity measure. Also, the new distance based algorithm versions (Db_SHADE, DbL_SHADE, and DISH) have obtained significantly better optimization results than their canonical counterparts (SHADE, L_SHADE, and jSO) in 30, 50, and 100 dimensional functions.

QUasi-Affine TRansformation Evolution with External ARchive (QUATRE-EAR): An enhanced structure for Differential Evolution

Optimization demands are ubiquitous in science and engineering. The key point is that the approach to tackle a complex optimization problem should not itself be difficult. Differential Evolution (DE) is such a simple method, and it is arguably a very powerful stochastic real-parameter algorithm for single-objective optimization. However, the performance of DE is highly dependent on control parameters and mutation strategies. Both tuning the control parameters and selecting the proper mutation strategy are still tedious but important tasks for users. In this paper, we proposed an enhanced structure for DE algorithm with less control parameters to be tuned. The crossover rate control parameter Cr is replaced by an automatically generated evolution matrix and the control parameter F can be renewed in an adaptive manner during the whole evolution. Moreover, an enhanced mutation strategy with time stamp mechanism is advanced as well in this paper. CEC2013 test suite for real-parameter single objective optimization is employed in the verification of the proposed algorithm. Experiment results show that our proposed algorithm is competitive with several well-known DE variants.

A balanced fuzzy Cultural Algorithm with a modified Levy flight search for real parameter optimization

Over the last few decades, a plethora of improved evolutionary algorithms was developed with exquisite performance on numerical and real-world problems. Among such algorithms, the Cultural Algorithm is a hyper-heuristic evolutionary algorithm, which explicitly utilizes the knowledge represented in the belief space as an essential component to guide the evolutionary search. In this paper, a new enhanced Cultural Algorithm incorporates a fuzzy system with a modified Levy flight search that is introduced as a new component. The new algorithm namely, b-fCA+mLF, utilizes a balanced search mode using a customized belief space with a quality function to harmonize how the knowledge sources work in parallel. The communication protocols between the population space and the belief space are established through the modified fuzzy acceptance and influence functions. Using these new functions, the best individuals are selected to create new knowledge in an effective manner. Similarly, the best knowledge is selected to evolve the individuals in the population space and guide the evolutionary search towards the promising regions. A modified Levy flight search is proposed and utilizes the information from the belief space as an input to support the evolution process to generate better solutions. The algorithm is tested on the benchmark suite taken from the IEEE-CEC’15 competition on learning-based real-parameter single objective optimization, and is compared with other algorithms including the best performer algorithms in this competition. The results suggest that the proposed algorithm is statistically better and is able to produce higher quality solutions than the other state-of-the-art algorithms. A case study on the well-known 120-bar dome truss design problem is also presented to test the validity of the proposed algorithm for the solution of complex design problems. The results of this problem show the ability of the proposed algorithm to generate good solutions with fewer function evaluations, compared to reported results in the literature and other well-known algorithms.

Ensemble of parameters in a sinusoidal differential evolution with niching-based population reduction

Abstract Many parameter adaptation methods were proposed for Differential Evolution (DE) algorithm. Although these methods succeed in enhancing the performance of DE when solving a diverse set of optimization problems, locating the optimal solution is still a challenging task in most of these methods for complex optimization problems. To improve the performance of DE, this study presents a new enhanced algorithm based on our published work namely LSHADE with ensemble parameter sinusoidal adaptation, LSHADE-EpSin, which ranked the joint winner in IEEE CEC2016 competition on real-parameter single objective optimization. The method proposes a mixture of two sinusoidal formulas and a Cauchy distribution to balance the exploration and the exploitation of already found best solutions. A restart method is used at later generations to enhance the quality of the found solutions. The proposed algorithm also introduces a novel approach to adapt the population size by using a niching-based reduction scheme. In this mechanism, two separate niches are used before performing the population reduction, to reduce the population size in an effective manner. The proposed algorithm namely ensemble sinusoidal differential evolution with niching reduction, EsDEr-NR, is tested on the IEEE CEC2014 problems used in the special session and competitions on real-parameter single objective optimization of the IEEE CEC2016. The results statistically affirm the efficiency of the proposed approach to obtain better results compared to the other state-of-the-art algorithms from the literature including CMA-ES variants.

