optimization

PD-01 - Linear Programming and GIS

Linear programming is a set of methods for finding optimal solutions to mathematical models composed of a set of linear functions. Many spatial location problems can be structured as linear programs. However, even modest-sized problem instances can be very difficult to solve due to the combinatorial complexity of the problems and the associated computational expense that they incur. Geographic Information Systems software does not typically incorporate formal linear programming functionality, and instead commonly uses heuristic solution procedures to generate near-optimal solutions quickly. There is growing interest in integrating the spatial analytic tools incorporated in Geographic Information Systems with the solution power of linear programming software to generate guaranteed optimal solutions to spatial location problems.

AM-78 - Genetic Algorithms and Evolutionary Computing

Genetic algorithms (GAs) are a family of search methods that have been shown to be effective in finding optimal or near-optimal solutions to a wide range of optimization problems. A GA maintains a population of solutions to the problem being solved and uses crossover, mutation, and selection operations to iteratively modify them. As the population evolves across generations, better solutions are created and inferior ones are selectively discarded. GAs usually run for a fixed number of iterations (generations) or until further improvements do not obtain. This contribution discusses the fundamental principles of genetic algorithms and uses Python code to illustrate how GAs can be developed for both numerical and spatial optimization problems. Computational experiments are used to demonstrate the effectiveness of GAs and to illustrate some nuances in GA design.

PD-01 - Linear Programming and GIS

Linear programming is a set of methods for finding optimal solutions to mathematical models composed of a set of linear functions. Many spatial location problems can be structured as linear programs. However, even modest-sized problem instances can be very difficult to solve due to the combinatorial complexity of the problems and the associated computational expense that they incur. Geographic Information Systems software does not typically incorporate formal linear programming functionality, and instead commonly uses heuristic solution procedures to generate near-optimal solutions quickly. There is growing interest in integrating the spatial analytic tools incorporated in Geographic Information Systems with the solution power of linear programming software to generate guaranteed optimal solutions to spatial location problems.