Designing satellite communication networks by zero—one quadratic programming

Abstract

In satellite communications networks, distinctive facilities called homing stations perform special transmission functions. Local demand nodes clustered around each homing station communicate with each other via a local switch at the homing station; demand nodes in different clusters communicate with each other via satellite earth stations at the homing stations. Designing such a communication network requires choices on the locations of the earth stations and on the assignments of demand nodes to the local clusters at the earth stations. We formulate this problem as a zero-one quadratic facility location problem and transform it into an equivalent zero-one integer linear program.Computational experience on real data shows that a branch and bound procedure is effective in solving problems with up to forty demand nodes (major cities) and that the solutions that this algorithm finds improve considerably upon management generated solutions. We also show that a greedy add heuristic, as implemented on an IBM PC, consistently generates optimal or near-optimal solutions.

An improved linearization strategy for zero-one quadratic programming problems

“…Such problems arise in a host of contemporary application areas such as telecommunications [3,13,18], manufacturing and scheduling [2,24], and epileptic seizure warning [6,14,20], and subsume unconstrained zero-one quadratic programs, zero-one quadratic knapsack problems, and quadratic assignment problems.…”

Star p-hub center problem and star p-hub median problem with bounded path lengths

“…Moreover, any 0-1 vector x which satisfies clique inequalities (20) does not violate the path length restrictions. Let SpHMP-BP-3 be the formulation obtained from SpHMP-BP-2 by replacing constraints (19) with (20).…”

Solving the hub location problem in a star–star network

“…A very similar problem to the UHLP-S has been considered by Helme and Magnanti [25] for satellite communication networks. The authors propose a quadratic formulation and a linearization that does not increase the order of number of variables.…”