Differential evolution with an evolution path: a DEEP evolutionary algorithm

Utilizing cumulative correlation information already existing in an evolutionary process, this paper proposes a predictive approach to the reproduction mechanism of new individuals for differential evolution (DE) algorithms. DE uses a distributed model (DM) to generate new individuals, which is relatively explorative, whilst evolution strategy (ES) uses a centralized model (CM) to generate offspring, which through adaptation retains a convergence momentum. This paper adopts a key feature in the CM of a covariance matrix adaptation ES, the cumulatively learned evolution path (EP), to formulate a new evolutionary algorithm (EA) framework, termed DEEP, standing for DE with an EP. Without mechanistically combining two CM and DM based algorithms together, the DEEP framework offers advantages of both a DM and a CM and hence substantially enhances performance. Under this architecture, a self-adaptation mechanism can be built inherently in a DEEP algorithm, easing the task of predetermining algorithm control parameters. Two DEEP variants are developed and illustrated in the paper. Experiments on the CEC'13 test suites and two practical problems demonstrate that the DEEP algorithms offer promising results, compared with the original DEs and other relevant state-of-the-art EAs

Composite Differential Evolution for Constrained Evolutionary Optimization

When solving constrained optimization problems (COPs) by evolutionary algorithms, the search algorithm plays a crucial role. In general, we expect that the search algorithm has the capability to balance not only diversity and convergence but also constraints and objective function during the evolution. For this purpose, this paper proposes a composite differential evolution (DE) for constrained optimization, which includes three different trial vector generation strategies with distinct advantages. In order to strike a balance between diversity and convergence, one of these three trial vector generation strategies is able to increase diversity, and the other two exhibit the property of convergence. In addition, to accomplish the tradeoff between constraints and objective function, one of the two trial vector generation strategies for convergence is guided by the individual with the least degree of constraint violation in the population, and the other is guided by the individual with the best objective function value in the population. After producing offspring by the proposed composite DE, the feasibility rule and the ϵ constrained method are combined elaborately for selection in this paper. Moreover, a restart scheme is proposed to help the population jump out of a local optimum in the infeasible region for some extremely complicated COPs. By assembling the above techniques together, a constrained composite DE is proposed. The experiments on two sets of benchmark test functions with various features, i.e., 24 test functions from IEEE CEC2006 and 18 test functions with 10 dimensions and 30 dimensions from IEEE CEC2010, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods

Weight optimization of steel lattice transmission towers based on Differential Evolution and machine learning classification technique

Transmission towers are tall structures used to support overhead power lines. They play an important role in the electrical grids. There are several types of transmission towers in which lattice towers are the most common type. Designing steel lattice transmission towers is a challenging task for structural engineers due to a large number of members. Therefore, discovering effective ways to design lattice towers has attracted the interest of researchers. This paper presents a method that integrates Differential Evolution (DE), a powerful optimization algorithm, and a machine learning classification model to minimize the weight of steel lattice towers. A classification model based on the Adaptive Boosting algorithm is developed in order to eliminate unpromising candidates during the optimization process. A feature handling technique is also introduced to improve the model quality. An illustrated example of a 160-bar tower is conducted to demonstrate the efficiency of the proposed method. The results show that the application of the Adaptive Boosting model saves about 38% of the structural analyses. As a result, the proposed method is 1.5 times faster than the original DE algorithm. In comparison with other algorithms, the proposed method obtains the same optimal weight with the least number of structural analyses

Migration in Multi-Population Differential Evolution for Many Objective Optimization

The paper proposes a novel extension of many objective optimization using differential evolution (MaODE). MaODE solves a many objective optimization (MaOO) problem by parallel optimization of individual objectives. MaODE involves N populations, each created for an objective to be optimized using MaODE. The only mode of knowledge transfer among populations in MaODE is the modified version of mutation policy of DE, where every member of the population during mutation is influenced by the best members of all the populations under consideration. The present work aims at further increasing the communication between the members of the population by communicating between a superior and an inferior population, using a novel migration strategy. The proposed migration policy enables poor members of an inferior population to evolve with a superior population. Simultaneously, members from the superior population are also transferred to the inferior one to help it improving its performance. Experiments undertaken reveal that the proposed extended version of MaODE significantly outperforms its counterpart and the state-of-the-art techniques

