Topics
Applied Physics: Lasers and Accelerators, Condensed Matter, Soft matter and materials science
plenary speech
Prof. Nodari Vakhania
Sate University Morelos, Mexico
Title: On some optimality measures for multi-criteria optimization
Abstract: Multi-criteria optimization problems are difficult to address since different objectives
are often contradictory. A commonly used compromise is to look for a Pareto-optimal frontier
of the feasible solutions consisting of those that are not dominated by any other feasible
solution (with respect to any of the given criteria). Finding the Pareto-optimal frontier
often remains NP-hard. This is always the case if at least one of the
corresponding single-criterion problem is NP-hard. Finding the Pareto-optimal set of
solutions may be NP-hard even if none of the single-criterion problem is NP-hard.
Here we give a brief comparative analysis of the Pareto-approach with another
practical multi-criteria optimality measure that we call threshold-optimization measure.
The threshold-optimization problem seeks for a feasible schedule whose objective
values are acceptable for a given particular application for all objective
functions, in particular, they do not exceed (for minimization problems) or are no
smaller (for maximization problems) than the components of a threshold vector
specified by the practitioner whose $i$th component is some threshold value for
the $i$th objective function. As we observe, depending on the components of the above
vector, it might be possible to solve the threshold-optimization problem in a low degree
polynomial time even if all the corresponding single-criteria problems are NP-hard.
A threshold vector with specific threshold values for each objective function
is supposed to have a direct practical meaning. For practically useful values of the threshold
vector, the threshold-optimization problem might be solved in a low-degree polynomial
time by a kit of heuristic algorithms, each one being designed for one of the
corresponding single-criterion problems. If the kit of heuristic algorithms fails
to find a feasible solution respecting the threshold vector, then the heuristics
for NP-hard single-criterion problems can be replaced by implicit enumeration
algorithms. In fact, the replacement can be accomplished step-by-step, starting
from the most critical heuristics. This kind of approach may be more practical
since the practitioner may not be interested, in general, in the minimization of
each objective function but rather in an solution of an acceptable quality
for every objective function: in practice, there may be different tolerances to the
quality of the delivered solution for each objective function.
Bio: To be anancioud soon
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