Differential evolution (DE) is a population-based metaheuristic search technique that optimizes a problem by evolving a candidate solution. Such algorithms make few or no assumptions about the optimization problem they are trying to solve and can quickly look at many possible designs.

In evolutionary computation, DE is a method that tries to find the best solution to a problem by trying over and over to improve a candidate solution based on a certain measure of quality. These methods are called metaheuristics because they make few assumptions about the optimization problem and can try numerous solutions. But metaheuristics like DE don't guarantee that the best answer will ever be found.

DE is used to optimize multidimensional real-valued functions, but it doesn't use the gradient of the problem being optimized. It means that the optimization problem doesn't have to be differentiable like it does for gradient descent and quasi-Newton methods. As a result, DE can solve optimization problems that aren't even continuous, are noisy, change over time, etc.

DE optimizes a problem by maintaining a population of candidate solutions, creating new ones by merging current ones with its basic equations and retaining the candidate solution with the highest score or fitness. In this manner, the optimization issue is viewed as a black box that gives a quality measure for a candidate solution; hence, the gradient is unnecessary.

Storn and Price introduced DE in the 1990s. Books have documented theoretical and practical elements of applying DE in parallel computing, multiobjective optimization, constrained optimization, and application field assessments. In addition, journal articles provide reviews of the numerous research facets of DE.

Algorithm

A straightforward way the DE algorithm works is by having a group of possible solutions (called agents). These agents are moved around in the search space by combining the positions of existing agents from the population with simple math formulas. If an agent's new position is better, it is accepted and added to the population. If it isn't, the new position is just thrown away. By doing this repeatedly, it is hoped, but not guaranteed, that a good solution will be found in the end.

Law of DE

In evolutionary computation, DE is a method that tries to find the best solution to a problem by repeatedly trying to improve a candidate solution based on a specific quality measure.

Parameters

Currently, the differential evolution algorithm has four random tuning parameters: population size, differential weight, crossover, and generation number.

Difference

Differential Evolution is distinct from conventional genetic algorithms in that it incorporates directional information within the population by employing a target and unit vector. These characteristics permit differential evolution to converge on solutions more quickly at the expense of exploration.

Application

Differential evolution (DE) is a population-based evolutionary algorithm often used to solve multidimensional global optimization problems over continuous spaces. It has been used successfully to solve many different kinds of issues.

Benefits

DE algorithm is a new stochastic optimization algorithm that is based on populations. The pros of DE are that it is simple, fast, and uses real coding. It is also easy to use, has a local search feature, and is quick.