Local optimumIn applied mathematics and computer science, a local optimum of an optimization problem is a solution that is optimal (either maximal or minimal) within a neighboring set of candidate solutions. This is in contrast to a global optimum, which is the optimal solution among all possible solutions, not just those in a particular neighborhood of values. Importantly, a global optimum is necessarily a local optimum, but a local optimum is not necessarily a global optimum.
Combinatorial optimizationCombinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combinatorial optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such as the ones previously mentioned, exhaustive search is not tractable, and so specialized algorithms that quickly rule out large parts of the search space or approximation algorithms must be resorted to instead.
Fitness landscapeIn evolutionary biology, fitness landscapes or adaptive landscapes (types of evolutionary landscapes) are used to visualize the relationship between genotypes and reproductive success. It is assumed that every genotype has a well-defined replication rate (often referred to as fitness). This fitness is the "height" of the landscape. Genotypes which are similar are said to be "close" to each other, while those that are very different are "far" from each other.
Multi-objective optimizationMulti-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one 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.
No free lunch in search and optimizationIn computational complexity and optimization the no free lunch theorem is a result that states that for certain types of mathematical problems, the computational cost of finding a solution, averaged over all problems in the class, is the same for any solution method. The name alludes to the saying "no such thing as a free lunch", that is, no method offers a "short cut". This is under the assumption that the search space is a probability density function. It does not apply to the case where the search space has underlying structure (e.
AnsatzIn physics and mathematics, an ansatz ('aensaets; ˈʔanzats, meaning: "initial placement of a tool at a work piece", plural ansätze 'aensɛtsə; ˈʔanzɛtsə) is an educated guess or an additional assumption made to help solve a problem, and which may later be verified to be part of the solution by its results. An ansatz is the establishment of the starting equation(s), the theorem(s), or the value(s) describing a mathematical or physical problem or solution.
Computational intelligenceThe expression computational intelligence (CI) usually refers to the ability of a computer to learn a specific task from data or experimental observation. Even though it is commonly considered a synonym of soft computing, there is still no commonly accepted definition of computational intelligence. Generally, computational intelligence is a set of nature-inspired computational methodologies and approaches to address complex real-world problems to which mathematical or traditional modelling can be useless for a few reasons: the processes might be too complex for mathematical reasoning, it might contain some uncertainties during the process, or the process might simply be stochastic in nature.
Artificial immune systemIn artificial intelligence, artificial immune systems (AIS) are a class of computationally intelligent, rule-based machine learning systems inspired by the principles and processes of the vertebrate immune system. The algorithms are typically modeled after the immune system's characteristics of learning and memory for use in problem-solving. The field of artificial immune systems (AIS) is concerned with abstracting the structure and function of the immune system to computational systems, and investigating the application of these systems towards solving computational problems from mathematics, engineering, and information technology.
Inductive biasThe inductive bias (also known as learning bias) of a learning algorithm is the set of assumptions that the learner uses to predict outputs of given inputs that it has not encountered. Inductive bias is anything which makes the algorithm learn one pattern instead of another pattern (e.g. step-functions in decision trees instead of continous function in a linear regression model). In machine learning, one aims to construct algorithms that are able to learn to predict a certain target output.
Trial and errorTrial and error is a fundamental method of problem-solving characterized by repeated, varied attempts which are continued until success, or until the practicer stops trying. According to W.H. Thorpe, the term was devised by C. Lloyd Morgan (1852–1936) after trying out similar phrases "trial and failure" and "trial and practice". Under Morgan's Canon, animal behaviour should be explained in the simplest possible way. Where behavior seems to imply higher mental processes, it might be explained by trial-and-error learning.
