Specifying optimum water resources based on cost-benefit relationship for settlements by artificial immune systems: Case study of Rutba City, Iraq Open Access

Water supply is vital for all cities. It has become difficult to find sufficient available water resources since they are decreasing day by day (Aalipour et al. 2018, 2022a, 2022b; Noon et al. 2021; Sulaiman et al. 2021b). Also, the cost of the electrical energy (to pump the water) is one of the essential expenses for supplying water without gravity. Therefore, the operating cost should be considered while determining water resources for settlements. In this regard, a cost-benefit relationship becomes more of an issue. In the literature, there are several studies regarding a cost-benefit relationship/analysis for water resources. Mackle et al. (1995) applied a genetic algorithm to the scheduling of multiple pumping units in a water supply system to minimize the overall cost of the pumping operation. Aravossis et al. (2003) improved a methodology which is an innovative cost-benefit-analysis decision support system for water resources management. Khare et al. (2007) performed a cost and benefit analysis on the total cost of ownership (capital investment, maintenance, and operational costs) for water supplies. Varouchakis et al. (2016) applied a cost-benefit analysis approach and a Bayesian decision analysis to assist the decision-making in constructing a water reservoir for irrigation purposes. Yu et al. (2017) used a cost-benefit analysis method based on a multi-objective optimization model for understanding the effect of desalinated seawater's variable costs on a multi-source water supply. Zhang et al. (2019) developed a new theoretical cost-benefit analysis framework to determine the optimal water transfer capacity of water transfer systems. Galioto et al. (2020) improved a methodology consisting of a comparative cost-benefit analysis based on the ‘value of information’ approach to evaluate the comparative advantages of new methods for planning irrigation. An et al. (2021) established a dynamic optimization model for socioeconomic development, water resources supply structure, and water environment of Qinhuangdao city and evaluated policy feasibility by a cost-benefit analysis. Arfanuzzaman et al. (2021) used a comprehensive cost-benefit analysis approach to assess the promising adaptation practices, economic return, and social welfare in the lower Teesta River basin. Fraga et al. (2022) proposed sustainable urban drainage techniques to match urban and natural demands and performed a cost-benefit analysis of sustainable drainage systems considering ecosystem services benefits. Teague et al. (2021) proposed a serious gaming framework for the decision-making process in water resources planning and hazard mitigation, and developed a web-based decision support tool for analyzing a cost-benefit relationship for potential hazard mitigation strategies with dynamic analytics tools. Wang et al. (2021) developed an integrated graphical method for industrial water conservation projects by considering a cost-benefit analysis. To optimize a cost-benefit relationship, numerous trial-and-error processes should be carried out, therefore making a determination of optimum water resources difficult. Within this study, in order to facilitate this task and contribute to the related literature, a heuristic optimization model using artificial immune systems is proposed to specify optimum water resources depending on total net income (total difference between daily incomes based on water charge tariff and daily electricity operating expenses/costs of pumped pipelines) and water demand for residential areas. The optimization model was applied to a case study of Rutba City in Iraq to test its performance.

Rutba City is close to Al-Qa'im (about 250 km away), an Iraqi border town located approximately 400 km northwest of Baghdad near the Syrian border and situated along the Euphrates River (Sulaiman et al. 2021a) (see Figure 1). The city has approximately 50,000 inhabitants and needs 15,000 m³/day and 10,000 m³/day of drinking water for the first six months and second six months each year, respectively. It is planned to supply the water demand of the city by four water resources. There are three water treatment plants in the city. Therefore, the water coming from the four sources will be collected in a 20,000 m³ storage tank and then transmitted to these three plants to be distributed to the city. The first and second sources are two reaches (upstream and downstream) of the Euphrates River, as shown in Figures 1 and 2. Pipeline 1, a cast iron pipeline with a diameter of 500 mm, is currently constructed. There is no limit for withdrawing water from the river by pump station 1, which is 161 m above sea level (a.s.l.).