Particle state change algorithm

The matter state change, which is a common phenomenon in nature, shows the process that the matter how to reach the optimal state in the environment. This paper presents a novel particle state change model (PSCM) inspired by mimicking the process of the matter state change. Based on PSCM, a novel particle state change (PSC) algorithm is proposed for solving continuous optimization problems. As a new algorithm, PSC has many differences from other similar nature-inspired algorithms in terms of the basic principle models, mathematical formalization and properties. This paper considers three states of the matter, namely gas state, liquid state and solid state. In a certain circumstance, the matter always converts from an unstable state into a stable state. It is similar to find the optimal solution of an optimization problem. The proposed algorithm also has the advantages in the respects of higher intelligence, effectiveness and lower computation complexity. And the convergence property of PSC is discussed in detail. In order to illustrate the ability of solving optimization problems in continuous domain, the new proposed algorithm is tested on basic function optimization, CEC2016 single-objective real-parameter numerical optimization and CEC2016 learning-base real-parameter single-objective optimization, and compared with eleven existing algorithms. The numerous simulations have shown the effectiveness and suitability of the proposed approach.

APDDE: self-adaptive parameter dynamics differential evolution algorithm

In real-time high-dimensional optimization problem, how to quickly find the optimal solution and give a timely response or decisive adjustment is very important. This paper suggests a self-adaptive differential evolution algorithm (abbreviation for APDDE), which introduces the corresponding detecting values (the values near the current parameter) for individual iteration during the differential evolution. Then, integrating the detecting values into two mutation strategies to produce offspring population and the corresponding parameter values of champion are retained. In addition, the whole populations are divided into a predefined number of groups. The individuals of each group are attracted by the best vector of their own group and implemented a new mutation strategy DE/Current-to-lbest/1 to keep balance of exploitation and exploration capabilities during the differential evolution. The proposed variant, APDDE, is examined on several widely used benchmark functions in the CEC 2015 Competition on Learning-based Real-Parameter Single Objective Optimization (13 global numerical optimization problems) and 7 well-known basic benchmark functions, and the experimental results show that the proposed APDDE algorithm improves the existing performance of other algorithms when dealing with the high-dimensional and multimodal problems.

Cooperative particle swarm optimization using MapReduce

Cooperative particle swarm optimization (short in CPSO) is an effective evolutionary algorithm for optimization and has attracted a lot of research attention. As real-world optimization problems become complex and large scale, population-based optimization algorithms may take a long time to complete a task. Responding to this trend, CPSO, as a serial evolutionary algorithm, also needs to be updated and accelerated. On the other hand, MapReduce is a programming model for parallel computation and accelerates many tasks successfully. In this paper, we present MapReduce cooperative particle swarm optimization (short in MRCPSO) which implements CPSO-S, a version of CPSO, using MapReduce model. MRCPSO is compared with the original CPSO-S and two algorithms in CEC 2013 special session and competition on real-parameter single-objective optimization. The result on benchmarks shows that MRCPSO outperforms the original CPSO-S significantly on both time and the quality of solution. And in the comparisons with the other two algorithms, MRCPSO has better performance on several problems, while the advantage on time is significant.

A modified cultural algorithm with a balanced performance for the differential evolution frameworks

Numerous different methodologies have been introduced in the last few decades to provide efficient solutions for complex real-world problems and other optimization problems. This work focuses on the development of a simple hybrid cultural learning theme with a balanced performance for differential evolution frameworks. It is intended to be always efficient for a diverse set of optimization tasks. As different optimization algorithms behave differently depending on the problems, the combination of the best behaviors from different search strategies seems desirable. The proposed work explores the combination of the explorative/exploitative strengths of two heuristic search techniques, which discretely provide competitive results. Differential evolution is used as the population space for Cultural Algorithm, and is used to guide knowledge dissemination from the knowledge sources in the belief space. Here, a new influence function is introduced that adjusts the membership of each of the knowledge sources. The algorithm has been tested with the conditions and benchmark problems defined for the IEEE CEC2013 special session and competition on real-parameter single objective optimization. The paper also investigates the application of the new algorithm to a set of real-life problems concerning optimizing the weight a tension/compression spring and minimizing the fabrication cost of a welded beam engineering problem. The proposed algorithm appears to have a significant impact on the algorithmic functioning as it reliably augments the performance of the differential evolution frameworks with which it is integrated. Benchmark results for most of the synthetic functions from the special session show that the balanced hybrid obtains superior performance compared to the other competent algorithms. It scales well with the increasing dimensionality and converges in the close proximity of the global optimum for complex functions.

