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Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization , some or all of the variables used in a discrete optimization problem are restricted to be discrete variables —that is, to assume only a discrete set of values, such as the integers .
Hasse diagram of the search graph of the algorithm for 3 variables. Given e.g. the subset = {, ¯, ¯, ¯ ¯, ¯ ¯} of the bottom-level nodes (light green), the algorithm computes a minimal set of nodes (here: {¯,}, dark green) that covers exactly .
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. [ 1 ] [ 2 ] It is generally divided into two subfields: discrete optimization and continuous optimization .
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic [1] – do not vary smoothly in this way, but have distinct, separated values. [2]
SDA Optimization Algorithm SDA Nature-inspired Bio-inspired 2014 [42] Artificial Root Foraging Algorithm ARFA Nature-inspired Plant-based 2014 [43] Bumble Bees Mating Optimization BBMO 2014 Chicken Swarm Optimization CSO Nature-inspired Bio-inspired 2014 [44] Colliding Bodies Optimization CBO 2014 [45] Coral Reefs Optimization Algorithm CROA 2014
Metaheuristic in computer science and mathematical optimization is a higher-level procedure or heuristic designed to find, generate, tune, or select a heuristic (partial search algorithm) that may provide a sufficiently good solution to an optimization problem or a machine learning problem, especially with incomplete or imperfect information or limited computation capacity.
Mathematical Optimization Society; Mathematical programming with equilibrium constraints; Max–min inequality; Maximum and minimum; Maximum theorem; MCACEA; Mean field annealing; Minimax theorem; Mirror descent; Mixed complementarity problem; Mixed linear complementarity problem; Moreau envelope; Multi-attribute global inference of quality
In terms of mathematical optimization, dynamic programming usually refers to simplifying a decision by breaking it down into a sequence of decision steps over time. This is done by defining a sequence of value functions V 1 , V 2 , ..., V n taking y as an argument representing the state of the system at times i from 1 to n .