People vs Differential Evolution in Search of The Shortest Path

The Differential Evolution (DE) algorithm, under the family of Evolutionary Algorithms (EAs), is one of the powerful algorithms used for solving continuous parameter optimization challenges. The simplistic nature and robustness of the classical DE algorithm have drawn researchers' attention towards its progressive enhancement. This work reports on an investigation of the behavioral changes of the classical DE algorithm, evoked when its mutation and crossover components are fine tuned for enhancement of DE's performance. The scope of this study covers the implementation of a mutation level enhancement and a crossover level enhancement, followed by their integration. The mutation and the crossover components are augmented by incorporation of Centroid DE and Superior-Superior & Superior-Inferior DE logics, respectively. The algorithms appraised in this inquiry were classical DE, Centroid based DE(cDE), Superior-Superior based DE (ssDE), Superior-Inferior DE (siDE), Centroid Superior-Superior DE (cssDE) and Centroid Superior-Inferior DE (csiDE). These algorithms were evaluated by comparison of the values of their mean objective function (MOV), and their speed, at solving the global optimization problems in a simple benchmarking function suite with 4 functions of different categories. The study concludes that the DE algorithm shows enhancement performance with modified mutation and crossover components. However, with a trend for inconsistency for varying values of its control parameters and benchmarking problems.

Over the past few decades, various evolutionary algorithms (EAs) have been applied to the optimization design of water distribution systems (WDSs). An important research area is to compare the performance of these EAs, thereby offering guidance for the selection of the appropriate EAs for practical implementations. Such comparisons are mainly based on the final solution statistics and, hence, are unable to provide knowledge on how different EAs reach the final optimal solutions and why different EAs performed differently in identifying optimal solutions. To this end, this paper aims to compare the real-time searching behaviour of three widely used EAs, which are genetic algorithms (GAs), the differential evolution (DE) algorithm and the ant colony optimization (ACO). These three EAs are applied to five WDS benchmarking case studies with different scales and complexities, and a set of five metrics are used to measure their run-time searching quality and convergence properties. Results show that the run-time metrics can effectively reveal the underlying searching mechanisms associated with each EA, which significantly goes beyond the knowledge from the traditional end-of-run solution statistics. It is observed that the DE is able to identify better solutions if moderate and large computational budgets are allowed due to its great ability in maintaining the balance between the exploration and exploitation. However, if the computational resources are rather limited or the decision has to be made in a very short time (e.g., real-time WDS operation), the GA can be a good choice as it can always identify better solutions than the DE and ACO at the early searching stages. Based on the results, the ACO performs the worst for the five case study considered. The outcome of this study is the offer of guidance for the algorithm selection based on the available computation resources, as well as knowledge into the EA’s underlying searching behaviours.

Social learning differential evolution

A local search enhanced differential evolutionary algorithm for sparse recovery

Evaluation of stochastic global optimization methods for modeling vapor–liquid equilibrium data

Researchers can solve Simple optimization problems using various methods. But differential Evolution (DE) is a method(population based) to solve complex optimization problems in some easy steps that is not possible to handle by mathematical optimization methods. For global optimization problems DE is a probabilistic approach. DE when tested over some bench mark functions and real world problems it performed better than some evolutionary algorithms and swarm - intelligence based algorithms. Balancing between Exploration and Exploitation using DE mutation and crossover with control parameters F and CR (fine tunned) is to be done. DE does not complete demand of good convergence and stagnation. DE Explore better but this exploration capability sometimes may skip the true solution and exhibit premature convergence. To improve this we can decrease the step size but this exhibit stagnation. So for Better exploitation, another approach called Memetic algorithm based on levy flight based local search strategy is used with DE. Further to balance exploration and exploitation in local search area in this paper a population or generation based exploitation of local search area in LFDE is proposed that is called PGLFDE. To show better result proposed strategy is tested on some bench mark functions and compare with recent variants of DE.

