Preference-based methods are classical optimization techniques, that integrate
decision maker's preferences at some stage of the resolution process. These preferences
are required before the resolution process begins. In this class of methods, we find the
value function method, the -constraint method, goal programming, and the generalized
center methods. The foundation of the value function method is the individual choices
theory. DM’s preferences are based on rationality assumptions. The DM compares pairs
of alternatives (i.e., pairs of objective functions), and ranks them according to preference
relations. The different types of preferences are Leontief, Cobb-Douglas or CES
preferences. The -constraint method requires the selection of one objective while all
other objectives are constrained to some value. A payoff table is constructed by solving
for each chosen objective a SOO problem with additional constraints. Goal programming
is another preference-based method for which DM decides a particular goal for each
objective. The programming problem is to minimize the total deviation of solutions from
the targets using a specified distance. In the generalized center method, level constraints
on the objective function value restrict the feasible region by successive steps. Less
performant half-spaces level sets are discarded in the process. The method can be
described as a sequence of unconstrained minimization problems using a distance
function. Numerical examples from literature illustrate the different classical methods.
Keywords: Basic feasible region, Chebyshev’s problem, -constrained method,
Generalized center method, Goal programming, Neighboring nonbasic solution,
Neighboring point, Non-inferior solution, Payoff table, Pivot, Scalarization,
Simplex tableau, Simplex-based Algorithm, Slack variable, Value function method,
Weakly Pareto-optimal, Weighted exponential method, Weighted metric method,
Weighted sum method, Zeleny’s simplex algorithm.
