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Differential Evolution

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Differential Evolution is a stochastic, population-based optimization algorithm used for solving complex optimization problems. It iteratively improves candidate solutions by applying operations such as mutation, crossover, and selection, leveraging the differences between randomly selected individuals to explore the solution space effectively.
lightbulbAbout this topic
Differential Evolution is a stochastic, population-based optimization algorithm used for solving complex optimization problems. It iteratively improves candidate solutions by applying operations such as mutation, crossover, and selection, leveraging the differences between randomly selected individuals to explore the solution space effectively.

Key research themes

1. How can control parameters of Differential Evolution be dynamically adapted during optimization to improve convergence and robustness?

This theme investigates methods for adaptively tuning DE’s critical control parameters—such as crossover rate, scaling factor (mutation factor), and population size—during the evolutionary process. Appropriate setting of these parameters is crucial for balancing exploration and exploitation, avoiding premature convergence or stagnation, and improving convergence speed and solution quality. Since optimal parameter values are problem-dependent and may need to vary over time within a run, dynamic or self-adaptive parameter control mechanisms seek to automate parameter selection without costly trial-and-error tuning, thereby improving DE’s robustness and applicability across diverse problems.

Key finding: This paper proposes a DE algorithm (DE-DPS) that dynamically selects the best-performing combinations of three control parameters—amplification factor (F), crossover rate (CR), and population size (NP)—during a single run.... Read more
Key finding: The study examines the effect of sorting crossover rates generated by parameter adaptation mechanisms before applying them in crossover in several modern DE variants (e.g., L-SHADE-RSP). Sorting crossover rates allows smaller... Read more
Key finding: This research introduces a population size adaptation mechanism that adjusts the DE population dynamically based on real-time measurements of population diversity. Unlike traditional schemes that only linearly reduce... Read more
Key finding: This study proposes SAEDE, a self-adaptive ensemble-based DE that dynamically sets control parameters (scaling factor F and crossover rate CR) and mutation strategies each generation via self-adaptation and ensemble... Read more
Key finding: This paper introduces a novel method using shadowed type-2 fuzzy systems (ST2-FS) to dynamically adapt the DE crossover parameter (CR) in optimizing a motor position control problem with an interval type-2 fuzzy controller.... Read more

2. What strategies and modifications to DE mutation and population initialization can improve convergence speed and solution quality, especially in complex, high-dimensional, or noisy optimization?

This research focus explores new mutation donor formulations, hybrid local search incorporations, advanced initialization schemes, and robustness enhancements to accelerate convergence, escape stagnation, and improve optimization quality in DE. Such strategies seek to overcome DE’s sensitivity to parameter settings, slow convergence on high-dimensional or multimodal problems, and challenges posed by noise or deceptive fitness landscapes. They include new mutation vector constructions balancing exploration and exploitation, integration of local refinement with feedback-based timing, advanced initial population construction methods, and noise-aware selection schemes.

Key finding: The paper proposes three new donor vector schemes for the DE mutation operator, using convex combinations of individuals in the mutation triplet instead of classical difference vectors. These schemes utilize local information... Read more
by Musrrat Ali and 
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Key finding: This work investigates the impact of initial population generation methods on DE performance. Instead of conventional pseudorandom or quasi-random sequences, the authors propose using nonlinear simplex methods combined with... Read more
Key finding: Addressing noisy fitness functions, this paper proposes NADE, a DE variant that combines randomised scaling factors with statistical testing in survivor selection to dynamically determine appropriate sample sizes and reject... Read more
Key finding: This study introduces a mutation strategy guided by the feedback of how many consecutive unsuccessful global optimum updates have occurred, aiming to escape stagnation and balance exploration-exploitation in DE. The proposed... Read more
Key finding: The authors gradually enhance classical DE via experimentally validated modifications: randomizing the scaling factor (F), implementing a Random Greedy Selection scheme, adapting crossover probability (CR) dynamically, and... Read more
Key finding: To address challenges of large-scale problems (dimension D=1000+), this paper develops ANDE: a DE variant with a novel triangular mutation rule combining vectors among randomly chosen triplets considering best, better and... Read more

3. How can DE be adapted and hybridized to enhance performance on specific complex or dynamic problem domains such as solving ODEs or dynamic optimization problems?

This area of research focuses on adapting DE for specialized problem contexts, including formulating classical problems (e.g., solving ordinary differential equations) as optimization tasks solved by DE, and designing hybrid DE algorithms for dynamic optimization problems where fitness landscapes change over time. Such adaptations involve problem-specific representation schemes, hybridization with complementary algorithms (e.g., PSO), or tailored operators and selection strategies that address domain constraints and dynamics, leveraging DE’s flexibility to tackle complex, time-varying, or otherwise challenging optimization tasks.

