1.5. Previous Work in Optimal Planning for a Water Resources System
35
The work of Hufschmidt, Wallace, Young, Orlob, and Woolsey will be
briefly summarized in this section because these authors illustrate the
main approaches used so far in solving the problem of the sequencing of
construction of system elements and the increasingly sophisticated problems that may be solved.
One of the most extensive works in the last two decades treating water
resources systems including their optimization was carried out by the
Harvard Water Program [Maass, 1962]. This study introduced the
objectives, defined the concepts, improved the methodology, and pointed
out the factors that were relevant to improving water resources systems.
For the first time, both simulation and optimization techniques were combined to find the best policies. As part of the Harvard study, Hufschmidt
carried out the first systematic study of the optimal sizing of reservoirs in
a water resources system designed to maximize the return on investment
and to meet a schedule of water demands. He assumed (1) a configuration
of dams and rivers, (2) an operating rule for each dam (not necessarily
the "optimal" one), (3) a deterministic hydrology of sixty years, and (4)
that the demand schedule did not vary from year to year. For each combination of dam sizes a simulation gave the revenue from operating the
system as well as any irrigation water and energy shortages incurred. The
strategy of searching for the optimum was as follows:
1. By random sampling over the independent variables, reduce the
range of the variables that have to be searched. The probability that the
combination of dam sizes having the highest revenue lies within a fixed
percentage of the optimum can also be calculated [Young et al. } 1969].
2. Pick a "likely" starting point from within the reduced ranges for
search. Then use a gradient search technique to find the optimum point.
3. In the region of the optimum point, use a grid sampling technique
and/or "marginal" (incremental) analysis to ensure that the point is a
"local" optimum.
4. Select other "likely" points from which the optimum solution can be
obtained. If the response function is not convex, the gradient search technique cannot guarantee that the local optimal point has been found. If the
same optimum point is located from several disparate starting points, one
can be reasonably sure that a reasonable optimum point has been found.
Wallace [1966] advanced the work of Hufschmidt in certain respects.
He used linear programming to plan the sizing of new reservoirs to meet
projected power and irrigation demands in the Maule River (in Central
Chile) and to provide the reservoir operating rules.
35
The work of Hufschmidt, Wallace, Young, Orlob, and Woolsey will be
briefly summarized in this section because these authors illustrate the
main approaches used so far in solving the problem of the sequencing of
construction of system elements and the increasingly sophisticated problems that may be solved.
One of the most extensive works in the last two decades treating water
resources systems including their optimization was carried out by the
Harvard Water Program [Maass, 1962]. This study introduced the
objectives, defined the concepts, improved the methodology, and pointed
out the factors that were relevant to improving water resources systems.
For the first time, both simulation and optimization techniques were combined to find the best policies. As part of the Harvard study, Hufschmidt
carried out the first systematic study of the optimal sizing of reservoirs in
a water resources system designed to maximize the return on investment
and to meet a schedule of water demands. He assumed (1) a configuration
of dams and rivers, (2) an operating rule for each dam (not necessarily
the "optimal" one), (3) a deterministic hydrology of sixty years, and (4)
that the demand schedule did not vary from year to year. For each combination of dam sizes a simulation gave the revenue from operating the
system as well as any irrigation water and energy shortages incurred. The
strategy of searching for the optimum was as follows:
1. By random sampling over the independent variables, reduce the
range of the variables that have to be searched. The probability that the
combination of dam sizes having the highest revenue lies within a fixed
percentage of the optimum can also be calculated [Young et al. } 1969].
2. Pick a "likely" starting point from within the reduced ranges for
search. Then use a gradient search technique to find the optimum point.
3. In the region of the optimum point, use a grid sampling technique
and/or "marginal" (incremental) analysis to ensure that the point is a
"local" optimum.
4. Select other "likely" points from which the optimum solution can be
obtained. If the response function is not convex, the gradient search technique cannot guarantee that the local optimal point has been found. If the
same optimum point is located from several disparate starting points, one
can be reasonably sure that a reasonable optimum point has been found.
Wallace [1966] advanced the work of Hufschmidt in certain respects.
He used linear programming to plan the sizing of new reservoirs to meet
projected power and irrigation demands in the Maule River (in Central
Chile) and to provide the reservoir operating rules.