### Use of Multi-Objective Particle Swarm Optimization in Water Resources Management

Abstract

Water resources management presents a large variety of multi-objective problems that
require powerful optimization tools to fully characterize the existing trade-offs. Different
optimization methods, based on mathematical programming at first and on evolutionary
algorithms (EA) more recently, have been applied with various degrees of success. This
dissertation presents a multi-objective implementation of a relatively recent evolutionary
technique called particle swarm optimization (PSO). The multi-objective PSO (MOPSO)
algorithm was implemented as a generalized solver for Microsoft Excel, and applied to
a set of test functions commonly used in the EA literature and to selected water resources
management problems, including a classic multi-purpose reservoir operation problem, a
problem of selective withdrawal from thermally stratified reservoirs, and a reservoir
operation problem using storage guide curves with fuzzy objectives.
Three other multi-objective solvers were developed: a second EA approach, using the
non-dominated sorting genetic algorithm II (NSGA-II), a traditional mathematical
programming method, the e-constraint with nonlinear optimization, and a pure random
search approach.
In most problems, the MOPSO and the NSGA-II algorithms provided good
approximations to the true Pareto optimal sets. The NSGA-II algorithm seems to be more
robust perfoming well in a wider range of problems, although MOPSO showed better
performance for some problems. The main advantage of the MOPSO is associated with
the simplicity of the algorithm. The basic MOPSO algorithm is much simpler and easier
to implement than the NSGA-II. This makes MOPSO more flexible to accommodate
necessary changes to deal with specific problems.
A method to visualize and explore solutions of multi-objective optimization was
introduced. The Interactive Compromise Coordinate (ICC) method allows the projection
of all alternative solutions in a single unit circle graph. The decision maker (DM) can
explore Pareto optimal sets and rank alternatives using a compromise programming
approach based on weights that can be interactively changed. The method’s basic
assumptions are that the DM’s preference structure can be modeled by a set of weights
and that all alternatives are transitively comparable to each other, i.e. a complete preorder
is obtainable. The mathematical basis for the method is presented and the method
of projection is illustrated.