Bacterial foraging optimization using novel chemotaxis and conjugation strategies

Bacterial foraging optimization (BFO) has attracted much attention and been widely applied in a variety of scientific and engineering applications since its inception. However, the fixed step size and a lack of information communication between bacterial individuals during the optimization process have significant impacts on the performance of BFO. To address these issues on real-parameter single objective optimization problems, this paper proposes a new bacterial foraging optimizer using new designed chemotaxis and conjugation strategies (BFO-CC). Via the new chemotaxis mechanism, each bacterium randomly selects a standard-basis-vector direction for swimming or tumbling; this approach may obviate calculating a random unit vector and could effectively get rid of interfering with each other between different dimensions. At the same time, the step size of each bacterium is adaptively adjusted based on the evolutionary generations and the information of the globally best individual, which readily makes the algorithm keep a better balance between a local search and global search. Moreover, the new designed conjugation operator is employed to exchange information between bacterial individuals; this feature can significantly improve convergence. The performance of the BFO-CC algorithm was comprehensively evaluated by comparing it with several other competitive algorithms (based on swarm intelligence) on both benchmark functions and real-world problems. Our experimental results demonstrated excellent performance of BFO-CC in terms of solution quality and computational efficiency.

Chaos particle swarm optimization with Eensemble of chaotic systems

In this study the Chaotic Particle Swarm Optimization (CPSO) algorithm with six simultaneously used chaotic pseudo-random number generators (CPRNG) is investigated. The implementation of chaotic sequences is detailed and discussed. The Ensemble learning approach is used for assigning CPRNGs to particles. The results of proposed algorithm on IEEE CEC′13 Real-Parameter Single Objective Optimization benchmark set are presented and compared with the SPSO-2011.

Self-adaptive control parameters׳ randomization frequency and propagations in differential evolution

This paper presents insight into an adaptation and self-adaptation mechanism within differential evolution, covering not only how but moreover – when this mechanism generates new values for control parameters, focusing on the iteration-temporal randomness of the self-adaptive control parameters. In particular, this randomness is controlled by a randomness level parameter, which influences the control parameters values׳ dynamics and their propagation through suitable individuals׳ improvement contributions during ellitistic selection. Thereby, the randomness level parameter defines the chaotic behavior of self-adaptive control parameter values׳ instances. A Differential Evolution (DE) algorithm for Real Parameter Single Objective Optimization is utilized as an application of this mechanism, to analyze the impact of the randomness level parameter as used inside the evolutionary algorithm parameter adaptation and control mechanism, yielding statistically significant different algorithm performances and ranks on different randomness level parameter values. Moreover, the impacts of different randomness configurations on the number of improvements, improvement scales, and adaptation frequencies, are shown, in order to present a deeper insight into the influences and causes using different randomness level parameter configurations, to present the influence of randomization frequency on propagation stability. Since DE variant algorithms with the mechanism of control parameters self-adaptation are widely applied, this study might help in increasing the performances of these different variants and their applications.

Adaptive pair bonds in genetic algorithm: An application to real-parameter optimization

Genetic algorithm (GA) is a heuristic search technique that draws inspiration from principles and mechanisms of natural selection. Conventionally, parents selection takes place at every generation and offspring are reproduced through genetic operators like crossover and mutation. The process reiterates until some termination conditions are met. Until recently, little attention has been paid on the enduring relationship between parent solutions. In this paper, we take on and further extend the idea of monogamous genetic algorithm to solving real-coded numerical optimization problems. In this GA model, each monogamous pair of parents yields two offspring, and only the best two offspring survive into the next generation. Occasional infidelity generates variety and promotes diversity in the population. Simulation results over the IEEE-CEC’13 (IEEE Congress on Evolutionary Computation 2013) contest for real parameter single objective optimization with 28 benchmark functions demonstrate the effectiveness of the proposed approach.

