Harmony Search

Article Review

Geem, Z.W., Kim, J.H., Loganathan, G.V. (2001) “A New Heuristic Optimization Algorithm: Harmony Search”. 76(2): 60-68.

This paper presents the algorithm Harmony Search (HS), a new heuristic optimization algorithm inspired in the way musician improvise harmonies. The analogy with music is: musical performance seeks a harmony with maximum aesthetic estimation, as the optimization algorithm seeks the best solution. The aesthetic estimation represents the objective function and the pitches of instruments represent decision variables. The decision variables achieve better solution by a process of practice. After each iteration, the solution is evaluated. If the harmony is better than the previous ones, it is included in the Harmony Memory. The process is repeated until the stopping criteria is satisfied.

The harmony memory is initialized with random values. A new harmony is generated based on the solutions already present in the harmony search. If the new harmony is better than the ones in the harmony memory, it is included on it, and the worst harmony is excluded. In order to increase the decision space and find the global optimum, a parameter called Harmony Memory Considering Rate (HMCR), ranging from 0 to 1, is used to randomly generate new solutions. HMCR is uniformly generated. If it is above the current value of the HMCR, the algorithm selects a new variable with certain probability and introduces the new random value.
Another operator is used to escape local optima, similar to crossover in the genetic algorithm (GA). The Pitch Adjusting Rate (PAR) is used to select a variable with certain probability and shifts the value with its neighbors. The article uses the example of the solution {1,3,4,6,7,9}. The value {6} can be moved to neighboring {4} or {7}.

The article illustrates the harmony search with 3 problems found in the literature. The first one is the Traveling Salesman Problem (TSP), which tries to find the shortest path for a salesman that has to visit a certain number of cities once. The second problem is a 2 dimension constrained minimization problem. The performance of HS is compared with others methods like GA, Generalized Reduced Gradient (GRC) and Evolutionary Programming (EP). HS had better performance compared to the other methods. The last problem is the design of a pipeline network for water supply consisted of 32 nodes, 34 links and 3 loops. The results were compared with GA and Nonlinear Programming Gradient (NLPG). The HS produced the solution with the least cost related to the other methods.

Discussion

The HS algorithm is a very interesting methodology. Particularly for me that play the guitar, was very curious to see how real life phenomena can be invently used to develop new techniques to solve older and new problems. This paper was also interesting because I had the opportunity to attend the talk of one of the authors in the 2009 US-Korea Conference on Science, Technology and Entrepreneurship, last July 16-19, 2009 in Raleigh, North Carolina.

During our weekly discussion meeting, we tried to compared the differences and similarities between HS and GA. As a heuristic method, HS is similar to GA. One aspect that seems important is that HS creates a new solution based in all existing solutions presented in the harmony memory, while GA creates a new solution only with two previous solutions (parents).

Downstream Effects of Stormwater Management Basins

Article Review

McCuen, R.H. (1979) “Downstream effects of Stormwater Management Basins” Journal of the Hydraulics Division, Vol. 105, No. 11.

Prof. McCuen addresses the problem of hydrological alteration due urbanization. The use of impervious materials decreases natural storage, increasing peak rates, decreasing time-to-peak, and increasing the volumes of runoff and sediments. To mitigate these detrimental effects storm water management (SWM) is required. However, according to the paper, many SWM strategies fail in mitigate the urbanization effects because “they only attempt to limit peak flow rates and sediments volumes” to predevelopment conditions. This is in general attempted by the use of detention basins. This strategy, however, is not sufficient. This problem lead to main question of the article: “Are SWM basins effectively meeting the intent of stormwater management?”

“Urban development causes a decrease in natural storage, including infiltration, interception, and depression storage”. SWM basin is an attempt to restore the loss of natural storage in the watershed. This volume can be artificially restored, but the timing characteristics introduced by detention basins are significantly different from the predevelopment conditions. In natural conditions, the major part of the storage volume is filled during the storm event, while in a detention facility this storage is rapidly filled during the risen portion of the hydrograph.

A second effect introduced by detention basin is that the increased volume of direct runoff is released at a higher rate when compared to natural storage. This cause increase in the duration of bankfull flows.

Due the reasons explained so far, the work examines the hypothesis “that, when changes in both timing characteristics and flow volumes are not corrected by SWM, they may have an adverse effect on flow conditions downstream from the SWM basin.”

