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In this paper, we propose a T wo-stage D ifferential E volution (TDE) with novel parameter control for real parameter single objective global optimization. In the TDE algorithm, the whole evolution is divided into two stages and each stage employs a unique mutation strategy. The mutation strategy in the first stage is a novel historical-solution based mutation strategy, which can get better perception of the landscape of the objective; the mutation strategy in the second stage is an inferior-solution based mutation strategy, which can maintain better diversity of trial vector candidates while keeping better convergence speed. Furthermore, the parameter control of our TDE is novel, which means that these adaptations of control parameters are different from those in the literature: First, the adaptation schemes both for scale factor F and crossover rate CR are fitness-independent. Second, different from the fixed population size and the gradually reduced population size, the population adaptation in TDE has two different stages. Third, a stagnation indicator is proposed and a population enhancement technique can be launched if necessary when a certain individual is in the stagnation status. We examine the TDE algorithm under a relative large number of benchmarks from CEC2013, CEC2014 and CEC2017 test suites for real-parameter single objective global optimization, and the experiment results show the competitiveness of our TDE algorithm with several recently proposed state-of-the-art DE variants, e.g. it obtained 20 similar or better performance improvements out of the total 30 benchmarks in comparison with the winner algorithm, the LSHADE algorithm, of the CEC2014 competition and it also obtained 19 similar or better performance improvements out of the total 30 benchmarks in comparison with the winner DE variant, the jSO algorithm, of the CEC2017 competition. [ABSTRACT FROM AUTHOR]

Particle Swarm Optimization(PSO) is a well-known and powerful meta-heuristic algorithm in Swarm Intelligence (SI), and it was invented by simulating the foraging behavior of bird flock in 1995. Recently, many different PSO variants were proposed to tackle different optimization applications, however, the overall performance of these variants were not satisfactory. In this paper, a new PSO variant is advanced to tackle single-objective numerical optimization, and there are three contributions mentioned in the paper: First, a sorted particle swarm with hybrid paradigms is proposed to improve the optimization performance; Second, novel adaptation schemes both for the ratio of each paradigm and the constriction coefficients are proposed during the iteration; Third, a fully-informed search scheme based on the global optimum in each generation is proposed which helps the algorithm to jump out the local optimum and improve the overall performance. A large test suite containing benchmarks from CEC2013, CEC2014 and CEC2017 test suites on real-parameter single-objective optimization is employed in the algorithm validation, and the experiment results show the competitiveness of our algorithm with the famous or recently proposed state-of-the-art PSO variants. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE) is one of the most effective approaches in Evolutionary Computation to tackling complex black-box optimization, however, the overall performance of a DE variant is heavily dependent on its mutation strategy and the associated parameter control schemes. According to the "No free Lunch theorem", every mutation strategy has its own fatal defect, therefore, DE variant with a single mutation strategy can not tackle all optimization problems. Furthermore, DE variant with ensemble of mutation strategies usually needs more parameter control schemes, which inevitably decreases the practicality of it. Here in this paper, a novel Cooperative Strategy based DE (CS-DE) with population diversity enhancement is proposed, and the CS-DE algorithm has the following contributions: First, a cooperative strategy pool containing two similar mutation strategies is advanced in the algorithm, and the two mutation strategies share the same parameter control. Second, a novel grouping strategy is proposed, then the two mutation strategies can be chosen in an adaptive manner by different individuals in generating trial vectors during the evolution. Third, novel adaptation schemes for the three control parameters F , CR and PS as well as a stagnation based re-initialization mechanism are also proposed in our CS-DE algorithm. 58 benchmarks from the CEC2013 and CEC2014 test suites are employed in algorithm validation, and experiment results show the competitiveness of the CS-DE algorithm with several state-of-the-art DE variants. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE) was a powerful population-based evolutionary algorithm for global optimization, and it achieved great success in both evolutionary computation competitions and engineering applications. Despite the excellent performance of the state-of-the-art DE variants, there are still two main weaknesses existing within them: one is the weakness in a given mutation strategy and the other is the weakness in the corresponding parameter control (of the mutation strategy). By reviewing the existing mutation strategies in the recent state-of-the-art DE variants, it can be seen that all of them have insufficient use of the knowledge obtained during the evolution because the historical information of the population is not taken into consideration, which inevitably leads to a bad perception of the landscapes of the objectives. Moreover, the adaptations of the control parameters including F and CR in these state-of-the-art DE variants are interlaced with one another. A bad F and a good CR may produce a good trial vector candidate, then the bad F is of misuse in the parameter control and vice versa. In this paper, a novel DE variant, called Hip-DE, meaning the latest fashion of DE, with historical population based mutation strategy was proposed to tackle the above mentioned weaknesses. Moreover, novel parameter adaptive mechanisms for control parameters F and CR as well as a platform based step-decrease scheme of population size were proposed to enhance capacity of the mutation strategy. By incorporating these three advancements, the novel Hip-DE algorithm secured an overall better performance on the tested benchmarks in comparison with the recent proposed state-of-the-art DE variants. [ABSTRACT FROM AUTHOR]

