Differential evolution for dynamic environments with unknown numbers of optima

This paper proposes a novel distributed differential evolution framework called distributed mixed variants (dynamic) differential evolution ( $$dmvD^{2}E)$$ d m v D 2 E ) . This novel framework is a heterogeneous mix of effective differential evolution (DE) and dynamic differential evolution (DDE) variants with diverse characteristics in a distributed framework to result in $$dmvD^{2}E$$ d m v D 2 E . The $$dmvD^{2}E$$ d m v D 2 E , discussed in this paper, constitute various proportions and combinations of DE/best/2/bin and DDE/best/2/bin as subpopulations with each variant evolving independently but also exchanging information amongst others to co-operatively enhance the efficacy of $$dmvD^{2}E$$ d m v D 2 E as whole. The $$dmvD^{2}E$$ d m v D 2 E variants have been run on 14 test problems of 30 dimensions to display their competitive performance over the distributed classical and dynamic versions of the constituent variants. The $$dmvD^{2}E$$ d m v D 2 E , when benchmarked on a different 13 test problems of 500 as well as 1,000 dimensions, scaled well and outperformed, on an average, five existing distributed differential evolution algorithms.

This paper introduces the optimization of a quantum control application, the so-called molecular alignment problem, subject to a dynamic environment. Given the relative simplicity of optimized pulse-shapes in the low-intensity variant of the problem, versus the high complexity of the optimized pulse-shapes in the high-intensity case, a dynamic-intensity environment is simulated in a noise-free calculation. Specific evolution strategies, natural candidates for optimization in dynamic environments, are applied to this task. The calculations reveal the evolution of the pulse-shapes and their underlying evolving structures, that allow a complete physical interpretation. The combination of an optimization in a dynamic environment with the examination of the intermediate optimized solutions offers a sharper physics view of the problem, and accomplishes a fruitful interdisciplinary study.

Differential evolution is a population-based optimisation algorithm and has been successfully applied in many fields. However, when tackling large-scale optimisation problem, it still encounters serious challenges. To meet these challenges, a dynamic differential evolution with oppositional orthogonal crossover is proposed in this paper. A new oppositional learning is proposed and then it is used in the orthogonal crossover to improve the exploitation ability of the dynamic differential evolution. During the evolution process in dynamic differential evolution, only one individual is randomly chosen to undergo this oppositional orthogonal crossover operation. Thirteen benchmark problems with 1,000 dimensions were used to evaluate its performance. The results show that the proposed method is very competitive in terms of solution quality obtained.

A prediction mechanism for Memetic Algorithm is presented in this paper. The Predictive Memetic Algorithm (PMA) uses a nonlinear regression method to estimate the parameters used by the algorithm to obtain good solutions in a dynamic and stochastic environment. The algorithm is applied to nonlinear data sets and performance is compared with genetic and simulated annealing algorithms. When compared with the existing methods, the proposed method generates a relatively small error difference after prediction thereby proving its superior performance. A dynamic stochastic environment is used for experimentation, so as to determine the efficacy of the algorithm on non-stationary problem environments.

In the real world, many optimization problems are dynamic. This requires an optimization algorithm to not only find the global optimal solution under a specific environment but also to track the trajectory of the changing optima over dynamic environments. To address this requirement, this paper investigates a clustering particle swarm optimizer (PSO) for dynamic optimization problems. This algorithm employs a hierarchical clustering method to locate and track multiple peaks. A fast local search method is also introduced to search optimal solutions in a promising subregion found by the clustering method. Experimental study is conducted based on the moving peaks benchmark to test the performance of the clustering PSO in comparison with several state-of-the-art algorithms from the literature. The experimental results show the efficiency of the clustering PSO for locating and tracking multiple optima in dynamic environments in comparison with other particle swarm optimization models based on the multiswarm method.

In recent years, optimization in dynamic environments has attracted a growing interest from the genetic algorithm community due to the importance and practicability in real world applications. This paper proposes a new genetic algorithm, based on the inspiration from biological immune systems, to address dynamic traveling salesman problems. Within the proposed algorithm, a permutation-based dualism is introduced in the course of clone process to promote the population diversity. In addition, a memory-based vaccination scheme is presented to further improve its tracking ability in dynamic environments. The experimental results show that the proposed diversification and memory enhancement methods can greatly improve the adaptability of genetic algorithms for dynamic traveling salesman problems.

Based on the polar coordination particle swarm optimization (PPSO), this paper presents a novel method for the robot path planning in dynamic environment. It decomposes the task into a global planning stage and a local planning stage. PPSO algorithm can search for the global optimal path based on static obstacles information. When the robot moves along the optimal global path, an on-line real-time path planning strategy is adopted to avoid dynamic obstacles by means of predicting the future positions of moving obstacles. Simulation experiment shows that the method is more efficient than traditional particle swarm optimization (TPSO) and genetic algorithm (GA) for solving path planning problem. The feasibility and high stability of real-time obstacle avoidance strategy are demonstrated in dynamic environment.

