Assessment of Application of Harmony Search Optimization Algorithm in Optimal Multi- Reservoir and Real Single- Reservoir Systems (Case Study: Dez Dam)

Existence periods of drought in the past decade, increasing growth of population, limitation surface water resources, cause the proper management of the reservoirs of dams. Operation of reservoirs is influenced by a lot of goals and generally many of these goals are incompatible with each other. The inflows to the reservoir and the storage volumes are uncertain which increases the operation of the complexity of the reservoir. The main challenge is to find the best release of the reservoir and hydrosystems optimization. Various optimization methods have been introduced for the operation of the reservoir. But some of these methods have disadvantages that use of them are not possible for all issues. Bozorg Haddad (2005) used Honey Bees Mating optimization for solving design problems and o The ant colony algorithm was also used to exploit a four-reservoir system in a discrete space that was able to optimize the problem with greater accuracy and less computing time than the genetic algorithm (Jalali et al 2007). Mousavi et al (2017) used the Harmony Search Algorithm to the optimization of water powerhouse storage projects and reported satisfactory results. Harmony search algorithm was presented by Geem et al for the first time in 2000. In this research Harmony Search Algorithm (HSA) is evaluated to determine the optimal operation of multi-reservoir systems. Then in order to evaluate the ability of the algorithm to solve real problems, the optimal operation of Dez Dam reservoir in Khuzestan province has been considered for a period of 10 years (1990-1992) with 120 months. In the single- reservoir issue of Dez Dam, the goal is to provide of agricultural demand of downstream or to determine the optimal monthly release for 10 years operation. The optimum value was obtained by using a linear programming model (Lingo). Lingo model has the ability to solve nonlinear models and provides the global optimum in some cases such as the intended problem where the objective function is convex. Therefore, the solutions obtained from the HSA model were compared with the solutions obtained from Lingo software program. A new heuristic algorithm derived from an artificial phenomenon found in musical performance namely the process of searching for better harmony can be introduced. Music harmony is a combination of sounds considered pleasing from an aesthetic point of view. Harmony in nature is a special relationship between several sound waves that have different frequencies. Musical performances seek the best state (fantastic harmony) determined by aesthetic estimation, as the optimization algorithms seek the best state (global optimum-minimum cost or maximum benefit or efficiency) determined by objective function evaluation. Aesthetic estimation find by the set of the sounds played by joined instruments, just as objective function evaluation find by the set of the values produced by component variables; the sounds for better aesthetic estimation can be improved through practice after practice, just as the values for better objective function evaluation can be improved iteration by iteration. The new algorithm is named Harmony Search (HS) and the steps in the procedure of HS are as follows: Step 1) Initialize a Harmony Memory (HM). Step 2) Improvise a new harmony from HM. Step 3) If the new harmony is better than least harmony in HM, include the new harmony in HM, and exclude the minimum harmony from HM. Step 4) If stopping criteria are not satisfied, go to Step 2. Harmony Memory Considering Rate (HMCR), which ranges from 0 to 1. If a uniformly generated value between 0 -1 occurs above the current value of the HMCR, then HS finds notes randomly within the possible playable range without considering HM. An HMCR of 0.85 means that at the next step, the algorithm chooses a variable value from HM with an 85% probability. For improving solutions and escaping local optima, yet another option may be introduced. This option mimics the pitch adjustment of each instrument for tuning the ensemble. For computation, the pitch adjustment mechanism is devised as shifting to neighboring values within a range of possible values. A Pitch Adjusting Rate (PAR) of 0.10 means that the algorithm chooses a neighboring value with 10% probability (an upper value with 5% or lower value with 5%. In the present study, first HSA was used to the optimization of a four-reservoir system. The objective function was calculated to equal to 308.2915 by using Lingo software, and this amount was calculated to equal to 308.2900 by using HSA that had a different of 0.0005 percent with the global optimum. After the success of HSA in solving the four-reservoir system, a ten-reservoir system was considered. The Objective function was calculated to equal to 1194.4 by using Lingo software, and this value was calculated to equal to 1193.1 by using HSA that had a different of 0.1 percent with the global optimum. In the single- reservoir issue of Dez Dam, the value of global optimum of the objective function was calculated by using software Lingo 1.9188 and by using HSA 1.944 that had a different of 1.31% with the global optimum. So it can be concluded that this algorithm has the ability to solve optimization problems of the real system