Differential Evolution is a well-known stochastic algorithm in Evolutionary Computation (EC) for single-objective numerical optimization, and its powerful variants secured excellent ranks in recent competitions. These winner DE variants all employed binomial crossover which tackles the positional bias in crossover operation by treating the D parameters separately and independently, however, the binomial crossover in these winner DE variants still have bias from the spatial search perspective, and this was the reason why the QU asi- A ffine TR ansformation E volution (QUATRE) algorithm in the literature was proposed. In this paper, a novel QUATRE algorithm with novel adaptation of E volution M atrix and S election operation (QUATRE-EMS) was proposed to further improve the overall performance of the QUATRE variants for numerical optimization and the main highlights can be summarized as follows. First, the number of control parameters is reduced from three in DE to two in QUATRE-EMS by proposing an auto-generated evolution matrix. Second, a novel adaptation scheme of the evolution matrix M is proposed for a better adaptation of the landscape of the objective during evolution; Third, a new selection operation is proposed instead of employing the canonical selection operation in DE. Finally, a large test suite containing 100 benchmarks from CEC2013, CEC2014, CEC2017 and CEC2022 test suites for single-objective numerical optimization is used for algorithm validation, and total 11 state-of-the-art algorithms including our QUATRE-EMS are taken into comparison. The experimental results show the superiority of our algorithm in comparison with former QUATRE variants and several state-of-the-art DE variants. [ABSTRACT FROM AUTHOR]

Surrogate-assisted evolutionary algorithms (SAEAs) have gained considerable attention owing to their ability of tackling expensive optimization problems (EOPs). The surrogate model can be used to replace real fitness value with approximated one, thus greatly reducing computational cost in expensive function evaluations. However, most existing SAEAs are designed for expensive optimization with low or medium dimensions owing to the curse of dimensionality. To improve the performance for solving high-dimensional expensive optimization problems (HEOPs), a surrogate-assisted Differential Evolution with fitness-independent parameter adaptation (SADE-FI) is proposed in the paper. The SADE-FI algorithm consists of a global surrogate-assisted prescreening strategy (GSA-PS) and a local surrogate-assisted DE with fitness-independent parameter adaptation (LSA-FIDE). The main highlights of the paper can be summarized as follows: First, both global and local surrogates are employed to approximate the fitness value of candidate offspring in GSA-PS and LSA-FIDE, respectively. Second, a fitness-independent parameter adaptation mechanism is firstly incorporated into the framework of surrogate-assisted DE as an efficient parameter adaptation for surrogate-assisted search. Third, both the kernel space determination mechanism and linear population size reduction strategy are implemented to enhance the exploitation capability of LSA-FIDE. To validate the performance of SADE-FI, it was tested on expensive benchmark functions on 30D, 50D, 100D, and 200D, as well as a real-world antenna array design problem. The optimization results were compared with state-of-the-art algorithms, and the results indicate that SADE-FI has a significant performance advantage in solving HEOPs. [ABSTRACT FROM AUTHOR]