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Differential Evolution
Differential evolution (DE) is an evolutionary algorithm to optimize a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. Such methods are commonly known as metaheuristics as they make few or no assumptions about the optimized problem and can search very large spaces of candidate solutions. However, metaheuristics such as DE do not guarantee an optimal solution is ever found. DE is used for multidimensional real-valued functions but does not use the gradient of the problem being optimized, which means DE does not require the optimization problem to be differentiable, as is required by classic optimization methods such as gradient descent and quasi-newton methods. DE can therefore also be used on optimization problems that are not even continuous, are noisy, change over time, etc. DE optimizes a problem by maintaining a population of candidate solutions and creating new candidate solutions by combining existing ones accor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiobjective Optimization
Multi-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of MCDM, multiple-criteria decision making that is concerned with Mathematical optimization, mathematical optimization problems involving more than one Loss function, objective function to be optimized simultaneously. Multi-objective is a type of vector optimization that has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives. Minimizing cost while maximizing comfort while buying a car, and maximizing performance whilst minimizing fuel consumption and emission of pollutants of a vehicle are examples of multi-objective optimization problems involving two and three objectives, respectively. In practical problems, there can be more than three objectives. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evolution Strategy
Evolution strategy (ES) from computer science is a subclass of evolutionary algorithms, which serves as an optimization (mathematics), optimization technique. It uses the major genetic operators mutation (evolutionary algorithm), mutation, recombination (evolutionary algorithm), recombination and selection (evolutionary algorithm), selection of parents. History The 'evolution strategy' optimization technique was created in the early 1960s and developed further in the 1970s and later by Ingo Rechenberg, Hans-Paul Schwefel and their co-workers. Methods Evolution strategies use natural problem-dependent representations, so Genetic representation, problem space and Genetic representation, search space are identical. In common with evolutionary algorithms, the operators are applied in a loop. An iteration of the loop is called a generation. The sequence of generations is continued until a termination criterion is met. The special feature of the ES is the self-adaptation of mutation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CMA-ES
Covariance matrix adaptation evolution strategy (CMA-ES) is a particular kind of strategy for numerical optimization. evolution strategy, Evolution strategies (ES) are stochastic, Derivative-free optimization, derivative-free methods for numerical optimization of non-Linear map, linear or non-Convex function, convex continuous optimization problems. They belong to the class of evolutionary algorithms and evolutionary computation. An evolutionary algorithm is broadly based on the principle of biological evolution, namely the repeated interplay of variation (via recombination and mutation) and selection: in each generation (iteration) new individuals (candidate solutions, denoted as x) are generated by variation of the current parental individuals, usually in a stochastic way. Then, some individuals are selected to become the parents in the next generation based on their fitness or objective function value f(x). Like this, individuals with better and better f-values are generated ove ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Bee Colony Algorithm
In computer science and operations research, the artificial bee colony algorithm (ABC) is an optimization algorithm based on the intelligent foraging behaviour of honey bee swarm, proposed by Derviş Karaboğa (Erciyes University) in 2005. Algorithm In the ABC model, the colony consists of three groups of bees: employed bees, onlookers and scouts. It is assumed that there is only one artificial employed bee for each food source. In other words, the number of employed bees in the colony is equal to the number of food sources around the hive. Employed bees go to their food source and come back to hive and dance on this area. The employed bee whose food source has been abandoned becomes a scout and starts to search for finding a new food source. Onlookers watch the dances of employed bees and choose food sources depending on dances. The main steps of the algorithm are given below: * Initial food sources are produced for all employed bees * REPEAT ** Each employed bee goes to a fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rules Of Thumb
In English, the phrase ''rule of thumb'' refers to an approximate method for doing something, based on practical experience rather than theory. This usage of the phrase can be traced back to the 17th century and has been associated with various trades where quantities were measured by comparison to the width or length of a thumb. An erroneous folk etymology began circulating in the 1970s falsely connecting the origins of the phrase "rule of thumb" to legal doctrine on domestic abuse. The error appeared in a number of law journals, and the United States Commission on Civil Rights published a report on domestic abuse titled "Under the Rule of Thumb" in 1982. Some efforts were made to discourage the phrase, which was seen as taboo owing to this false origin. During the 1990s, several authors correctly identified the spurious folk etymology; however, the connection to domestic violence was still being cited in some legal sources into the early 2000s. Origin and usage The exact or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Number
In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and in many other branches of mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers, sometimes called "the reals", is traditionally denoted by a bold , often using blackboard bold, . The adjective ''real'', used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of . The real numbers include the rational numbers, such as the integer and the fraction . The rest of the real numbers are called irrational numbers. Some irrational numbers (as well as all the rationals) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Row Vector
In linear algebra, a column vector with elements is an m \times 1 matrix consisting of a single column of entries, for example, \boldsymbol = \begin x_1 \\ x_2 \\ \vdots \\ x_m \end. Similarly, a row vector is a 1 \times n matrix for some , consisting of a single row of entries, \boldsymbol a = \begin a_1 & a_2 & \dots & a_n \end. (Throughout this article, boldface is used for both row and column vectors.) The transpose (indicated by ) of any row vector is a column vector, and the transpose of any column vector is a row vector: \begin x_1 \; x_2 \; \dots \; x_m \end^ = \begin x_1 \\ x_2 \\ \vdots \\ x_m \end and \begin x_1 \\ x_2 \\ \vdots \\ x_m \end^ = \begin x_1 \; x_2 \; \dots \; x_m \end. The set of all row vectors with entries in a given field (such as the real numbers) forms an -dimensional vector space; similarly, the set of all column vectors with entries forms an -dimensional vector space. The space of row vectors with entries can be regarded as the dual spac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formula
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship between given quantities. The plural of ''formula'' can be either ''formulas'' (from the most common English plural noun form) or, under the influence of scientific Latin, ''formulae'' (from the original Latin). In mathematics In mathematics, a formula generally refers to an equation or inequality relating one mathematical expression to another, with the most important ones being mathematical theorems. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion. However, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume of a sphere in terms of its radius: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Candidate Solutions
In mathematical optimization and computer science, a feasible region, feasible set, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down. For example, consider the problem of minimizing the function x^2+y^4 with respect to the variables x and y, subject to 1 \le x \le 10 and 5 \le y \le 12. \, Here the feasible set is the set of pairs (''x'', ''y'') in which the value of ''x'' is at least 1 and at most 10 and the value of ''y'' is at least 5 and at most 12. The feasible set of the problem is separate from the objective function, which states the criterion to be optimized and which in the above example is x^2+y^4. In many problems, the feasible set reflects a constraint that one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constrained Optimization
In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to be minimized, or a reward function or utility function, which is to be maximized. Constraints can be either hard constraints, which set conditions for the variables that are required to be satisfied, or soft constraints, which have some variable values that are penalized in the objective function if, and based on the extent that, the conditions on the variables are not satisfied. Relation to constraint-satisfaction problems The constrained-optimization problem (COP) is a significant generalization of the classic constraint-satisfaction problem (CSP) model. COP is a CSP that includes an ''objective function'' to be optimized. Many algorithms are used to hand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
