Local search algorithms for combinatorial optimization problems are in general of pseudopolynomial running time and polynomial-time algorithms are often not known for finding locally optimal solutions for NP-hard optimization problems. We introduce the concept of epsilon-local optimality and...

Neighborhood search algorithms are a wide class of improvement algorithms where at each iteration an improving solution is found by searching the "neighborhood" of the current solution. This paper discusses neighborhood search algorithms where the size of the neighborhood is "very large" with...

We consider neighborhood search defined on combinatorial optimization problems. Suppose that N is a neighborhood for combinatorial optimization problem X. We say that N' is LO-equivalent (locally optimal) to N if for any instance of X, the set of locally optimal solutions with respect to N and...