A novel culture-based multiswarm artificial bee colony (CMABC) algorithm was proposed to address dynamic optimization problems. The historical experience of sub-swarms is preserved as cultural knowledge to guide the subsequent evolutionary process. Experiments were conducted on the moving peaks benchmark function. The results show that the CMABC algorithm was better than, or at least comparable to, the basic ABC algorithm, and other state-of-the-art algorithms.

A novel immune algorithm suitable for dynamic environments (GIDE) is proposed based on a biological immune mechanism. GIDE models the dynamic process of artificial immune response with gradient-based diversity operators. Unlike traditional artificial immune algorithms, which require that randomly generated cells be added to the current population to explore its fitness landscape, GIDE uses a gradient-based diversity operator to speed up optimization in dynamic environments. Other immune algorithms are compared to GIDE by using Moving Peaks Benchmarks. Preliminary experiments showed that GIDE can maintain high population diversity during the search process, while simultaneously speeding up optimization. Thus, GIDE is useful for optimization of dynamic environments.

Optimisation in dynamic environments is a very active and important area which tackles problems that change with time (as most real-world problems do). The possibility to use a new centralised cooperative strategy based on trajectory methods (tabu search) for solving Dynamic Optimisation Problems (DOPs) was previously introduced showing good results against state of the art methods like the Particle Swarm Optimisation (PSO) variant with multiple swarms and different types of particles. The analysis of this previous work are further extended here by exploring more possibilities for the cooperation rules used in the strategy. The results show that different classes of cooperation can lead to quite different results, some of them greatly outperforming the previous ones.

The power system reactive power optimization model mainly establishes a model to reduce the line active power loss as an indicator. The model is established with the least active power loss, the highest voltage stability margin and the smallest voltage deviation. Aiming at the shortcomings of differential evolution algorithm which is easy to fall into local optimum, this paper proposes to apply dynamic multi-subgroup differential evolution algorithm to power system reactive power optimization. The dynamic subgroup partitioning feature of the algorithm improves the global search ability, and increases the polymorphism of species during the iterative process. The dynamic multi-subgroup differential evolution algorithm and differential evolution algorithm are substituted into the power system IEEE-14 nodes for simulation comparison, and the feasibility and superiority of the algorithm are verified. Comparing the simulation diagrams of the two algorithms, it can be seen that the dynamic multi-subgroup differential evolution algorithm has significant advantages in power system reactive power optimization.

Dynamic multi-objective evolutionary algorithms (Dynamic MOEAs) use the evolutionary algorithms to solve the dynamic multi-objective optimization problems (DMOPs). It has become one of the hot areas of research. The challenge of DMOPs is that the objective functions, the constraints or the parameters may change over time. This paper tries to provide a comprehensive overview of the related work, which is organized by the common process of Dynamic MOEAs, such as, the detection of change, the maintenance of diversity, the prediction of change, the test problems and the performance metrics. Finally, topics for further research are suggested.

An improved dynamic multi-objective optimization approach for nonlinear equation systems

The application of two techniques for the reconstruction of shape reconstruction of a metallic cylinder from scattered field measurements is studied in this paper. These techniques are applied to two-dimensional configurations, for which the method of moment (MoM) is applied to solve the integral equations. Considering that the microwave imaging is recast as a nonlinear optimization problem, an objective function is defined by the norm of the difference between the measured scattered electric fields and those calculated for each estimated metallic cylinder. Thus, the shape of a metallic cylinder can be obtained by minimizing the objective function. In order to solve this inverse scattering problem, two techniques are employed. The first one is based on dynamic differential evolution (DDE) algorithm, while the second one is an improved version of the DDE algorithm with self-adaptive control parameters, called SADDE. Both techniques are tested for the simulated data contaminated by additive white Gaussian noise. Numerical results indicate that SADDE algorithm outperforms DDE algorithm in terms of reconstruction accuracy and convergence speed.

The insertion of atypical solutions (immigrants) in Evolutionary Algorithms populations is a well studied and successful strategy to cope with the difficulties of tracking optima in dynamic environments in single-objective optimization. This paper studies a probabilistic model, suggesting that centroid-based diversity measures can mislead the search towards optima, and presents an extended taxonomy of immigration schemes, from which three immigrants strategies are generalized and integrated into NSGA2 for Dynamic Multiobjective Optimization (DMO). The correlation between two diversity indicators and hypervolume is analyzed in order to assess the influence of the diversity generated by the immigration schemes in the evolution of non-dominated solutions sets on distinct continuous DMO problems under different levels of severity and periodicity of change. Furthermore, the proposed immigration schemes are ranked in terms of the observed offline hypervolume indicator.