It is well known that the gradient-projection algorithm plays an important role in solving constrained convex minimization problems. In this paper, based on Xu’s method [Xu, H. K.: Averaged mappings and the gradient-projection algorithm, J. Optim. Theory Appl. 150, 360-378(2011)], we use the idea of regularization to establish implicit and explicit iterative methods for finding the approximate ...

In this paper we discuss several heuristic strategies which allow one to solve the Whitehead’s minimization problem much faster (on most inputs) than the classical Whitehead algorithm. The mere fact that these strategies work in practice leads to several interesting mathematical conjectures. In particular, we conjecture that the length of most non-minimal elements in a free group can be reduced...

The cutwidth minimization problem consists of finding a linear layout of a graph so that the maximum linear cut of edges is minimized. This NP-hard problem has applications in network scheduling, automatic graph drawing and information retrieval. We propose a heuristic method based on the Scatter Search (SS) methodology for finding approximate solutions to this optimization problem. This metahe...

We define the timetable constrained distance minimization problem (TCDMP) which is a sports scheduling problem applicable for tournaments where the total travel distance must be minimized. The problem consists of finding an optimal home-away assignment when the opponents of each team in each time slot are given. We present an integer programming, a constraint programming formulation and describ...

We study the problem of minimizing the profile of a network and develop a solution method by following the tenets of scatter search. Our procedure exploits the structure of the problem and includes strategies that produce and agile search with computational efficiencies. Among several mechanisms, our search includes path relinking as the basis for combining solutions to generate new ones. The p...

In this paper we will examine the following problem: What is the minimum number of unit edges required to construct k identical size regular polygons in the plane if sharing of edges is allowed?

It is known that some NP-Complete problems exhibit sharp phase transitions with respect to some order parameter. Moreover, a correlation between that critical behavior and the hardness of finding a solution exists in some of these problems. This paper shows experimental evidence about the existence of a critical behavior in the computational cost of solving the bandwidth minimization problem fo...

In applications such as design of integrated circuits (chips), it is sometimes required to connect the terminals (receivers) and the central vertex (source) by a weight-minimal tree where the signal delays between the source and the terminals are the same or differ by a minimal value. Simple necessary conditions for existence of the desired tree, heuristic rules for displacement of the terminal...

This paper proposes a closed form solution to L2sensitivity minimization of second-order state-space digital filters. Restricting ourselves to the 2-nd order case of state-space digital filters, we can formulate L2-sensitivity minimization problem by hyperbolic functions. As a result, L2-sensitivity minimization problem can be converted into a problem to find the solution to a 4-th degree polyn...

We study single machine scheduling problems, where processing times of the jobs are exponential functions of their start times. For increasing functions, we prove strong NP-hardness of the makespan minimization problem with arbitrary job release times. For decreasing functions, maximum lateness minimization problem is proved to be strongly NP-hard and total weighted completion time minimization...