Today, a variety of heuristic approaches are available to the operations research practitioner. One methodology that has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors is GRASP (Greedy Randomized Adaptive Search Procedures). GRASP is an iterative randomized sampling technique in which each iteration provides a solution to the problem at hand. The incumbent solution over all GRASP iterations is kept as the final result. There are two phases within each GRASP iteration: the first intelligently constructs an initial solution via an adaptive randomized greedy function; the second applies a local search procedure to the constructed solution in hope of finding an improvement. In this paper, we define the various components comprising a GRASP and demonstrate, step by step, how to develop such heuristics for combinatorial optimization problems. Intuitive justifications for the observed empirical behavior of the methodology are discussed. The paper concludes with a brief literature review of GRASP implementations and mentions two industrial applications.

/pdf/greedy-randomized-adaptive-search-procedures-2nqug06z4x.pdf

Greedy Randomized Adaptive Search Procedures

Introduction to linear and nonlinear programming

A method and system for placing an order to purchase an item via the Internet. The order is placed by a purchaser at a client system and received by a server system. The server system receives purchaser information including identification of the purchaser, payment information, and shipment information from the client system. The server system then assigns a client identifier to the client system and associates the assigned client identifier with the received purchaser information. The server system sends to the client system the assigned client identifier and an HTML document identifying the item and including an order button. The client system receives and stores the assigned client identifier and receives and displays the HTML document. In response to the selection of the order button, the client system sends to the server system a request to purchase the identified item. The server system receives the request and combines the purchaser information associated with the client identifier of the client system to generate an order to purchase the item in accordance with the billing and shipment information whereby the purchaser effects the ordering of the product by selection of the order button.

Method and system for placing a purchase order via a communications network

Greedy Randomized Adaptive Search Procedures.

Survey: Graph clustering

Hub location in backbone/tributary network design: a review

In the discretep-hub location problem, various nodes interact with each other by sending and receiving given levels of traffic (such as telecommunications traffic, data transmissions, airline passengers, packages, etc.). It is necessary to choosep of the given nodes to act as hubs, which are fully interconnected; it is also necessary to connect each other node to one of these hubs so that traffic can be sent between any pair of nodes by using the hubs as switching points. The objective is to minimize the sum of the costs for sending traffic along the links connecting the various nodes. Like many combinatorial problems, thep-hub location problem has many local optima. Heuristics, such as exchange methods, can terminate once such a local optimum is encountered. In this paper, we describe new heuristics for thep-hub location problem, based on tabu search and on a greedy randomized adaptive search procedure (GRASP). These recently developed approaches to combinatorial optimization are capable of examining several local optima, so that, overall, superior solutions are found. Computational experience is reported in which both tabu search and GRASP found “optimal” hub locations (subject to the assumption that nodes must be assigned to the nearest hub) in over 90% of test problems. For problems for which such optima are not known, tabu search and GRASP generated new best-known solutions.

Avoiding local optima in the p -hub location problem using tabu search and grasp

Heuristics for the p-hub location problem

Facility location models are applicable to problems in many diverse areas, such as distribution systems and communication networks. In capacitated facility location problems, a number of facilities with given capacities must be chosen from among a set of possible facility locations and then customers assigned to them. We describe a Lagrangian relaxation heuristic algorithm for capacitated problems in which each customer is served by a single facility. By relaxing the capacity constraints, the uncapacitated facility location problem is obtained as a subproblem and solved by the well-known dual ascent algorithm. The Lagrangian relaxations are complemented by an add heuristic, which is used to obtain an initial feasible solution. Further, a final adjustment heuristic is used to attempt to improve the best solution generated by the relaxations. Computational results are reported on examples generated from the Kuehn and Hamburger test problems.

https://link.springer.com/content/pdf/10.1057%2Fjors.1986.84.pdf

A Lagrangian Relaxation Heuristic for Capacitated Facility Location with Single-Source Constraints

The Core Optical Networks (CORONET) program addresses the development of architectures, protocols, and network control and management to support the future advanced requirements of both commercial and government networks, with a focus on highly dynamic and highly resilient multi-terabit core networks. CORONET encompasses a global network supporting a combination of IP and wavelength services. Satisfying the aggressive requirements of the program required a comprehensive approach addressing connection setup, restoration, quality of service, network design, and nodal architecture. This paper addresses the major innovations developed in Phase 1 of the program by the team led by Telcordia and AT&T. The ultimate goal is to transfer the technology to commercial and government networks for deployment in the next few years.

John G. Klincewicz

Papers

Hub location in backbone/tributary network design: a review

Avoiding local optima in the p -hub location problem using tabu search and grasp

Heuristics for the p-hub location problem

A Lagrangian Relaxation Heuristic for Capacitated Facility Location with Single-Source Constraints

Architectures and Protocols for Capacity Efficient, Highly Dynamic and Highly Resilient Core Networks [Invited]