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.
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.
Ant colony optimization algorithmsIn computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs. Artificial ants stand for multi-agent methods inspired by the behavior of real ants. The pheromone-based communication of biological ants is often the predominant paradigm used. Combinations of artificial ants and local search algorithms have become a method of choice for numerous optimization tasks involving some sort of graph, e.
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.
ColumnA column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above to other structural elements below. In other words, a column is a compression member. The term column applies especially to a large round support (the shaft of the column) with a capital and a base or pedestal, which is made of stone, or appearing to be so. A small wooden or metal support is typically called a post.
Doric orderThe Doric order was one of the three orders of ancient Greek and later Roman architecture; the other two canonical orders were the Ionic and the Corinthian. The Doric is most easily recognized by the simple circular capitals at the top of columns. Originating in the western Doric region of Greece, it is the earliest and, in its essence, the simplest of the orders, though still with complex details in the entablature above. The Greek Doric column was fluted or smooth-surfaced, and had no base, dropping straight into the stylobate or platform on which the temple or other building stood.
Corinthian orderThe Corinthian order (Κορινθιακός ρυθμός, Korinthiakós rythmós; Ordo Corinthius) is the last developed and most ornate of the three principal classical orders of Ancient Greek architecture and Roman architecture. The other two are the Doric order which was the earliest, followed by the Ionic order. In Ancient Greek architecture, the Corinthian order follows the Ionic in almost all respects other than the capitals of the columns, though this changed in Roman architecture.