A 2.12 square mile watershed was simulated using the Soil Conservation Service TR-20 hydrological model. The predominant soils are silt loams, characterized as deep, well-drained, and moderately erodible. Simulations indicate that peak flow increases from 11.7 to 59.3 cfs (factor of five!!!) from pre-development to urbanized condition of one catchment for the 10 yr-storm. In terms of volume, there is an increase of 100%. The time-to-peak decrease 7 minutes. Introducing a detention basin, the peak flow is reduced to 13.08 cfs, but the time-to-peak is 36 minutes greater than that which existed prior to development. A compared analysis is done for the 100 yr-storm. The effects are the same, but the differences are much lower.

Looking further downstream in the watershed, the computation indicates that for the 100 yr-storm the SWM basin increases the peak flow compared to the post development with no control. This is true for approximately 5 miles downstream the storage facility. The reason for that is changes in timing characteristics affects the runoff conditions downstream.

After the hydrological analysis, the author has approached the bedload transport. Although its is recognized the difficulty in estimating bedload discharges, a theoretical model can be used to assess different scenarios and trace comparisons between them. A model developed by Goncharov was used to predict the sediment discharge as a function of mean flow velocity, mean sediment diameter, the critical velocity of sediment, and the mean depth. The previous discussed scenarios were evaluated to generate estimative of sediment yield. The results indicate that even with the SWM basin there is a significant increase in total volume of sediment. This is due the sustain flow introduced by the basin, which induce higher velocities than the critical velocity over a longer period.

The author finalizes the article with some considerations related with SWM policies and designs. He considers three aspects important:

(1) “The recognition of a comprehensive interpretation to the definition of the intent of SWM;

(2) A policy statement that reflects this interpretation and provides the guidelines that are required to institute proper design methods;

(3) Design methods and construction practices that are representative of the state-of-art and the fully consider hydrologic changes that go along with the urbanization process.”

He suggests that alternatives like grass-lined swales, rooftops detention, and porous pavements are SWM measures that better represents the natural storage found in predevelopment conditions, both in volume and temporal characteristics. A second alternative is to make change in the basin designs, although that may cause conflicts between flood control and pollution/sediment control, for example.

Flow duration curves

Article Review

Fan, C., Li, James (2004) “A Modelling Analysis of Urban Stormwater Flow Regimes and their Implication for Stream Erosion” Water Quality Re. Journal Canada, Vol. 39, No. 4.

The objective of this paper is to analyze flow-duration characteristics of a stream, with and without control measures applied during and after urbanization and its potential for erosion.

“Flow duration curve is the complement of the cumulative distribution function of stream flow. It represents the relationship between the magnitude and frequency of daily, weekly, monthly or even longer period of time of stream flow for a particular watershed.” The flow duration curve is the relationship between exccedance probability and discharge.

According to the authors, stream erosion is a continuous process of removal and deposition of sediments. Urbanization can alters drastically this balance due alteration of the flow regime. Since measuring both discharge of solid and liquid is something difficult to perform, especially in the planning process of development, the hypothesis of this work is that hydrological models can be used to estimate the flow regimes alteration by the flow-duration curve and evaluate the implication on stream erosion.

A period of 3 months of measure data were used to calibrate the model ISWMS (Integrated Storm Water Management Simulator). The watershed was discretized in 9 sub catchments. The calibrated parameters were base flow and horton’s equation for infiltration. Twenty-seven years of hourly rainfall data was used in the long-term simulations.

Different degrees of development were tested by changing the percent of imperviousness (20, 30 and 40 %), of all catchment, with exception of catchment #5 which represents a wetland area. It was noted that urbanized duration curves are shifted from the original curve as more imperviousness is used, indicating that for the same discharge, the frequency is higher.

To analyze the impact of flow control measures, three scenarios were tested: (1) an extended detention basin was added to each subcatchment except subcatchment 5 (the wetland); (2) two extended detention basins were added, one more upstream and other downstream; and (3) an extended detention basin was added downstream of all the subcatchments. The basins were sized considering the criteria of capturing 5 mm of rainfall and the outlet orifices were sized for 24 and 48 hours.

The first analysis compared the use of detention basin in the outlet of the watershed (scenario 3). The results indicate that both 24 hrs and 48 hrs extended basins control the runoff greater than 0.1 m³/s. For lower flow than 0.05 m³/s, 24 hrs basins performed slightly better than 48 hrs basins, and the opposite for flows varying from 0.1 to 0.05 m³/s.

When other locations are analyzed, it was found that regional control (scenario 2) provide better control performance than scenario 3 for flows greater than 0.07 m³/s. Local control (scenario 1) generally performs best when the flow is less than 0.09 m³/s. The authors conclude that the optimal location of detention basis is dependent on the flow regime.