In recent years, Differential Evolution (DE) algorithm that is one of the most important delegate of the evolutionary algorithms have been successfully used for solving different optimization problems with its both serial and parallel variants. In this study, the performance of DE algorithm powered with cooperative emigrant creation strategy was investigated over the different types of numerical problems and obtained results were compared with the results of the serial DE and parallel DE algorithm supported with conventional emigrant creation strategy. Experimental studies showed that the convergence speed of the parallel DE algorithm is significantly improved with the cooperative emigrant creation strategy and the proposed parallel DE algorithm produces better results compared to the serial DE algorithm and parallel DE algorithm with the conventional emigrant creation strategy.

\nThis paper present the parameter identification of damped compound pendulum using differential evolution algorithm. The procedure used to achieve the parameter identification of the experimental system consisted of input output data collection, ARX model order selection and parameter estimation using conventional method least square (LS) and differential evolution (DE) algorithm. PRBS signal is used to be input signal to regulate the motor speed. Whereas, the output signal is taken from position sensor. Both, input and output data is used to estimate the parameter of the ARX model. The residual error between the actual and predicted output responses of the models is validated using mean squares error (MSE). Analysis showed that, MSE value for LS is 0.0026 and MSE value for DE is 3.6601×10-5. Based results obtained, it was found that DE have lower MSE than the LS method.\n

Evolutionary Algorithms (EAs) have become much popular in tackling kinds of complex optimization problems nowadays, and Differential Evolution (DE) is one of the most popular EAs for real-parameter numerical optimization problems. Here in this paper, we mainly focus on an external hierarchical archive based DE algorithm. The external hierarchical archive in the mutation strategy of DE algorithm can further improve the diversity of trial vectors and the depth information extracted from the hierarchical archive can achieve a better perception of the landscape of objective function, both of which consequently help this new DE variant secure an overall better optimization performance. Commonly used benchmark functions are employed here in verifying the overall performance and experiment results show that the new algorithm is competitive with other state-of-the-art DE variants.

Abstract: This paper presents a new multi-objective evolu-tionary algorithm based on differential evolution. The pro-posed approach adopts a secondary population in order to re-tain the nondominated solutions found during the evolution-ary process. Additionally, the approach also incorporates theconcept of † -dominance to get a good distribution of the solu-tions retained. The main goal of this work was to keep thefast convergence exhibited by Differential Evolution in globaloptimization when extending this heuristic to multi-objectiveoptimization. We adopted standard test functions and perfor-mance measures reported in the specialized literature to vali-date our proposal. Our results are compared with respect toanother multi-objective evolutionary algorithm based on differ-ential evolution (Pareto Differential Evolution) and with respectto two approaches that are representative of the state-of-the-artin the area: the NSGA-II and † -MOEA. I. Introduction Most real world problems involve the simultaneous opti-mization of two or more (often conflicting) objectives. Thesolution of such problems (called “multi-objective”) is differ-ent from that of a single-objective optimization problem. Themain difference is that multi-objective optimization problemsnormally have not one but a set of solutions which are allequally good.In the past, a wide variety of evolutionary algorithms (EA’s)have been used to solve multi-objective optimization prob-lems [5]. However, from the several types of EAs available,few researchers have attempted to extend Differential Evo-lution (DE) [25] to solve multi-objective optimization prob-lems. DE has been very successful in the solution of a va-riety of continuous (single-objective) optimization problemsin which it has shown a great robustness and a very fast con-vergence. These are precisely the characteristics of DE thatmake it attractive to extend it to solve multi-objective opti-mization problems.In this paper, we propose a new multi-objective evolution-ary algorithm based on differential evolution. Our approachuses an external archive in which the relaxed form of Paretodominance known as

