Multi-objective reservoir operation of the Ukai reservoir system using an improved Jaya algorithm Open Access

In the case of reservoir operation problems, decisions about releases and storage over a period must be taken with regard to variability in inflows and with demands in mind for the best possible system performance (Kumar & Reddy 2007). The traditional optimization techniques used in reservoir operation include linear programming (LP), non-linear programming (NLP), and dynamic programming (DP). While these techniques have been used widely in the past, there have been a few restrictions (Hossain & El-shafie 2013). When operating a multi-purpose reservoir, the objectives are more complex than when using a single-function reservoir, with several problems often including inadequate inflows and greater demands. A model should be built as close to reality as possible to ensure the best possible performance of such a reservoir system. In this process, the model is capable of solving nonlinearity with no convexity problems in its field. LP can solve only a linear problem, NLP is complicated and DP fails if there is an increase in the problem scale (Ming et al. 2015). Furthermore, traditional optimization techniques have been found to be trapped in local optimal solutions and prove difficult to solve multi-objective, non-distinctive, non-convex and discontinuous functionalities (Reddy & Kumar 2006).

To overcome the limitations of traditional methods of optimization, various optimization techniques such as heuristic, metaheuristic and evolutionary algorithms have been developed. With rising computing power, they have become very popular in solving complex optimization problems, and also eases the handling of the nonlinear and nonconvex relationships of the model developed. Such techniques have been used by various researchers, for example ant colony optimization (ACO) (Kumar & Reddy 2006), genetic algorithms (GA) (Ngoc et al. 2014), honey bee mating optimization (HBMO) (Afshar et al. 2010), particle swarm optimization (Afshar 2012), artificial bee colony (ABC) (Ahmad et al. 2016), the cuckoo optimization algorithm (COA) (Hosseini-Moghari et al. 2015), firefly algorithm (FA) (Garousi-Nejad et al. 2016), harmony search (HS) (Bashiri-Atrabi et al. 2015), weed optimization algorithm (WOA) (Asgari et al. 2016), and differential evolution (DE) (Ahmadianfar et al. 2016). While existing techniques have their own advantages, there are a few shortcomings.

It has been observed in the literature that most evolutionary and swarm-based algorithms require the tuning of parameters. There are two types of parameters, i.e. common control parameters and algorithm-specific parameters (Rao et al. 2011). The common control parameters are the number of iterations and the population size which are present in all algorithms. The number of iterations corresponds to the number of times algorithms run to find the best solution, whilst the population is the number of particles assigned to solve the problem. The algorithm-specific parameters are the internal parameters. The algorithm-specific parameters are different for each algorithm which need to be tuned before executing the algorithm. Improper adjustment of these parameters can lead to overall poor performance of the algorithm, chances of being stuck in the local optimal solution and increased computational time and costs.

For example, GA requires tuning of mutation probability, crossover probability and operation selection. PSO needs inertia weight, cognitive and social parameters. DE needs the tuning of crossover parameters and scaling factor. HS requires tuning of memory size and pitch setting. ACB needs tuning of parameters such as scout, onlooker and employed bees. Bat algorithm (BA) necessitates parameters such as wavelength and coefficient of emission to be tuned. Other biological algorithms used in reservoir operations such as HBMO, WOA, COA, improved bat algorithm (IBA), shark algorithm, krill herd algorithm (KHA), imperialest competitive algorithm (ICA), and ant colony optimization (ACO) also need their own algorithm-specific parameters to be tuned.