Differential evolution with two-level parameter adaptation

The performance of differential evolution (DE) largely depends on its mutation strategy and control parameters. In this paper, we propose an adaptive DE (ADE) algorithm with a new mutation strategy DE/lbest/1 and a two-level adaptive parameter control scheme. The DE/lbest/1 strategy is a variant of the greedy DE/best/1 strategy. However, the population is mutated under the guide of multiple locally best individuals in DE/lbest/1 instead of one globally best individual in DE/best/1. This strategy is beneficial to the balance between fast convergence and population diversity. The two-level adaptive parameter control scheme is implemented mainly in two steps. In the first step, the population-level parameters F p and CR p for the whole population are adaptively controlled according to the optimization states, namely, the exploration state and the exploitation state in each generation. These optimization states are estimated by measuring the population distribution. Then, the individual-level parameters F i and CR i for each individual are generated by adjusting the population-level parameters. The adjustment is based on considering the individual's fitness value and its distance from the globally best individual. This way, the parameters can be adapted to not only the overall state of the population but also the characteristics of different individuals. The performance of the proposed ADE is evaluated on a suite of benchmark functions. Experimental results show that ADE generally outperforms four state-of-the-art DE variants on different kinds of optimization problems. The effects of ADE components, parameter properties of ADE, search behavior of ADE, and parameter sensitivity of ADE are also studied. Finally, we investigate the capability of ADE for solving three real-world optimization problems

Determination of an effective implementation of the differential evolution method to power shortage minimization

Constant development of electric power systems leads to their constant enlargement and complication; new ways of their control appear. In this regard, the existing models and software for adequacy assessment may work defective and ineffectively from the point of view of the adequacy of the obtained results, as well as the speed and accuracy of calculations. The key role in adequacy assessment of electric power systems (EPS) are played by optimization methods that allow to correctly determine the minimum of power shortage that occurs in various states of the EPS. A review of modern computational systems for adequacy assessment showed that the general concept of mathematical models is the same and can be described within the framework of the flow distribution problem. Despite this, each mathematical model is unique in its own way and requires an individual approach to its optimization. The purpose of this work is to analyze the efficiency of calculations in terms of accuracy and speed of various versions of the differential evolution (DE) method for the specified mathematical models within the framework of adequacy assessment of EPS. To achieve this goal, we solved several problems: two mathematical models were identified - a nonlinear model for minimizing the power shortage with the quadratic losses in flows and its modification with the controlled sections; differential evolution methods, including standard DE, composite DE, JDE, chaotic DE, adaptive DE; mutation strategies: DE/rand/1, DE/best/1, DE/rand/2, DE/best/2, DE/rand/3, DE/best/3, DE/current-to-rand/1, and DE/current-to-best/1. In this paper we tested the effectiveness of differential evolution methods, with different mutation strategies and different scales of EPSs. The experimental part was carried out using a software that was independent development by authors using C++. This complex includes the implementation of mathematical models and methods. The methods were tested on two systems with different numbers of adequacy zones, including those with three and seven adequacy zones. According to the research results, self-adaptive methods of DE are of the greatest interest for the further use and development of methods for this problem, due to automatic adjustment of the method parameters for each of the considered models and systems

Differential Evolution Optimal Parameters Tuning with Artificial Neural Network

Differential evolution (DE) is a simple and efficient population-based stochastic algorithm for solving global numerical optimization problems. DE largely depends on algorithm parameter values and search strategy. Knowledge on how to tune the best values of these parameters is scarce. This paper aims to present a consistent methodology for tuning optimal parameters. At the heart of the methodology is the use of an artificial neural network (ANN) that learns to draw links between the algorithm performance and parameter values. To do so, first, a data-set is generated and normalized, then the ANN approach is performed, and finally, the best parameter values are extracted. The proposed method is evaluated on a set of 24 test problems from the Black-Box Optimization Benchmarking (BBOB) benchmark. Experimental results show that three distinct cases may arise with the application of this method. For each case, specifications about the procedure to follow are given. Finally, a comparison with four tuning rules is performed in order to verify and validate the proposed method’s performance. This study provides a thorough insight into optimal parameter tuning, which may be of great use for users.The authors appreciate the support to the government of the Basque Country through research programs Grants N. ELKARTEK 20/71 and ELKARTEK: KK-2019/00099