# Dissertation Algorithm Development Tips For Developing Shuffled Complex Evolution Combined With Stochastic Ranking For Reservoir Scheduling

**In Brief**

• You will find the best dissertation research areas / topics for future researchers enrolled in Engineering and technology.

• In order to identify the future research topics, we have reviewed the Engineering literature (recent peer-reviewed studies) on Shuffled Complex Evolution and Stochastic Ranking for Reservoir Scheduling

• Nature-Inspired Optimization Algorithm is the recent trend in Cloud technology.

• Shuffled Complex Evolution Algorithm is one of Nature-Inspired Optimization Algorithm.

• Shuffled Complex Evolution Algorithm is used for Reservoir Scheduling and Stochastic Ranking.

Water is one of the most valuable resources and humans have built dams to optimize the use of this precious resource. Dams are a life-sustaining resource for people throughout the world (Hui et al., 2018). These dams have internally water storage spaces called reservoirs, and the operation priorities of these reservoirs are based on a sequence of rules to recognize the amount of water stored and released according to system constraints. The process of prioritizing the reservoir operation is known as “reservoir scheduling” and we use various machine learning methods or algorithms for reservoir scheduling (Liu et al., 2017). One such method is the “shuffled complex evolution (SCE)”, where its general purpose is global optimization. The SCE algorithm is capable of finding optimum globally and it does not rely on the availability of an explicit expression for the objective function or the derivatives. However, it encounters difficulty in solving unnatural optimization problems due to the lack of inherent constraint-handling techniques. Another method “stochastic ranking (SR)” is capable of balancing objectives and penalty functions and is highly competitive compared to other methods. The application of a “Shuffled Complex Evolution-Stochastic Ranking (SCE-SR)” therefore provides an effective solution to the above mentioned problems. Whereas, SCE combines the strengths of the simplex method and the complex algorithm of competitive evolution and SR is free from complicated parameter tuning, The SCE-SR takes advantage of both. SCE-SR makes SCE suitable for constrained reservoir scheduling problems and may achieve global convergence properties. The SCE-SR method is an efficient and effective method to optimize hydropower generation and quickly identify feasible areas, with adequate global convergence properties and robustness (Ping et al., 2018).

**1. SCE Algorithm**

SCE algorithm uses the concept of complex shuffling to solve the non- linear optimization problem. The method involves the following terminologies: points (candidate solutions), population (the community containing all points), complex (the community containing several points partitioned from the sample), and complex shuffling (points in complexes reassigned and mixed to generate a new community). The main idea of this algorithm is that the points evolve independently in each complex and shuffle in the sample population to guide the searching process towards the optimal solution of the problem.

One of the main components of SCE is the CCE algorithm, which can be described briefly as follows:

(1) Construction of a sub-complex (containing q points) according to the trapezoidal probability distribution.

(2) Ranking: identification of the worst point u of the sub-complex and computation of the centroid g of the q−1 points without including the worst one.

(3) Reflection: reflection of point u through the centroid to generate a new point r and calculation of its objective function value fr. If the newly generated point r is within the feasible space and fr>fu, where fu is the objective function value of point u, u is replaced with r, and the process moves to step (6). Otherwise, it goes to step (4).

(4) Contraction: determination of a point c halfway between the centroid and the worst point, and then calculation of fc. If point c is within the feasible space and fc>fu, u is replaced with the contraction point c and the process goes to step (6). Otherwise, it goes to step (5).

(5) Mutation: random generation of a point z within the feasible space and replacement of the worst point with z.

(6) Steps (2) through (5) are repeated α time, where α≥1 is the number of consecutive offspring generated by each sub-complex.

(7) Steps (1) through (6) are repeated β times, where β≥1 is the number of evolution steps taken by each complex before complexes are shuffled.

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**Figure 1 Flow Chart of SCE-SR Algorithm**

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2. SR – Stochastic Ranking

The SR is capable of balancing objective and penalty functions and improving the search performance. The main idea is to compare two adjacent individuals according to the objective function values or the degree of constraint violations by introducing a predetermined parameter Pf. An increase in the number of ranking sweeps (N) is effectively equivalent to changing parameter . Thus, the number of ranking sweeps is fixed to N = s (number of points in sample population generated by SCE), and is adjusted within [0, 1] to achieve the best performance. The comparison mechanism of two adjacent individuals can be briefly described as follows: if both individuals are feasible, or a randomly generated number w∈[0,1] is less than Pf, they are compared according to the objective function values; otherwise, they are compared based on the degree of constraint violations. Ranking of the whole sample population is then achieved through a bubble-like procedure.

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**3. SCE-SR algorithm **

Shuffled Complex Evolution (SCE) is a competitive global optimization algorithm; it faces difficulties in solving constrained reservoir scheduling problems due to the lack of constraint handling technique (CHT). The ranking process of SCE based only on the objective function values, due to which it provides a non-feasible optimal solution with no practical significance.

On the other hand, SR is an independent competitive CHT that is easy to implement and incorporate with other algorithms. Therefore, it is necessary to replace the ranking mechanism of SCE with SR to balance the objective and constraints and enable it to be applicable for the constrained reservoir scheduling problems.

**There are two main characteristics of SCE-SR:**

The combination of the deterministic approach and competitive evolution. This is conducive to directing the search in an improving direction and improving global convergence efficiency by making use of information carried by both feasible and non-feasible individuals.

The combination of the probabilistic approach and complex shuffling. This guarantees the survivability of individuals and the flexibility and robustness of the algorithm.

These characteristics ensure the global convergence properties of SCE-SR over a variety of problems. There are four vital parameters of SCE are assigned default values:

The number of points in a complex, m=2n+1, where n is the dimension of the decision vector,

The number of points in a sub-complex, q=n+1,

The number of consecutive offspring generated by each sub-complex, α=1,

The number of iterations taken by each complex, β=m.

