A Rigorous Computational Comparison of Alternative Solution Methods for the Generalized Assignment Problem

Abstract

Statistical experimental design and analysis is a cornerstone for scientific inquiry that is rarely applied in reporting computational testing. This approach is employed to study the relative performance characteristics of the four leading algorithmic and heuristic alternatives to solve the Linear Cost Generalized Assignment Problem (LCGAP) against a newly developed heuristic, Variable-Depth Search Heuristic (VDSH). In assessing the relative effectiveness of the prominent solution methodologies and VDSH under the effects of various problem characteristics, we devise a carefully designed experimentation of state-of-the-art implementations; through a rigorous statistical analysis we identify the most efficient method(s) for commonly studied LCGAPs, and determine the effect on solution time and quality of problem class and size.combinatorial optimization, generalized assignment problem, variable-depth search, experimental design and analysis

Explicit-Constraint Branching for Solving Mixed-Integer Programs

“…The problem that instigated our search for better branching techniques is a version of the generalized assignment problem (GAP) (e.g., Amini andRacer 1994, Ross andSoland 1975) that we call the "elastic GAP" or "EGAP." The GAP arises in a number of contexts but is described here as a minimum cost assignment of a collection of orders to delivery trucks.…”

A simple dual algorithm for the generalised assignment problem

“…The algorithm of Amini and Racer (1994) is claimed to run slower than MTHG, but produce solutions which are closer to the optimal. It should be noted that algorithm MTHG first obtains a feasible solution and then seeks to improve it.…”

“…The main reference for approximate algorithms and a full discussion of the problem is Martello and Toth (1990). Recent discussions on comparative performance of algorithms is contained in Amini and Racer (1994), which also lists applications and extensions to the problem and Osman (1995), updating Osman (1990), which describes various heuristics and comprehensively surveys the field. This paper will describe a simple 'dual' type approximate algorithm for GAP which is inspired by the algorithm MTHG described in Martello and Toth (1990).…”

Testing cut generators for mixed-integer linear programming

“…By carefully devising random instances with and without a particular property, one can test how the property impacts the performances of the two algorithms and test if one is significantly better than the other when the property is present in the instance. Studies of this type can be found in the literature, e.g., for the Bin Packing Problem [26], for the Generalized Assignment Problem [3], for the Computer Network Design Problem [32], for computing asymptotic estimates of algorithm complexity [30], for analysis of Integer Linear Programming algorithms [21], for Network Reoptimization Techniques [2], and for an analysis of the effect of the choice in starting points for Nonlinear Optimization Algorithms [15].…”