Most of the existing evolutionary algorithms to deal with many-objective problems are based on the enhancing of selection strategy. Among them, the reference vector-guided evolutionary algorithm (RVEA) achieves excellent performance. In this paper, a new search engine is combined with RVEA to achieve further performance enhancement of the differential evolutionary (DE) algorithm. In the optimization process of differential evolution algorithm on many-objective problems, improving convergence and maintaining diversity are two different optimization directions, and it is usually difficult to maintain a balance between them. To solve this problem, a new search engine based on DE is proposed. The proposed search engine is implemented based on a cooperative scheme of local and global search strategies. In the local search, the population is divided into several sub-populations, each of which evolves independently using the proposed mutation strategy. The distance between the individuals in each sub-population is relatively close. Therefore, it has a strong exploitation capability, and will not make the population lose diversity. Meanwhile, the selection strategy of RVEA enables the population to maintain diversity, and the DE/rand/1 utilized in global search is sufficient to keep a strong exploration capability. Therefore, the proposed approach can achieve a good balance between exploration and exploitation. The experimental results show that the proposed algorithm performs well in many-objective optimizations up to more than 10 objectives.

Multi-layer competitive-cooperative framework for performance enhancement of differential evolution

Differential evolution (DE) is one of the most successful evolutionary algorithms (EAs) for global numerical optimization. Like other EAs, maintaining population diversity is important for DE to escape from local optima and locate a near-global optimum. Using a multi-population algorithm is a representative method to avoid early loss of population diversity. In this paper, we propose a multi-population DE algorithm (MPDE) which manipulates multiple sub-populations. Different sub-populations in MPDE exchange information via a novel mutation operation instead of migration used in most multi-population EAs. The mutation operation is helpful to balance the fast convergence and population diversity of the proposed algorithm. Moreover, the performance of MPDE is further improved by an adaptive parameter control scheme designed based on the multi-population approach. Each sub-population in MPDE evolves with its own set of control parameters, and a learning strategy is used to adaptively adjust the parameter values. A set of benchmark functions is used to test the proposed MPDE algorithm. The experimental results show that MPDE performs better than, or at least comparably, to the classical single population DE with fixed parameter values and three existing state-of-the-art DE variants.

Differential Evolution (DE) is a new branch of Evolutionary Algorithms (EAs) and has been successfully applied to solve the optimal reactive power flow (ORPF) problems in power systems. Although DE can avoid premature convergence, large population is needed and the application of DE is limited in large-scale power systems. Grid computing, as a prevalent paradigm for resource-intensive scientific application, is expected to provide a computing platform with tremendous computational power to speed up the optimization process of DE. When implanting DE based ORPF on grid system, fault tolerance due to unstable environment and variation of grid is a significant issue to be considered. In this paper, a fault tolerant DE-based ORPF method is proposed. In this method, when the individuals are distributed to the grid for fitness evaluation, a proportion of individuals, which returns from the grid slowly or fails to return, are replaced with new individuals generated randomly according to some specific rules. This approach can deal with the fault tolerance and also maintain diversity of the population of DE. The superior performance of the proposed approach is verified by numerical simulations on the ORPF problem of the IEEE 118-bus standard power system.

Evolutionary algorithms (EAs) have been widely used to search for optimal strategies for the planning and management of water resources systems, particularly reservoir operation. This study provides a comprehensive diagnostic assessment of state of the art of the non-animal-inspired EA applications to reservoir optimization. This type of EAs does not mimic biologic traits and group strategies of animal (wild) species. A search of pertinent papers was applied to the journal citation reports (JCRs). A bibliometric survey identified 14 pertinent non-animal-inspired EAs, such as the genetic algorithm (GA), simulated annealing (SA), and differential evolution (DE) algorithms, most of which have a number of modified versions. The characteristics of non-animal-inspired EAs and their modified versions were discussed to identify the difference between EAs and how each EA was improved. Additionally, the type of application of non-animal-inspired EAs to different case studies was investigated, and comparisons were made between the performance of the applied EAs in the studied literature. The survey revealed that the GA is the most frequently applied algorithm, followed by the DE algorithm. Non-animal-inspired EAs are superior to the classical methods of reservoir optimization (e.g., the non-linear programming and dynamic programming) due to faster convergence, diverse solution space, and efficient objective function evaluation. Several non-animal-inspired EAs of recent vintage have been shown to outperform the classic GA, which was the first evolutionary algorithm applied to reservoir operation.