Civil Engineering Reference
In-Depth Information
finally reached is the optimal one. Also, the selection of a representative set of
alternatives is usually a difficult problem, while the final solution is heavily
affected by these predefined alternatives. On the opposite case, i.e., when
numerous alternatives are defined, the required evaluation and selection process
may become extremely difficult to handle. In any case, however, the MCDA
approach limits the study to a potentially large but certainly finite number of
alternatives, when the real opportunities are enormous considering all the available
ECM that may be employed (Diakaki et al.
2008
).
2.3.2 MOP Approaches (Alternatives Implicitly in a Mathematical
Model)
Decision support for improving energy efficiency in buildings problems is also
tackled using multi-objective optimization models stated as mathematical pro-
gramming models with multiple competing objective functions to be optimized,
being the set of feasible solutions implicitly defined by a set of constraints.
Multi-objective Programming (MOP) Approaches
The modeling of real-world problems generally requires the consideration of dis-
tinct axes of evaluation of the merits of potential solutions. In engineering prob-
lems, aspects of operational, economical, environmental, and quality of service
nature are at stake. Therefore, mathematical models must explicitly address these
multiple, incommensurate, and often conflicting aspects of evaluation as objective
functions to be optimized. Besides, MOP models enlarge the variety of potential
solutions to be considered and enable to grasp the trade-offs between the objective
functions helping to reach a satisfactory compromise solution. The essential con-
cept in multi-objective optimization is the one of non-dominated (efficient, Pareto
optimal) solutions, that is, feasible solutions for which no improvement in all
objective functions is possible simultaneously; in order to improve an objective
function, it is necessary to accept worsening at least another objective function
value. In real-world problems, a high number of non-dominated solutions are likely
to exist. Figure
6
illustrates this concept for a problem with two objective functions
to be minimized. Although it is the essential concept in MOP, the concept of non-
dominated solution is a poor one, in the sense that it lacks discriminative power for
decision recommendation purposes. Non-dominated solutions are not comparable
between them, so no solution naturally arises as the ''final'' one. The fact that multi-
objective optimization enables the characterization of the non-dominated front and
the trade-offs at stake between the objective functions is one of its advantages.
However, it is then necessary to reach a final compromise solution for practical
implementation of a reduced set of non-dominated solutions for further screening.
Pareto optimization was introduced in this area in the 1980s by Radford and
Gero (
1980a
,
b
), Gero et al. (
1983
), D'cruz and Radford (
1987
), and it is now
widely used in building design and less in retrofit optimization. It was used, for
example, by Asadi et al. (
2012a
,
b
) to optimize the retrofit cost and energy savings