The total length of pipeline 1 is 250 km, with rising elevation to become 740 m a.s.l. at a distance of 213 km. After that, the elevation of the pipeline decreases through the city to 635 m a.s.l. Therefore, three lift stations were constructed along the pipeline. Similarly, pipeline 2 is currently built (cast iron with a diameter of 800 mm for the first 140 km then 600 mm for 131 km to Rutba City). There is no limit for withdrawing water from the river by pump station 2, which is at 53 m a.s.l. The total length of pipeline 2 is 271 km, with the max elevation is 635 m a.s.l. at the city. Therefore, lifting stations were needed along the pipeline and six were constructed. Pipeline 3 is currently constructed in cast iron with a diameter of 200 mm. There is a limit for withdrawing groundwater of 4,000 m³/day from 16 pumping wells to a storage tank. Pump station 3, at elevation 595 m a.s.l., withdraws water from the storage tank to the city. The total length of pipeline 3 is 20 km, the max elevation of the line is 635 m a.s.l. at the city, with no need for a lift station along the pipeline. Pipeline 4 is planned but not constructed yet. It may be constructed in cast iron with a diameter of 400 mm to transmit water from a dam reservoir. There is a limit for withdrawing water of 3 million m³/year from the dam reservoir due to water scarcity. Pump station 4, at elevation 678 m a.s.l., withdraws water from the dam reservoir to the city at 635 m a.s.l. The total length of pipeline 4 is 29 km, the maximum elevation of the line is 635 m a.s.l. at the city, with no need for a lift station along the pipeline. In this study, these four water resources were optimized for supplying the water of Rutba city by considering a cost-benefit relationship/analysis. The cost-benefit relationship was performed according to daily incomes (water charge per m³) and expenses (electricity price of the pump stations) of the four pipelines, and daily demand (m³/day) of the city. Costs of electricity consumption and maximum discharges of the pump stations are given in Table 1. A water charge tariff is 25 cents/m³ for all the pipelines.

The optimization problem was solved by using a modified clonal selection algorithm (Clonalg) (Eryiğit 2015), a class of artificial immune system, as a heuristic optimization technique. This algorithm is based on the clonal selection theory of the natural immune system. The flow chart of the modified Clonalg is given in Figure 3, where Ab is the population of the antibody randomly created, f is the antibody's antigenic affinity (objective function), C is the population of the cloned antibodies, and C* is the population of the mutated antibodies. The steps of the algorithm are as below:

• (1)

  An antibody set (Ab) is randomly generated.

• (2)

  For each antibody in Ab, an objective function (f) is calculated to be optimized (maximized or minimized).

• (3)

  All antibodies are cloned.

• (4)

  All clones (C) are exposed to the maturation process (mutation) inversely proportional to their antigenic affinities (objective function values). Also, new genes are generated for the clones.

• (5)

  For each matured clone in C*, an objective function (f) is computed again.

• (6)

  The matured clones having the highest affinity (best individuals) are selected to replace the antibodies which have the lowest affinity in Ab. This loop proceeds until the iteration reaches a maximum number. Thus, the best result can be obtained.

OF_net was maximized under constraints of the required daily water demand of the city (15,000 m³/day for first six months and 10,000 m³/day for the second six months of the year) and pump capacities (maximum discharges of the pump stations). Also, another constraint was that 5 million USD as the initial cost of the unconstructed Pipeline 4 should be refunded by total net income in ten years (Pipeline 4 to transmit water from a reservoir of the existing dam; there is a limit for withdrawing water of 3 million m³/year from the dam reservoir). The algorithm was coded in Matlab programming language by using a PC with Intel Core I5-8300H CPU 2.3 GHz, and it was run ten times with a maximum number of iterations (IN_max) to test its stability. In this study, N_Ab, β, ρ, PR and IN_max were assigned as 100, 1, 10, 0.1, and 1,000 respectively.