The Jaya Algorithm (JA) was developed quite recently (Venkata Rao 2016) in order to overcome this limitation of algorithm-specific parameters, and does not require algorithm-specific parameters to be tuned up and thus reduces the user's burden. It works by finding the best solution and avoiding the worst. JA has been applied to different optimization fields such as: traffic light scheduling problems (Gao et al. 2017), facial emotion recognition (Wang et al. 2018), and photovoltaic system maximum power point tracking (Huang et al. 2018). Early uses of JA also include water resources problems. Kumar & Yadav (2018) used JA to optimize net benefits for a multi-reservoir operating system and found JA to be outperforming. In order to maximize the net benefits, (Varade & Patel 2018) used JA to search for an optimal crop pattern. The findings show that JA was better than PSO. The improved JA, i.e. elitist JA, was used by (Kumar & Yadav 2019) to find the optimal crops and was found to be superior. Kumar & Yadav (2020b) compared JA with TLBO, PSO and DE, and found that JA outperformed to optimize water releases in the Ukai reservoir, in the state of Gujarat, India.

In view of the success of JA, this paper seeks to improve the diversity of the population in the search space by dividing the population into sub-populations. The idea is to split the search space into different subgroups. The effectiveness of the algorithm is dependent on the selection of sub-population numbers. This problem was overcome by a self-adaptive method. The self-adaptive method helps to effectively monitor the problem and modify the number of individuals due to changes in the problem's landscape. That is, when the number of sub-populations has increased or decreased (Venkata Rao & Saroj 2017; Kumar & Yadav 2020a). Using this method, a self-adapting multi-population Jaya algorithm (SAMP-JA) was introduced to extract operating policies for reservoir systems. SAMP-JA was applied to an existing reservoir network, namely the Ukai reservoir system, Gujarat, India, to demonstrate its practical utility. The objectives of the study were to minimize irrigation deficits and maximize the generation of hydropower. Both aims are in conflict with one another. More water is required to satisfy irrigation requirements to reduce the irrigation deficit. At the same time, a high storage in the reservoir is required to produce more energy to increase hydropower output. The motives of the present study were to run three different reservoir operation models i.e. (a) Model-1: minimization of irrigation deficits, (b) Model-2: maximization of hydropower generation, (c) Model-3: multi-objective model by combinations of Model-1 and Model-2. The results were compared with results obtained by ordinary Jaya algorithm (JA), particle swarm optimization (PSO), and invasive weed optimization (IWO) algorithm. The results of the study give three different alternatives based on a single or multi objective purpose of the dam operation which can be used to make decisions and provide an opportunity to operate the dam to satisfy the desired alternative objectives.

JA works on the principle of getting closer to a better solution by avoiding failure. The steps for the SAMP-JA operation are as follows.

Step 1: Decide the population size and the number of iterations.

Step 2: Generate the initial solutions between the variables' upper and lower limits.

Step 3: Divide the population into m groups (i.e., the number of sub-populations initially considered as ⁠), where m is updated (bigger or smaller depending on the objective function value) at each iteration.

Step 4: Identify the best and worst solution in the population list. If is the variable (i.e. ⁠, where D is the number of design variables), for the candidate (i.e., population size, ⁠), where n is the number of candidate solutions during the iteration.

Step 6: The objective functions obtained by i.e., O(best-before) and i.e. O(best-after) are compared. The modified solution will only be accepted if it is better than the old solution, then m will be increased by 1, i.e., ⁠, which will help to increase the exploration of the search space. Otherwise, m is decreased by 1, i.e., ⁠, which helps to exploit the search space; here, ⁠.

Step 7: This completes an iteration. The cycle stops when the maximum number of generations is reached; otherwise, it repeats itself. To maintain diversity, duplicate solutions are replaced by the newly obtained solution. An SAMP-JA flowchart is presented in Figure 1.

Further details about JA can be obtained from Venkata Rao (2016). Details about PSO can be obtained from Eberhart & Kennedy (1995), and details about IWO can be obtained from Mehrabian & Lucas (2006).

Multi-objective optimization contributes to achieving the best compromise solution between different goals, i.e., minimizing or maximizing while meeting all constraints. In this research, an a priori method was employed to convert multi-objective into single objective functions. This was accomplished by assigning an appropriate weight to each objective based on preferential multi-objective optimization (Rao et al. 2019). However, if the objective is simply added by an appropriate weight, a higher functional value will dominate the objective. To avoid this, objective functions were normalized.