For SR, the required range of the parameter is 0.4<Pf<0.5, and for this method it is set to 0.45. The SCE-SR method is terminated whenever one of the following convergence criteria is satisfied:

The objective function value is not significantly improved after j times of iterations. Its expression is as follows:

|f_n-f_(n-j+1) |/f ̅≤TOL

where f_n and f_(n-j+1)are the objective function values of an optimized individual after n and n−j+1 times of iterations, respectively, f ̅ is the average absolute value of the objective function of the optimized individual after each iteration, and TOL is the predetermined acceptable degree.

The interval of variables is small enough. Its expression is as follows:

exp{∑_(i=1)^m▒〖lg[(x_(i max)-x_(i min))/c_i ]/m〗}≤TOL_⋋

Where x_(i max)and x_(i min) are the maximum and minimum values of the ith variable in the population after each iteration, respectively; c_i is the size of the feasible interval of the ith variable, and TOL_⋋ is the allowable concentrated degree of the variables.

The cumulative number of objective function calls (NOFC) reaches the predetermined value.

The SCE-SR method can be applied to both single reservoir and multi reservoir system. The scheduling period for each test is set for one year and the time step is for one month. The forebay elevation of different reservoirs at the beginning of each month is set as the decision vector. The convergence criterion is based on the pre-determined NOFC (number of objective function calls) and the performance of SCE-SR is evaluated by comparing its results with the results of the traditional methods used for reservoir scheduling (Mao et al., 2016).

Several statistical values are used to compare the performance of different methods like MAX, MIN, AVG, STD, FR, and NOFC. These parameters are compared for a fixed independent run, for example let’s compare with 30 independent runs for each test case. STD represents the (standard deviation) of the optimized hydropower of 30 independent runs. FR exhibits the percentage feasible runs, which have to generated at-least one feasible individual among 30 runs, and its range decided is [0,1]. NOFC denotes the no. of objectives function calls when finding first feasible individual .when these parameters value is compared with the values of traditional method it is found that the SCE-SR method is much more efficient in reservoir stochastic scheduling.

**Conclusion**

Shuffled Complex Evolution – Stochastic Ranking Algorithm (SCE-SR) optimization method can solve the complex constrained reservoir scheduling problems. The method is also very easy to implement and requires little parameter tuning. It is simple to use this method for the combination of deterministic and probabilistic approaches. When the result of SCE-SR is compared with the traditional methods against hydropower scheduling problem in both single and multi-reservoir system with different inflow scenarios and population sizes, it is found that the performance of SCE-SR is excellent with better stability and higher computational efficiency than other methods and SCE-SR can converge the global optima in a consistent, efficient and fast way with both objectives and constraints considered. So, it can be used for scheduling many numbers of systems at a time. This SCE-SR method will pave the way for the application of unconstrained algorithm in this field as this is an effective, efficient and reliable optimization method for solving reservoir scheduling problems.

**Future Scope**

1. It is used in photovoltaic (PV) Model for parameter extraction problem (Chen et al., 2019).

2. The research on carbon fiber-epoxide composite pyrolysis from hydrogen tank(Liu et al., 2019).

3. It is used in Solar cell models parameter extraction (Gao et al., 2018).

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#### References

1.Chen, Y., Chen, Z., Wu, L., Long, C., Lin, P. & Cheng, S. (2019). Parameter extraction of PV models using an enhanced shuffled complex evolution algorithm improved by opposition-based learning. Energy Procedia. [Online]. 158. p.pp. 991–997. Available from: https://linkinghub.elsevier.com/retrieve/pii/S187661021930253X.

2.Gao, X., Cui, Y., Hu, J., Xu, G., Wang, Z., Qu, J. & Wang, H. (2018). Parameter extraction of solar cell models using improved shuffled complex evolution algorithm. Energy Conversion and Management. [Online]. 157. p.pp. 460–479. Available from: https://linkinghub.elsevier.com/retrieve/pii/S0196890417311858.

3.Hui, L., Li, J., Jun, Z., Xinyu, G., Qing, W. & Jun, A. (2018). Water Quality Traceability Based on Improved Genetic Algorithm. Journal of Hohai University. [Online]. 46 (5). p.pp. 402–407. Available from: http://jour.hhu.edu.cn/hhdxxbzr/ch/reader/view_abstract.aspx?doi=10.3876/j.issn.1000-1980.2018.05.005.

4.Liu, H., Wang, C., Chen, B. & Zhang, Z. (2019). A further study of pyrolysis of carbon fibre-epoxy composite from hydrogen tank: Search optimization for kinetic parameters via a Shuffled Complex Evolution. Journal of Hazardous Materials. [Online]. 374. p.pp. 20–25. Available from: https://linkinghub.elsevier.com/retrieve/pii/S0304389419303826.

5.Liu, Q., Fang, G., Sun, H. & Wu, X. (2017). Joint optimization scheduling for water conservancy projects in complex river networks. Water Science and Engineering. [Online]. 10 (1). p.pp. 43–52. Available from: https://linkinghub.elsevier.com/retrieve/pii/S1674237017300303.

6.Mao, J., Zhang, P., Dai, L., Dai, H. & Hu, T. (2016). Optimal operation of a multi-reservoir system for environmental water demand of a river-connected lake. Hydrology Research. [Online]. 47 (S1). p.pp. 206–224. Available from: https://iwaponline.com/hr/article/47/S1/206/1812/Optimal-operation-of-a-multireservoir-system-for.

7.Ping, F., Jun, L. & Bo, L. (2018). Impact of key parameter changes on the average annual power generation of the power station.