In summary, the paper concludes that urbanization can change significantly the hydrological regime of a watershed and that extended detention basins with 48 hours of detention time provide better control of flow-duration characteristics than 24 hours of detention for higher flows. For lower flows, the 24 hour basin perform better. This make the authors suggest that the detention basins should be sized based on the range of flows which determine the stability of a stream. Finally, the paper states that if a watershed is urbanized beyond 40 % of imperviousness, it may be impossible to restore the flow-duration curve to its original position.

Discussion

This paper seems valid in order to illustrate the impact of urbanization in the flow regime. It has used as a tool of analysis the flow duration curve, analyses that can be found in more literature (see last post). Some comments however I would like to do:

(1) The paper doesn’t specify the area of the watershed that is been analyzed. The findings of the work may not be extrapolate to other watershed with different scales;
(2) The period of calibration is very small (just 3 months). A period of verification of the modeling was not performed;
(3) The limit of 40 % of imperviousness indicating that it may be impossible to restore the flow-duration curve seems very specific for this particular watershed. Different hydrological characteristics may turn this number lower or even higher;
(4) The results shown in the work prove good control over the high flow portion of the flow duration curve. For lower flows (and high frequent event) none of the scenarios seems to replicate the predevelopment conditions (see last post);
(5) The original hypothesis of the work was partially proved. The hydrological alterations were demonstrated, but no further analysis was done to evaluate the implication of the alterations on stream erosion.

Are Best-Management-Practice really environmentally friendly?

Article Review

Roesner, L.A., Bledsoe, B.P., Brashear, R.W. (2001) “Are Best-Management-Practice really environmentally friendly?” Journal of Water Resources Planning and Management, v. 127, no. 3 (May/June).

This article examines the argument that best-management-pratice (BMP) doesn’t not protect urban streams properly. The definition of BMP is strategies to control of urban runoff, usually store structures as detention basins. The authors defend that the BMP is not the problem in itself, but rather the design guidance for BMP outlet flow control that doesn’t take into account the geomorphologic characteristics of the receiver stream.

The authors present a description of the impacts of urbanization in the hydrology of urban watershed. Some numbers illustrate the changes: the peak flow can increase by 2 to more than 10 in terms of magnitude. Also frequency of two-year peak runoff rate in the predevelopment state occurs three to eight times per year after urbanization. The effects of this changes cause severe stream channel erosion and downstream flooding. In terms of water quality, the effects of urban runoff also harm aquatic habitats.

Considering the increase of runoff, many municipalities require big storms to be controlled, in order that the post-development peak flow does not exceed the pre-development discharge. Common recurrence times are 10 and 25 years. Few locals control the 2-year storm. The article states that while detention basins reduce flooding, they are not effective in reducing erosion. One reason is due the sustained flow that detention ponds induce downstream. The outlet flow is prolonged, subjecting the stream channel for a longer period of time. The second reason is the basin only attenuates the flow of the design storm. Attenuation of different storms is coincidental. Considering that urbanization increases the frequency of pre-development peakflow and basins are designed to regulate storms higher than the 10 or 25 year-storms, most storms will pass through the structure unregulated, subjecting the downstream channel to erosive velocities more frequently.

For correcting the problem, the writers believe that “integrating the design of storage and outlet controls for flood control and BMPs it is possible to better control wet weather discharges to receiving waters over the entire range of flows that the facility experiences.” The question that stormwater managers should ask is: “given the potential flow of sediment and water out of the watershed, what are our options for achieving desired social and biological endpoints?”

The article proposes a two step approach to link biological indices to watershed parameters. The first step is to develop a relationship between stream geomorphologic characteristics and biologic indicators. The second step is to develop a relationship between watershed hydrogeometric parameters and stream geomorphologic parameters. It is believed that with this approach is possible to design holistic runoff control facilities into urban development so both flood protection and maintenance of ecosystem can be achieved.

Blog 10 - Generating Alternatives

Article Review

Pan TC, Kao JJ (2009) GA-QP Model to Optimize Sewer System Design, JOURNAL OF ENVIRONMENTAL ENGINEERING, 135(1) 17-24

Pan and Kao implemented a Genetic-Algorithm (GA) and Quadratic Programming (QP) to generate alternative to the problem of designing sanitary sewer systems. This approach is proposed in order to reduce excessive computational effort presented by other optimization techniques. An alternative method is discrete differential dynamic programming (DDDP). DDDP, however, restricts the search space decreasing the chances of locating global optimum. Also, DDDP must be manually implemented, difficult to generalize to different systems. Another approach would be a GA-LP (linear programming) model, but linearization of nonlinear functions is complex.

