Optimal location of infiltration-based best management practices for storm water management

Perez-Pedini C, Limbrunner JF, Vogel RM (2005) “Optimal location of infiltration-based best management practices for storm water management,” JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT, 131(6) pp. 441-448

In this study, genetic algorithm is used to determine optimal places of best management practices (BMPs) in a watershed for storm water management. Especially, using hydrologic response units (HRUs) with curve number method, the impacts caused by installing infiltration-based BMPs are estimated for optimizing this multi-objective model. The result would show a Pareto frontier which is the trade-off between BMPs number and flooding in the watershed.

In the past, approaches for storm water management tended to focus on detention and retention basin and those facilities which consider storage-based BMPs. This article, however, tries to introduce infiltration approaches for the storm water management and shows the strategic integration of storage and infiltration storm water controls. Other difference with past studies is that the considered number of HRUs is much more detailed and increased in number. Another improvement in this study is the connectivity among the HRUs because multivariate regression showed failure of sufficient explanation about the influence of cell contributions at the basin outflow point in the past.

The objective of this optimization is to find the best location of installation of certain number of BMPs, which results in minimizing peak stream-flow at the watershed outlet. After making some assumption for decrease in computational time, genetic algorithm is used to solve this problem with increase in number of BMPs, the number means increasing cost as increase in BMPs install number. Then, we can get the trade-off or Pareto frontier of peak flow reduction and the BMPs cost. We can also find an interesting thing that the most results occur near major highway intersections in the study area. Another thing is that larger number of BMPs is not always inclusive of smaller BMPs solution. From some examination, the author discovered that the real optimal solution will occur when a larger BMPs solution includes all of the smaller BMP solution.

Discussion

 This article is interesting because it shows a reasonable and improved approach for optimizing the best BMPs place in a watershed. Increase in BMPs grid points and use of CN approach and connectivity among the grid point are most interesting thing in this article. An advantage of using genetic algorithm for complex calculation and the inclusion resulting from increase in number of BMPs are also interesting. However, I think the budget of placing BMPs would be different at each site because each site should have various topography and land-use. If I tried to do this research, I would add the budget variable in the optimization to provide better alternatives for the storm water management.

USE OF OPTIMIZATION MODELS IN PUBLIC-SECTOR PLANNING

BRILL ED (1979) USE OF OPTIMIZATION MODELS IN PUBLIC-SECTOR PLANNING, MANAGEMENT SCIENCE, Vol. 25, No. 5, pp. 413-422.

The purpose of optimization is to obtain ‘the answer’ and is useful for simple problem. However, in a public-sector problem, there are many problems for solving or optimizing because of a multitude of local optima and elusive elements. Because of the reason, the author maintains that the optimization for public-sector problem should play the role of generating alternatives and in facilitating their evaluation and elaboration. He also said that several models and new types of formulations should be required for the better optimization.

The author points out the limitation of using optimization model which are difficulties of considering equity or distribution of income, and which are empirical inadequacies in evaluating benefits and costs. Specifically, the article demonstrates that the incomplete multi-objective models usually show that the optimal solution in public-sector problem occurs at inferior region, not at non-inferior region. Even if the model was completely formulated, it is impossible to obtain the overall best solution.

To reduce the limitations, the author suggests several methods to make the optimization models play the important role of providing alternatives for decision makers in public-sector problems. First, ‘joint use of models’ should be used such as combining analytical and optimization models or using a tool box of models. The author also recommends us to use optimization models which generate alternatives and facilitate evaluation such as branch-and-bound method, random method, and HSJ method.

In conclusion, the solution of optimization model would be a synthesized solution resulting in their alternatives, which require unlike formulations and methods. Planners and their decision can be aided by the offered alternatives with gaining better understanding of the relationship, objectives, and constraints in public-sector problems.

Discussion

Generating alternatives from a solution in a specific optimization model is interesting because people’s thinking cannot be formulated. By offering alternatives, decision makers can refer to the alternatives and they could not always select the optimal solution, but could possibly select one of the alternatives. However, I think that the article is necessary to provide more various ways or methods to generate such alternatives, and we need to improve or invent skills generating alternatives for the future research or their application.

Use of mathematical models to generate alternative solutions to water resources planning problems

Chang, S.-Y., Brill, E.D., Jr., and Hopkins, L.D. (1982) Use of mathematical models to generate alternative solutions to water resources planning problems, WATER RESOURCES RESEARCH, VOL. 18, NO. 1, PP. 58-64, 1982

The author provides Modeling Generate Alternatives (MGA) techniques to reduce the weakness of optimization models, which do not usually give us a perfect solution about a complex problem in real world. The author argues that various alternatives from MGA should be also provided for decision makers to minimize the weakness. Introducing three kinds of methods to generate alternatives, the definition and characteristic of each method are informed and compared by applying an example of water resources planning problems.

1.      Hop, Skip, and Jump (HSJ)

‘The sum of the nonzero variables in the initial solution is minimized subject to a target constraint on the cost objective.’

2.      Ransom Generation Method

‘Maximizing the sum of several randomly selected decision variables and the number of variables selected can be arbitrarily specified or randomly determined.’

3.      Branch and Bound Screening

‘Obtaining feasible solutions within a certain limit of the objective function value’

From the analysis of a provided example, the result of HSJ method is binding with the cost constraint, and the random and BBS method’s result is little better about the cost. All the methods can generate many alternatives but BBS method can generate less number of alternatives comparing to the other methods.

We can also know that HSJ method tends to generate different number of plants in centralization, the random method tends to change the location of plants and interceptors in the similar number, and BBS tends to rearrange the certain system with making the other system constant.

In conclusion, the author argues that these three methods can be potential to help decision maker to be able to choose the best solution in a public sector problem. Though an optimization model can only contain one objective, MGA techniques make it possible to include multi-objective in the model.

Discussion

This article is interesting because it shows how to generate alternatives from an optimization model, which would be helpful for decision maker and can improve a role of optimization in public scale problem. It also provides examples the methods for generating the alternatives to easier understand us. However, I am unsatisfied with the lack of various examples because the article shows the characteristics and patterns of the models only from one example. Therefore, I would like to apply the methods into various problems to verify the characters of each method for generating alternatives.