Parameter Estimation in Rainfall-Runoff Modelling Using Distributed Versions of Particle Swarm Optimization Algorithm

The presented paper provides the analysis of selected versions of the particle swarm optimization (PSO) algorithm. The tested versions of the PSO were combined with the shuffling mechanism, which splits the model population into complexes and performs distributed PSO optimization. One of them is a new proposed PSO modification, APartW, which enhances the global exploration and local exploitation in the parametric space during the optimization process through the new updating mechanism applied on the PSO inertia weight. The performances of four selected PSO methods were tested on 11 benchmark optimization problems, which were prepared for the special session on single-objective real-parameter optimization CEC 2005. The results confirm that the tested new APartW PSO variant is comparable with other existing distributed PSO versions, AdaptW and LinTimeVarW. The distributed PSO versions were developed for finding the solution of inverse problems related to the estimation of parameters of hydrological model Bilan. The results of the case study, made on the selected set of 30 catchments obtained from MOPEX database, show that tested distributed PSO versions provide suitable estimates of Bilan model parameters and thus can be used for solving related inverse problems during the calibration process of studied water balance hydrological model.

Optimal filter design using an improved artificial bee colony algorithm

The domain of analog filter design revolves around the selection of proper values of the circuit components from a possible set of values manufactured keeping in mind the associated cost overhead. Normal design procedures result in a set of values for the discrete components that do not match with the preferred set of values. This results in the selection of approximated values that cause error in the associated design process. An optimal solution to the design problem would include selection of the best possible set of components from the numerous possible combinations. The search procedure for such an optimal solution necessitates the usage of Evolutionary Computation (EC) as a potential tool for determining the best possible set of circuit components. Recently algorithms based on Swarm Intelligence (SI) have gained prominence due to the underlying focus on collective intelligent behavior. In this paper a novel hybrid variant of a swarm-based metaheuristics called Artificial Bee Colony (ABC) algorithm is proposed and shall be referred to as CRbABC_Dt (Collective Resource-based ABC with Decentralized tasking) and it incorporates the idea of decentralization of attraction from super-fit members along with neighborhood information and wider exploration of search space. Two separate filter design instances have been tested using CRbABC_Dt algorithm and the results obtained are compared with several competitive state-of-the-art optimizing algorithms. All the components considered in the design are selected from standard series and the resulting deviation from the idealized design procedure has been investigated. Additional empirical experimentation has also been included based on the benchmarking problems proposed for the CEC 2013 Special Session & Competition on Real-Parameter Single Objective Optimization.

Group counseling optimization

In this paper, a new population-based optimization algorithm – which we call a group counseling optimizer (GCO) – is developed. Instead of mimicking the behavior of living organisms such as birds, fish, ants, and bees, we emulate the behavior of human beings in life problem solving through counseling within a group. This is motivated by the fact that the human's thinking is often predicted to be the most reasonable and influential. The inspiration radiates from the various striking points of analogy between group counseling and population-based optimization which we have discovered, as elucidated in Section 2. The algorithm is tested using seven unrotated benchmark functions and five rotated ones. Further, a comparison is made with the comprehensive learning particle swarm optimizer (CLPSO) which outperforms many other variants of the particle swarm optimizer. Using new eight composition benchmark functions, another comparison is made with the BI-population covariance matrix adaptation evolution strategy with alternative restart strategy (NBIPOP-aCMA-ES) which is the winner of the competition on real-parameter single objective optimization at IEEE CEC-2013. The results are all highly promising, demonstrating the soundness and efficacy of the proposed approach. GCO is applied to real-world application which is spacecraft trajectory design problem. Also, the results show that GCO outperforms well-known optimizers.