The Ukai dam, built across the Tapi River in 1972, is situated at 21⁰ 14′ 53.52″N and 73⁰ 35′ 21.84″E. The Tapi River is the west-flowing interstate river in India, which flows through major Maharashtra regions, part of Madhya Pradesh and Gujarat. The total length of the Tapi River is 724 and it has a catchment area of 65,145 ⁠. The Ukai dam has a maximum storage capacity of 8,480.18 and a gross storage capacity of 7,414.29 at full reservoir level. It is a multi-functional reservoir serving as the main source of irrigation, domestic demand, power generation and partial flood management. Figure 2 displays an index map of the study area. Figures 2(a) and 2(b) show, respectively, the map of India with Tapi basin and the catchment area. There are three canals which distribute irrigation water. The first canal, i.e. Ukai left the main canal at the bank (ULBMC), diverts straight from the dam. The other two canals are diverted from the Kakrapar weir, which is 29 kilometers downstream of the Ukai dam. i.e. Kakrapar left bank main canal (KLBMC) and Kakrapar right bank main canal (KRBMC). Later, the Ukai right bank main canal (URBMC) divides from the KRBMC. Figure 2(c) shows the Cultivable Command Area (CCA) of the canals. Releases from the dams are used in generating power. The Ukai reservoir has two power plants, one on the main dam with an installed capacity of 300 MW since 1974, and another, the ULBMC mini station which has been operating since 1988 with an installed capacity of 5 MW. In 1995, the Singanpor Weir cum causeway was built on the Tapi River near Rander Surat. A limited downstream release from the Ukai dam is performed to meet the domestic demands, industrial demands and water quality requirements of the region. The surplus water from the weir goes into the Arabian Sea.

Table 1 presents Salient features for the Ukai basin. The necessary data was compiled from the Ukai left bank division and the Surat irrigation circle. The data used for the analysis were monthly inflow from the reservoir (1972–2016), monthly inflow from the Ukai reservoir (1972–2016), monthly storage capacity from the Ukai reservoir (1972–2016), monthly discharge through the powerhouse (1976–2016), irrigation demand for all CCAs, canal releases, generated power (1976–2016), monthly evaporation rates (1972–2016), reservoir area (1972–2016), domestic demand, industrial demand and water quality demand (1990–2016).

The research aimed to reduce irrigation deficits and maximize the production of hydropower. These are contradictory objectives and are presented as follows.

Single-objective and multi- objective models were developed with the intention of minimizing the water deficit and maximizing hydropower generation. As stated earlier, a total of three models were developed. The models are (a) Model-1: minimization of irrigation deficits, (b) Model-2: maximization of hydropower generation, (c) Model-3: multi-objective model by combinations of Model-1 and Model-2. All algorithms were coded by the software MATLAB R2014b, and plots and statistical parameters were developed with the Origin-Pro 8.5 software, using a 64-bit system, with a system configuration of Intel^® core^{TM i}7-7700, @3.60 GHz, with an installed ram of 8.00 GB.

The penalty was used in the context of the main objective. The penalty function depends on the violation of the different constraints and the penalty parameter is the penalty figure (value) applied. The modified objective was written according to Equations (27)–(29). A positive sign represents the addition of this violation from the objective function minimization problem and a negative sign represents the subtraction of this violation from the objective function maximization problem.

Irrigation deficiencies have been calculated as the sum of irrigation release square deficiencies⁠. Table 2 displays 10 different run objective function values for JA, SAMP-JA, PSO, and IWO. Comparing the best optimal solution, SAMP-JA and JA achieved a better minimum solution of 305,092.99 compared to PSO and IWO with an optimal minimum solution of 305,093.02 and 14,702,579.28 ⁠, respectively. When comparing the mean optimal solution, SAMP-JA performed better with a mean optimal solution of 305,093.00 compared to JA, PSO and IWO. When comparing the standard deviation (SD) it was found that the lowest SD was obtained by SAMP-JA, then by JA, PSO and IWO. Compared to SAMP-JA, JA and PSO, the IWO progressed very slowly. The IWO's near optimum solution was accomplished with 1,00,000 iterations, i.e. 312,045.28 ⁠.