After running the optimization model ten times, the first and second six months’ results were obtained as shown in Tables 2 and 3, respectively. Required daily water demands of the city for both periods (15,000 m³/day and 10,000 m³/day for approximately 50,000 inhabitants) were accurately transmitted by the pipelines without exceeding the maximum discharges of the pump stations (see Table 1). This proves that the model satisfies the constraint of the required daily water demand of the city and does not violate the constraint of maximum capacities of the pump discharges while solving the optimization problem. Under these constraints, the best result obtained for total net income for the first six months was 541,680 USD (Pipeline 1: 4,600 m³/day, Pipeline 2: 0 m³/day, Pipeline 3: 2,400 m³/day, Pipeline 4: 8,000 m³/day). For the second six months, the best result obtained for total net income was 404,950 USD (Pipeline 1: 2,000 m³/day, Pipeline 2: 0 m³/day, Pipeline 3: 0 m³/day, Pipeline 4: 8,000 m³/day). As expected, the optimization model specified the daily water supplies of the pipelines according to the cost-benefit relationship. For the first 6 months, water supplies from Pipelines 1 and 4 were assigned as maximum capacity, while Pipeline 2 was zero due to the total cost of electricity. Although Pipeline 2 has the highest discharge capacity of the pipelines (meaning the highest income; the water tariff is 25 cents/m³), the model assigned no water from it since it has the highest cost of electricity consumption (see Table 1, Figure 2).

On the other hand, the model did not assign a maximum discharge from Pipeline 3. Therefore, this demonstrates that the total net benefit of maximum discharges supplied from Pipelines 1 and 4 is higher than from combinations of Pipelines 1 and 3 or Pipelines 3 and 4. For the second six months, similarly, water supply from Pipeline 4 was assigned at maximum capacity while Pipelines 2 and 3 were zero because of total cost of electricity and net income. Water supply from Pipeline 1 could have been assigned as a maximum discharge in addition to Pipeline 4 but the water demand of the city is already 10,000 m³/day for the second period. Therefore, Pipeline 1 was assigned by the model to supply the rest of the water demand (2,000 m³/day) of the city. This shows that Pipeline 4 is a better option than Pipeline 1 in terms of a cost-benefit relationship since the model assigned Pipeline 4 with a maximum discharge instead of Pipeline 1. According to the results, the best pipeline is Pipeline 4 while the worst pipeline is Pipeline 2.

By optimizing the water resources for the case study, total net income over ten years should refund the initial cost of the unconstructed Pipeline 4. The model results showed that total net income for ten years (9,466,300 USD) can easily cover the initial cost of Pipeline 4 (5,000,000 USD). Also, the annual amount of water transmitted by Pipeline 4 is 2,920,000 m³ (total of 1,464,000 m³/6 months and 1,456,000 m³/6 months) and does not exceed a limit of 3 million m³/year from the reservoir.

As seen in Tables 2 and 3, the differences between maximum and minimum total net incomes are 37 and 139 USD, and the standard deviations are 12.2 and 43.4 USD for the first and second 6 months, respectively, over ten runs (the model found almost the same values of total net income for both periods in each run). These results indicate that the model is stable. This view could be supported by performing a parameter sensitivity analysis of the model. On the other hand, there may not be a guarantee of obtaining the best result of total net income by solving manually. This may cause it to have a higher cost (lower income). Also, the manual solution to this problem could take hours or days because of numerous combinations and trial-and-error processes, whilst the optimization model can solve the problem in a short time (mean run time is 3.1 mins).

Optimizing water resources based on a cost-benefit relationship is very important for water management and planning, and it is a complex task. A maximum benefit with a minimum cost should be obtained. In this study, an optimization model was improved to make this task easier and obtain such an optimum solution. The case study of Rutba City was applied as an example. After running the model, the dam reservoir (Pipeline 4) and the upstream of the Euphrates River (Qa'im City, Pipeline 1) were specified as the optimum water resources for the city (they have the highest daily net incomes). Owing to the model, the case study for a cost-benefit relationship was easily optimized by complying with the constraints without the need for a long execution time (only 3.1 mins on average). Therefore, it can be said that the model is applicable, practical, and time saving. Nevertheless, the model may be tested for more complex optimization problems based on the cost-benefit relationship, and sensitivity analysis of the model parameters (N_Ab, β, ρ, PR) can be carried out to consolidate it in future studies.

The authors declare that there is no conflict of interest.

All relevant data are included in the paper or its Supplementary Information.