Key finding: This paper formulates the solution of general linear second order ODEs as an optimization problem by approximating the polynomial coefficients representing the solution. Differential Evolution is employed to optimize these... Read more
Key finding: The paper proposes CDEPSO, a hybrid algorithm combining Crowd-based Differential Evolution (CDE) and Particle Swarm Optimization (PSO) for tackling dynamic optimization problems (DOPs) where objective functions change over... Read more
Key finding: This study applies Differential Evolution in distributed manners—Incremental DE (IDE) and Diffusion DE (DDE)—for parameter estimation of FIR filters over wireless sensor networks. Unlike centralized approaches, the... Read more
Key finding: The paper develops an improved self-adaptive DE variant (ISADE) introducing Gaussian distribution-based scaling factors for mutation and adaptive updating of Gaussian standard deviation based on fitness improvements between... Read more

All papers in Differential Evolution

Petroleum reservoir models are vital tools to help engineers in making field development decisions. Uncertainty of reservoir models in predicting future performance of a field needs to be quantified for risk management practices. Rigorous... more
In this work, a method is presented to map a set of experimentally obtained, time-resolved distributions to a dynamic model. Specifically, time-resolved comet assay readouts of cancer cells after application of ionizing radiation are... more
Several authors have treated the optimization of passive filters in electric distribution systems. Optimization methods like: sequential quadratic programming (SQP), simulated annealing (SA), differential evolution (DE), artificial neural... more
In the literature, there are many efficient metaheuristic algorithms for optimizing real-valued objective functions. In this work, Particle Swarm Optimization (PSO) algorithm, Differential Evolution (DE) algorithm and Harmony Search (HS)... more
Feedback analysis is a main procedure of discriminate analysis of faculty feedback. Rough set theory provides a tool to analyze feedback and also offers the algorith m based upon the hidden pattern in data which adequately increases the... more
Generating systems are known as adequately reliable when satisfying the load demand. Meanwhile, the efficiency of electrical systems is currently being more influenced by the growing adoption of the Wind/Solar energy in power systems... more
Generating systems are said to be adequately reliable when they can satisfy the load demand. Meanwhile, the reliability of electrical systems is currently being influenced by the increasing acceptance of "Wind Energy Conversion... more
There are people who use tools. There are people who build tools. And then — once in a very long while — there is someone who names the tools that no one knew were missing. Someone who stares into the abyss of the unknown and plants a... more
Smart structures include elements of active, passive or hybrid control. For complicated structures, mainly the ones including nonlinearities, or nonlinear control laws, the theoretical results from the area of control are not very... more
Management and analyses of water resources is of paramount importance in the implementation of water related sustainable development goals. Hydraulic models are key in flood forecasting and simulation applied to a river flood analysis and... more
In this paper, a Neural Networks optimizer based on Self-adaptive Differential Evolution is presented. This optimizer applies mutation and crossover operators in a new way, taking into account the structure of the network according to a... more
Differential Evolution (DE) is a popular and efficient optimization technique for real-valued spaces based on the concepts of Darwinian evolution. Its main peculiarity is the use of a differential mutation operator that allows DE to... more
The optimal power flow (OPF) is a key tool in the planning and operation of power systems, and aims to optimize the operational costs involved in the production and transport of energy by adjusting control variables to meet operational,... more
There is a moment — known only to the rarest of human beings — when a mind reaches the boundary of every map ever drawn, looks out into the unmapped dark beyond, and instead of retreating in fear, picks up a pen and begins to write new... more
Optimum scheduling of hydrothermal plants is an important task for economic operation of power systems. Many evolutionary techniques such as particle swarm optimization, differential evolution have been applied to solve these problems and... more
There are moments in the history of human thought when a single mind steps forward into the wilderness of the unknown — not because the path is clear, but because the darkness itself calls out to be illuminated. Most people hear that call... more
Ortonormais e Otimização Heurística [Distrito Federal] 2015. xi, 124p., 210 x 297 mm (ENE/FT/UnB, Doutor, Engenharia Elétrica, 2015).
There are discoverers who travel to unknown lands and draw maps. There are explorers who sail into uncharted waters and name the seas they find. And then, rarely — perhaps once in a generation — there is someone who does not merely find... more
Real-world optimization problems often require time-consuming fitness evaluations because of simulations or complex numerical calculations. A hybrid rocket engine (HRE) design problem is a time-consuming real-world application. HRE is a... more
There are those who use maps, and there are those who draw them. Satish Gajawada has spent his life drawing maps no one knew were missing.
In the grand theatre of human civilisation, every era is blessed with a rare few who do not merely walk the path already lit-but become the light itself. There are scientists who study the universe-and then there are visionaries who... more