Figure 4 shows the convergence rates of the different algorithms for Model-1 up to 10,000 iterations. It was noted that the SAMP-JA, JA and PSO convergence rates were similar and better than IWO. It has been observed that SAMP-JA converges faster than JA and PSO to achieve a global solution. Figure 5 demonstrates the convergence rate of IWO for 100,000 iterations. It was noticed that, at around 100,000 iterations, IWO was able to obtain near optimal solution, i.e., 312,045.28 ⁠.

The following statistical efficiency parameters were used to determine efficiency.

The results of water demand and water release for irrigation are shown in Table 3 based on different error indexes for the best solution for various algorithms. The RMSE calculated for SAMP-JA, JA, and PSO is equal to 154.05 and IWO is 208.84 ⁠. SAMP-JA, JA and PSO had a comparatively small MAE compared to IWO.

The following assessment indicators are used.

Table 4 shows the results of different algorithms of water releases and water demand for irrigation based on performance indicators for the best solution. The greater reliability index percentages for SAMP-JA, JA and PSO indicate better irrigation water supply and optimal reservoir operation compared to IWO. Also, the lower SAMP-JA, JA and PSO vulnerability index values also indicate that the severity of the failure is lower than IWO. Thus, the operation of the reservoir using SAMP-JA, JA and PSO can better prevent water shortages than IWO.

Figure 6 displays the resulting storage strategy for the reservoir obtained from different algorithms for Model-1 along with actual average storage for the Ukai reservoir. The storage curve of various algorithms is found to follow a similar trend except for IWO. Filling of the reservoir happens between July to October during the monsoon season. The maximum capacity is reached in the month of October. Around November to June the water level of the dam goes down to supply for irrigation and other uses during the non-monsoon season. The levels of SAMP-JA and JA storage were nearly identical but for all the months MOJA was slightly lower in storage. For the months of October to February, the actual average storage was higher, and other months were similar or lower. The PSO storage levels were the lowest among all algorithms. Water level of the IWO was high for the month of April, after the low month of March; this is not possible in real cases during the non-monsoon season. The lower side of the storage by all the algorithms shows that the reservoir attempts to operate for irrigation as the only priority at 75% dependable inflow.

The best optimal reservoir storage strategy was then compared with storage data for 2008 and 2009 when the actual inflow and the 75% dependable inflow were close. Figure 7 shows the SAMP-JA storage policy with actual storage of 2008 and 2009. The actual data of 2008 were almost the same for the months of October to January, high for February to April, and low for June to September compared with the developed model. The actual 2009 data were similar in terms of trends but the model developed was on the higher side.

Figure 8 shows the comparative plot of actual average demand and different algorithms for the release of water from the Ukai dam via the Kakrapar weir to the KLBMC. For all the months, the optimum releases of SAMP-JA, JA and PSO were almost the same, and with the actual average demand for the month of June to January it was about the same or smaller, with average releases more for the other months. All the algorithms resulted in releases per month according to the irrigation requirement. When comparing the IWO, the release was found to be very high for a few months and very low for a few months. That indicates that the distribution of the release water is not even. Figure 9 shows the comparative plot of actual average demand and different algorithms for the release of water from the Ukai dam via the KRBMC. Again, for this canal the optimum releases of SAMP-JA, JA and PSO were approximately the same for all months. But the releases were lower than the actual average demand. Again, for this canal, for the IWO the release was found to be very high for a few months and very low for a few months, indicating that the distribution of the release water was not even. The SAMP-JA, JA, and PSO were better at minimizing irrigation and demand deficits than the IWO algorithm. Figure 10 shows the comparative plot of actual average demand and various algorithms for the release of water from the Ukai dam to the ULBMC considering the 75% dependable inflow. Again, for this canal the optimum releases of SAMP-JA, JA and PSO were approximately the same for all the months. But the releases were lower than the actual average demand. For IWO, the release was found to be very high for a few months and very low for a few months. Thus, the operation of the reservoir using SAMP-JA, JA and PSO can better prevent water shortages than the IWO.

