Optimization problemIn mathematics, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set.
Linear programming relaxationIn mathematics, the relaxation of a (mixed) integer linear program is the problem that arises by removing the integrality constraint of each variable. For example, in a 0–1 integer program, all constraints are of the form The relaxation of the original integer program instead uses a collection of linear constraints The resulting relaxation is a linear program, hence the name.
Convex optimizationConvex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
Artificial intelligenceArtificial intelligence (AI) is the intelligence of machines or software, as opposed to the intelligence of human beings or animals. AI applications include advanced web search engines (e.g., Google Search), recommendation systems (used by YouTube, Amazon, and Netflix), understanding human speech (such as Siri and Alexa), self-driving cars (e.g., Waymo), generative or creative tools (ChatGPT and AI art), and competing at the highest level in strategic games (such as chess and Go).
Set cover problemThe set cover problem is a classical question in combinatorics, computer science, operations research, and complexity theory. It is one of Karp's 21 NP-complete problems shown to be NP-complete in 1972. Given a set of elements {1, 2, ..., n} (called the universe) and a collection S of m sets whose union equals the universe, the set cover problem is to identify the smallest sub-collection of S whose union equals the universe. For example, consider the universe U = {1, 2, 3, 4, 5} and the collection of sets S = { {1, 2, 3}, {2, 4}, {3, 4}, {4, 5} }.
Revealed preferenceRevealed preference theory, pioneered by economist Paul Anthony Samuelson in 1938, is a method of analyzing choices made by individuals, mostly used for comparing the influence of policies on consumer behavior. Revealed preference models assume that the preferences of consumers can be revealed by their purchasing habits. Revealed preference theory arose because existing theories of consumer demand were based on a diminishing marginal rate of substitution (MRS).
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Artificial general intelligenceAn artificial general intelligence (AGI) is a hypothetical type of intelligent agent. If realized, an AGI could learn to accomplish any intellectual task that human beings or animals can perform. Alternatively, AGI has been defined as an autonomous system that surpasses human capabilities in the majority of economically valuable tasks. Creating AGI is a primary goal of some artificial intelligence research and of companies such as OpenAI, DeepMind, and Anthropic. AGI is a common topic in science fiction and futures studies.
Preference (economics)In economics and other social sciences, preference refers to the order in which an agent ranks alternatives based on their relative utility. The process results in an "optimal choice" (whether real or theoretical). Preferences are evaluations and concern matter of value, typically in relation to practical reasoning. An individual's preferences are determined purely by a person's tastes as opposed to the good's prices, personal income, and the availability of goods. However, people are still expected to act in their best (rational) interest.
Applications of artificial intelligenceArtificial intelligence (AI) has been used in applications to alleviate certain problems throughout industry and academia. AI, like electricity or computers, is a general purpose technology that has a multitude of applications. It has been used in fields of language translation, image recognition, credit scoring, e-commerce and other domains. Recommendation system A recommendation system predicts the "rating" or "preference" a user would give to an item.
Decision-makingIn psychology, decision-making (also spelled decision making and decisionmaking) is regarded as the cognitive process resulting in the selection of a belief or a course of action among several possible alternative options. It could be either rational or irrational. The decision-making process is a reasoning process based on assumptions of values, preferences and beliefs of the decision-maker. Every decision-making process produces a final choice, which may or may not prompt action.
Models of scientific inquiryModels of scientific inquiry have two functions: first, to provide a descriptive account of how scientific inquiry is carried out in practice, and second, to provide an explanatory account of why scientific inquiry succeeds as well as it appears to do in arriving at genuine knowledge. The philosopher Wesley C. Salmon described scientific inquiry: The search for scientific knowledge ends far back into antiquity.
Approximation algorithmIn computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one. Approximation algorithms naturally arise in the field of theoretical computer science as a consequence of the widely believed P ≠ NP conjecture. Under this conjecture, a wide class of optimization problems cannot be solved exactly in polynomial time.
Collaborative decision-making softwareCollaborative decision-making (CDM) software is a software application or module that helps to coordinate and disseminate data and reach consensus among work groups. CDM software coordinates the functions and features required to arrive at timely collective decisions, enabling all relevant stakeholders to participate in the process. The selection of communication tools is very important for high end collaborative efforts.
Randomized roundingWithin computer science and operations research, many combinatorial optimization problems are computationally intractable to solve exactly (to optimality). Many such problems do admit fast (polynomial time) approximation algorithms—that is, algorithms that are guaranteed to return an approximately optimal solution given any input. Randomized rounding is a widely used approach for designing and analyzing such approximation algorithms.
Ordinal utilityIn economics, an ordinal utility function is a function representing the preferences of an agent on an ordinal scale. Ordinal utility theory claims that it is only meaningful to ask which option is better than the other, but it is meaningless to ask how much better it is or how good it is. All of the theory of consumer decision-making under conditions of certainty can be, and typically is, expressed in terms of ordinal utility. For example, suppose George tells us that "I prefer A to B and B to C".
States' rightsIn American political discourse, states' rights are political powers held for the state governments rather than the federal government according to the United States Constitution, reflecting especially the enumerated powers of Congress and the Tenth Amendment. The enumerated powers that are listed in the Constitution include exclusive federal powers, as well as concurrent powers that are shared with the states, and all of those powers are contrasted with the reserved powers—also called states' rights—that only the states possess.
Abductive reasoningAbductive reasoning (also called abduction, abductive inference, or retroduction) is a form of logical inference that seeks the simplest and most likely conclusion from a set of observations. It was formulated and advanced by American philosopher Charles Sanders Peirce beginning in the last third of the 19th century. Abductive reasoning, unlike deductive reasoning, yields a plausible conclusion but does not definitively verify it. Abductive conclusions do not eliminate uncertainty or doubt, which is expressed in retreat terms such as "best available" or "most likely".
Explainable artificial intelligenceExplainable AI (XAI), also known as Interpretable AI, or Explainable Machine Learning (XML), either refers to an AI system over which it is possible for humans to retain intellectual oversight, or to the methods to achieve this. The main focus is usually on the reasoning behind the decisions or predictions made by the AI which are made more understandable and transparent. XAI counters the "black box" tendency of machine learning, where even the AI's designers cannot explain why it arrived at a specific decision.
Decision intelligenceDecision intelligence is an engineering discipline that augments data science with theory from social science, decision theory, and managerial science. Its application provides a framework for best practices in organizational decision-making and processes for applying machine learning at scale. The basic idea is that decisions are based on our understanding of how actions lead to outcomes. Decision intelligence is a discipline for analyzing this chain of cause and effect, and decision modeling is a visual language for representing these chains.