The nice contribution of this work is the recognition that some important design factors and unquantifiable issues (public preference, for example) are not included within the optimization model. So, “the solution obtained from existing sewer design models may not be the best one or even feasible when unmodeled factors or issues are simultaneously evaluated”. Therefore, a model to generate alternatives (MGA) has been developed to evaluate the differences among the designs generated by the GA-QP and DDDP models.

Discussion

This article presents a nice application of generating alternatives, proposed in the previous article by Brill. Specifically to the design of the sewer system, the decision variables considered were slopes and buried depths. However, in real projects, there are a lot of “more important” aspects that may be subject to change by the decision-makers. For example, the network topology. Also, geology is a very important aspect in economic viability.

Assignment # 10 - Alternatives

Article Review

BRILL ED (1979) USE OF OPTIMIZATION MODELS IN PUBLIC-SECTOR PLANNING, MANAGEMENT SCIENCE, 25.

According to the article, traditional optimization and multiobjective models fail in obtaining the best solution for public-sector planning. The limitations of using optimization models are failure in considering equity and difficulties in estimating benefits and costs. The author states that even a multiobjective approach, which should capture different perspectives of a problem, has practical limitations. In many problems, indifference curves are likely to reflect local optima. In a public planning problem, there might be issues not considered, which once introduced in the mathematical framework, likely bring the optimal to the inferior region of the original problem.

The article question which uses should optimization model be designed? There are set of problems that are inherently political in essence, which increase the complexity. In the second post I have addressed the article of Liebman (1978), which focus on “wicked” problems. Based on that, the authors argue that models should be used in a different way it has been used so far (1979).

The main idea the articles brings is that new types of optimization tools should be designed specifically to generate alternative plans and alternatives. To better understand the problem and generate alternatives is important creativity and inventiveness. Ways of using optimization models in a planning process are discussed in more detail in the article, like the use of optimization and simulation models. For this article, simulation model means examining a specific design in details. The optimization model identifies preliminary alternatives and the simulation model examines the solutions in more details. Use of analytical model and optimization models are also cited. The authors emphasize that there are a lot of gains in understanding the problem and feasible space in using a tool box of models.

The article comes up with the question: “optimization models should be capable of generating alternative solutions that: (1) meet minimal requirements, and (2) are different”? The question related to minimal requirements depends on the formulation of objective function and constraints. The issue of how different the solutions are is more difficult. A random sampling approach is suggested as an alternative method.

Discussion

The article brilliantly addresses how optimization problems should be used in order to effectively help the decision making process in the field of public planning. In real life, there will always be factors that cannot be incorporated in the optimization model, so generating multiple alternatives to be evaluated by decision-makers is a good idea. Some question, however, still remains: Brill says that a good set of alternatives should meet minimal requirements and be different. But how evaluate how different solutions are? He proposes an optimization approach to maximize the differences among solutions, but still this approach doesn’t contain all the aspects related to the decision-making process. I mean that two good solutions may be very similar in terms of modeling, but may contain completely different weights when evaluated by society. Or, two solutions may be different by the modeling, but for the decision-making process the solutions may be similar when intangible and incommensurable criteria are used.

Assignment # 9 - Multiobjective optmization

Shiau JT, Wu FC (2006) Compromise programming methodology for determining instream flow under multiobjective water allocation criteria, JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION, 42(5), pp. 1179-1191.

Instream flow is one of the most challenging issues in water resources systems. Using a multiobjective optimization criterion, this study implements a framework to allocate water for three different uses: agriculture, urban and instream flow. The methodology considered three objectives: overall degree of hydrological alteration, shortage ratio for agriculture withdrawals, and shortage ratio for municipal uses. The degree of hydrological alteration was assessed using the Range of Variability Approach (RVA), which use 32 indicators of hydrological alteration (IHA) to evaluate hydrological impacts. The decision variable is instream flow release, considered to be constant during time.

The methodology was applied in Kaoping watershed in southern Taiwan. A weir operation diverts a maximum of 35 m³/s for municipal uses but more than that is also diverted to irrigation districts.

Results indicate that actual 9.5 m³/s instream flow is not enough to restore the natural flows variability. Weighting the three objective functions equally, optimal instream flow discharge of 26 m³/s could reduce hydrological alterations from a high to moderate state. A discharge of 93 m³/s would bring the hydrological regime to a low alteration state.

Discussion

This paper presents a very important study for water resources management. It combines shortage ratios and hydrological alteration statistics to perform a multiobjective optimization. The degree of hydrological alteration considered a kind of average value of the 32 IHA to represent the overall alteration. Future improvements could consider each of 32 indicators or the five groups of IHA. Considering variable instream flow releases would also be a interesting application.