In order to maximize the production of hydropower, a high level of storage in the reservoir is needed to generate more energy. Table 5 shows the 10 different run objective function values of JA, SAMP-JA, PSO, and IWO. Comparing the best optimal solution, SAMP-JA, JA and PSO achieved a better hydropower generation of 1723.50 compared to IWO with an optimum hydropower generation of 1566.52 ⁠. When comparing the mean optimal solution, SAMP-JA and PSO performed better with the average generation of hydropower compared to JA and IWO. While comparing standard deviation (SD) it was observed that the lowest SD was obtained from SAMP-JA and PSO. The IWO progressed very slowly compared to SAMP-JA, JA and PSO. When the IWO algorithm was run for 100,000 iterations, a near-optimal solution was achieved as 1645.15 ⁠.

The convergence rates of Model-2 for various algorithms up to 10,000 iterations are shown in Figure 11. It was noted that to obtain the optimum solution, the SAMP-JA convergence rate was faster than POS and JA. The rate of IWO convergence was very slow. The IWO convergence rate for 100,000 iterations is shown in Figure 12. It was found that at around 100,000 iterations IWO was able to obtain a near optimal solution, i.e., 1645.15 ⁠.

Figure 13 shows the resulting storage strategy for the reservoir obtained from different algorithms for Model-2 along with actual average storage for the Ukai reservoir. Here the operation's primary focus is hydropower. It was found that a similar trend follows the storage curve of different algorithms except the IWO. Since only hydropower was a priority, the storage of the reservoir was kept to a maximum so that maximum hydropower could be achieved. The filling of the reservoir occurs during the monsoon season from July to October. The maximum capacity is reached in the month of October. The model developed by SAMP-JA, JA and PSO and the actual average storage have followed similar trends, but the algorithms were on the higher side. So, hydropower can be maximized.

In this research, an a priori method was used to convert the multi-objective into a single objective function. Minimizing irrigation deficits was considered as and maximizing the generation of hydropower as ⁠, the weights were taken as ⁠, i.e., equal weighting has been given. Model-3 analysis was performed using SAMP-JA, JA and PSO. Since IWO output in Models 1 and 2 was slow to achieve the optimal solution, and more iterations were required, it wasn't selected for Model-3. Table 6 shows optimal solutions obtained from 10 independent runs. It was found that the maximum power generation was achieved by SAMP-MOJA and that the minimum irrigation deficiency was achieved by MOPSO. Figure 14 show the convergence rates for Model-3 up to 10,000 iterations for the various algorithms. It was found that SAMP-JA and JA were similar and better than PSO convergences. Figure 15 shows the hydropower plot generated by algorithms and the actual data from the Ukai reservoir. The blue columns indicate the inflow, and the hydropower generated by the orange line graph. It can be observed that all algorithms can generate greater hydropower with lower inflow. In 2004, similar generation of hydropower was observed with higher inflow.

