Which of the following algorithm can be used for solving combinatorial optimization problem?

Combinatorial optimization problems can be viewed as searching for the best element of some set of discrete items; therefore, in principle, any sort of search algorithm or metaheuristic can be used to solve them.

What is combinatorial optimization used for?

Combinatorial optimization is an emerging field at the forefront of combinatorics and theoretical computer science that aims to use combinatorial techniques to solve discrete optimization problems. A discrete optimization problem seeks to determine the best possible solution from a finite set of possibilities.

What is combinatorial problem give example?

As an example of a combinatorial decision problem, consider the Graph Colouring Problem: given a graph G and a number of colours, find an assignment of colours to the vertices of G such that two vertices that are connected by an edge are never assigned the same colour.

Is combinatorial optimization convex?

We introduce the convex combinatorial optimization problem, a far-reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and discuss several applications.

Is combinatorial optimization NP hard?

Most of the well-known problems of combinatorial optimisation belong to the class of the so-called NP-hard problems and they are intrinsically very difficult in computation. State-of-the-art ILP solvers are able to solve many large-scale discrete optimisation problems routinely by branch-and-bound.

What is algorithms combinatorics and optimization?

program in algorithms, combinatorics, and optimization is intended to fill this gap. It brings together the study of the mathematical structure of discrete objects and the design and analysis of algorithms in areas such as: Graph Theory. Convex and Discrete Geometry.

What is linear in linear programming?

Linear programming is considered an important technique that is used to find the optimum resource utilisation. The term “linear programming” consists of two words as linear and programming. The word “linear” defines the relationship between multiple variables with degree one.

Is one of the fundamental combinatorial optimization problems?

The assignment problem is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics. In an assignment problem, we must find a maximum matching that has the minimum weight in a weighted bipartite graph.

How do you explain NP-hard?

In computational complexity theory, NP-hardness (non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally “at least as hard as the hardest problems in NP”. A simple example of an NP-hard problem is the subset sum problem.

What’s the difference between NP-hard and NP-complete?

A problem is said to be NP-hard if everything in NP can be transformed in polynomial time into it even though it may not be in NP. Conversely, a problem is NP-complete if it is both in NP and NP-hard. The NP-complete problems represent the hardest problems in NP.

Is combinatorial optimization AI?

What is Combinatorial Optimization? Combinatorial optimization is a class of methods to find an optimal object from a finite set of objects when an exhaustive search is not feasible. These optimization steps are the building blocks of most AI algorithms, regardless of the program’s ultimate function.

How to solve combinatorial optimization problems via map inference?

Solving constrained combinatorial optimization problems via MAP inference is often achieved by introducing extra poten- tial functions for each constraint.

What is combinatorics in Computer Science?

Combinatorics is the mathematics of discretely structured problems. Combinatorial optimization is an optimization that deals with discrete variables. It is very similar to operation research (a term used mainly by economists, originated during WW II in military logistics).

Can belief propagation solve combinatorial problems without in-creasing the Order?

This limits the practicality of such an approach, since inference with high order potentials is tractable only for a few special classes of functions. We propose an approach which is able to solve constrained combinatorial problems using belief propagation without in- creasing the order.