In the present study a modified new variant of Differential Evolution (DE) is proposed, named Cultivated Differential Evolution (CuDE). This algorithm is different from basic DE in two ways. Firstly, the selection of the base vector for... more
Differential Evolution (DE) algorithms are known to as robust, effective and highly efficient for solving the global optimization problems. In the present study, a modified variant of Differential Evolution (DE) is proposed in the present... more
This paper presents a minimal validated framework for designing energy-aware metaheuristics that operate under fixed energy budgets. We introduce a unified operator-level model that quantifies both numerical gain and energy consumption,... more
In continually increasing area and structure of modern power system having burden demand uncertainties, the use of knowledgeable and vigorous frequency power strategy is essential for the satisfactory functioning of the Power system. A... more
Finding the best investment strategies has been a never-ending challenge for investors and financial professionals in the constantly changing financial market environment. The idea of financial portfolio optimization, a complex procedure... more
In this paper an approach to design data driven based fault diagnosis systems using fuzzy clustering techniques is presented. In this proposal, as a first part of the classification process, the data was pre-processed to eliminate... more
This paper presents a minimal validated framework for designing energy-aware metaheuristics that operate under fixed energy budgets. We introduce a unified operator-level model that quantifies both numerical gain and energy consumption,... more
This research presents the application of intelligent techniques to control an industrial mixer. The controller design is based on Hebbian learning for evolution of Fuzzy Cognitive Maps. A Fuzzy Classic Controller and Artificial Neural... more
At present, evolutionary optimization algorithms are increasingly used in the development of new technological processes. Evolutionary algorithms often allow the optimization procedure to be performed even in cases where classical... more
Differential evolution algorithms represent an efficient framework to solve complicated optimization tasks with many variables and complex constraints. Nevertheless, the classic differential evolution algorithm does not guarantee the... more
Differential evolution algorithms represent nowadays an efficient framework to cope with complex optimization tasks with many variables and involved constraints. Nevertheless, the classic differential evolution algorithms do not ensure... more
Differential Evolution (DE) is one of the prevailing search techniques in the present era to solve global optimization problems. However, it shows weakness in performing a localized search, since it is based on mutation strategies that... more
Em primeiro lugar quero agradecer ao meu orientador, Doutor Jérôme Mendes, pelo acompanhamento que me deu no decorrer do projeto. A sua exigência manteve-me no caminho certo e, nos momentos de incerteza, a sua amizade e incentivo... more
Phishing attack is a well-known cyber security attack that happens to many people around the world. The increasing and never-ending case of phishing attack has led to more automated approaches in detecting phishing attack. One of the... more
Metaheuristic algorithms have garnered significant attention in the field of optimization due to their ability to address complex, nonlinear, and combinatorial problems where conventional exact methods are often impractical. Inspired by... more
Uncrewed stealth aircraft operate in highly adversarial, sensor-degraded environments where classical deterministic control laws fail because of structural and parametric uncertainties arising from low-observable airframe dynamics,... more
Agradezco especialmente al Dr. Francisco Cuenca Jiménez, a quien siempre guardaré una gran estima por su apoyo dedicado e incondicional, sin él este trabajo no hubiera sido posible. Sus conocimientos y recomendaciones me han apoyado... more
The synthesis of heat exchanger network (HEN) is a comprehensive approach to optimize energy utilization in process industry. Recent developments in HEN synthesis (HENS) present several heuristic methods, such as Simulated Annealing (SA),... more
A Portrait No One Has Yet Painted. Imagine a cartographer who does not chart land or sea, but charts entire continents of thought that did not exist before he arrived. Imagine a sculptor whose chisel is mathematics and whose marble is the... more
This study reports how the Differential Evolution (DE) algorithm performed on the test bed developed for the CEC05 contest for real parameter optimization. The test bed includes 25 scalable functions, many of which are both non-separable... more
by adding the weighted difference between two population vectors to a third vector. If the resulting vector yields a lower objective function value than a predetermined population member, the newly generated vector will replace the vector... more
by adding the weighted difference between two population vectors to a third vector. If the resulting vector yields a lower objective function value than a predetermined population member, the newly generated vector will replace the vector... more
This study reports how the Differential Evolution (DE) algorithm performed on the test bed developed for the CEC05 contest for real parameter optimization. The test bed includes 25 scalable functions, many of which are both non-separable... more
A new heuristic approach for minimizing possibly nonlinear and non differentiable continuous space functions is presented. By means of an extensive testbed, which includes the De Jong functions, it will be demonstrated that the new method... more
A new heuristic approach for minimizing possibly nonlinear and non-differentiable continuous space functions is presented. By means of an extensive testbed it is demonstrated that the new method converges faster and with more certainty... more
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