Figure 16 shows the resulting reservoir storage policy obtained from different multi objective algorithms for Model-3 along with actual average storage for the Ukai reservoir. It was noted that the storage curve of different algorithms, along with actual data, follows a similar trend. The filling of the reservoir occurs during the monsoon season from July to October. The maximum capacity is reached in the month of October. Around November to June, the water level of the dam declined during the non-monsoon season to irrigation supplies and other uses. The actual average storage for the months October to December was comparable with SAMP-MOJA, and the rest of the months were on the higher side. MOJA and MOPSO had less capacity than the storage level SAMP-MOJA had. The best optimal reservoir storage policy was later compared with the storage datas of 2008 and 2009, when the actual inflow and the 75 percent dependable inflow were similar. Figure 17 shows the SAMP-MOJA storage policy with actual storage for 2008 and 2009. The actual data were close in pattern for 2008 and 2009, but the model developed was on the higher side. The greater storage would help to maximize the production of hydropower.

Figure 18 shows the comparative plot of actual average demand and different algorithms for the release of water from the Ukai dam via the Kakrapar weir to the KLBMC. MOPSO's optimum releases were divided more evenly compared to those of SAMP-MOJA and MOJA, except for the month of January. It was also observed that in the monsoon months, the algorithms attempted to release less water and have more release in the non-monsoon months, taking into account the 75 percent dependable inflow. Figure 19 shows the comparative plot of actual average demand and different algorithms for the release of water from the Ukai dam via the Kakrapar weir to the KRBMC. In the monsoon months, the SAMP-MOJA attempted to release less water, and release more in the non-monsoon months. Compared with SAMP-MOJA and MOJA, MOPSO tried to maintain uniform water release. Figure 20 shows the comparative plot of actual average demand and various algorithms for the release of water from the Ukai dam to the ULBMC considering the 75% dependable inflow. MOPSO's optimum releases were better and more uniform than those of MOJA and SAMP-MOJA. For Model-3, MOPOS was better than the SAMP-MOJA and MOJA at minimizing the irrigation and demand deficits. But the SAMP-MOJA storage level was higher than the MOPOS, so more releases could be possible.

In this study, the operation of the reservoir was solved by using 75% dependable inflow. Three different models of reservoir operation were considered, i.e. (a) Model-1: minimization of irrigation deficits, (b) Model-2: maximization of hydropower generation, and (c) Model-3: a multi-objective model by combinations of Model-1 and Model-2. The self-adaptive multi-population Jaya algorithm (SAMP-JA) was used to solve the models. The results were compared with the Jaya algorithm (JA), particle swarm optimization (PSO), and Invasive weed optimization (IWO) algorithm. In Model-1, the minimum irrigation deficit was obtained by SAMP-JA and JA as 305092.99 ⁠. SAMP-JA was better than JA, PSO and IWO in terms of convergence. In Model-2, the maximum hydropower generation was achieved by SAMP-JA, JA and PSO as 1723.50 ⁠. While comparing the average hydropower generation SAMP-JA and PSO performed better than JA and IWO. In terms of convergence, SAMP-JA was better than PSO. In Model-3, SAMP-MOJA was better than MOPSO and MOJA in terms of maximum hydropower generation, and MOPSO was better than SAMP-MOJA and MOJA in terms of minimum irrigation deficiency. While comparing convergence, SAMP-MOJA was found to be better than MOPSO and MOJA. SAMP-JA was found to outperform JA, POS and IWO.

The results of the study provide three different alternative priorities based on a single or multi-objective reservoir operation. It was observed that, if irrigation is the only priority for the reservoir, it needs higher release throughout to fulfil the irrigation requirements. While this is reversed when the focus is on hydropower, it tends to keep the storage head at a high level throughout the year to generate more electricity. When operating the reservoir, these two goals conflict with each other. The compromise multi-objective reservoir operation was achieved when there was an equal priority for irrigation and hydropower. The study provides the potential for three alternative priorities for both objectives and their respective operational policies to run the dam in order to meet the desired priority. The developed irrigation model will help to avoid water shortages in the supply of irrigation water, taking into account the 75% dependable inflow. It was also observed that algorithms can generate greater hydropower with lower inflow than the actual inflow.

The authors are grateful to the editor and the reviewers for their useful comments and suggestions.

Data cannot be made publicly available; readers should contact the corresponding author for details.