Which of the following algorithms is used to solve combinatorial optimization problems?

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.

Why is combinatorial optimization hard?

The difficulty arises from the fact that unlike linear programming, the feasible region of the combinatorial problem is not a convex set. Thus, we must, instead, search a lattice of feasible points, or in the case of the mixed integer case, a set of disjoint half-lines or line segments to find an optimal solution.

Is combinatorial optimization NP hard?

When a decision version of a combinatorial optimization problem is proved to belong to the class of NP-complete problems, then the optimization version is NP-hard. The optimization problem, i.e., finding the minimum number (least k) of star-shaped polygons whose union is equal to a given simple polygon, is NP-hard.

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 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.

What is the most difficult in solving combinatorial problems?

But what makes an optimization problem difficult? For combinatorial problems, it is the problem size. Such problems have an exact solution method—just write down all possible solutions and pick the best one—but this approach is almost never feasible for realistic problem sizes.

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 optimization and machine learning algorithms are related?

Approximating a function can be solved by framing the problem as function optimization. Machine learning algorithms perform function approximation, which is solved using function optimization. Function optimization is the reason why we minimize error, cost, or loss when fitting a machine learning algorithm.

When can machine learning algorithms be used in optimization problems?

According to the type of optimization problems, machine learning algorithms can be used in objective function of heuristics search strategies. When can Validation Accuracy be greater than Training Accuracy for Deep Learning Models?

Can machine learning algorithms be used for heuristics search?

Today, heuristic search strategies such as GA are usually used rather than exhaustive search, due to the feasible region sets of some optimization problems are very large. According to the type of optimization problems, machine learning algorithms can be used in objective function of heuristics search strategies.

What is the heart of machine learning?

In simple words, the heart of machine learning is an optimization. Besides data fitting, there are are various kind of optimization problem. Moreover, over the last decades, different approaches were introduced in optimization problems for finding the best or satisfying solutions.

Can the same optimization problem be solved again and again?

In many real-world applications, it is typically the case that the same optimization problem is solved again and again on a regular basis, maintaining the same problem structure but differing in the data. This provides an opportunity for… Expand …