The dam is the wall that holds the water in, and the operation of multiple dams is complicated decisionmaking process as an optimization problem (Oliveira & Loucks, 1997). Traditionally researchers have used mathematical optimization techniques with linear programming (LP) or dynamic programming (DP) formulation to find the schedule. However, most of the mathematical models are valid only for simplified dam systems. Accordingly, during the past decade, some meta-heuristic techniques, such as genetic algorithm (GA) and simulated annealing (SA), have gathered great attention among dam researchers (Chen, 2003) (Esat & Hall, 1994) (Wardlaw & Sharif, 1999) (Kim, Heo & Jeong, 2006) (Teegavarapu & Simonovic, 2002). Lately, another metaheuristic algorithm, harmony search (HS), has been developed (Geem, Kim & Loganathan, 2001) (Geem, 2006a) and applied to various artificial intelligent problems, such as music composition (Geem & Choi, 2007) and Sudoku puzzle (Geem, 2007). The HS algorithm has been also applied to various engineering problems such as structural design (Lee & Geem, 2004), water network design (Geem, 2006b), soil stability analysis (Li, Chi & Chu, 2006), satellite heat pipe design (Geem & Hwangbo, 2006), offshore structure design (Ryu, Duggal, Heyl & Geem, 2007), grillage system design (Erdal & Saka, 2006), and hydrologic parameter estimation (Kim, Geem & Kim, 2001). The HS algorithm could be a competent alternative to existing metaheuristics such as GA because the former overcame the drawback (such as building block theory) of the latter (Geem, 2006a). To test the ability of the HS algorithm in multiple dam operation problem, this article introduces a HS model, and applies it to a benchmark system, then compares the results with those of the GA model previously developed.
Before this study, various researchers have tackled the dam scheduling problem using phenomenon-inspired techniques.
Esat and Hall (1994) introduced a GA model to the dam operation. They compared GA with the discrete differential dynamic programming (DDDP) technique. GA could overcome the drawback of DDDP which requires exponentially increased computing burden. Oliveira and Loucks (1997) proposed practical dam operating policies using enhanced GA (real-code chromosome, elitism, and arithmetic crossover). Wardlaw and Sharif (1999) tried another enhanced GA schemes and concluded that the best GA model for dam operation can be composed of real-value coding, tournament selection, uniform crossover, and modified uniform mutation. Chen (2003) developed a real-coded GA model for the long-term dam operation, and Kim et al. (2006) applied an enhanced multi-objective GA, named NSGA-II, to the real-world multiple dam system. Teegavarapu and Simonovic (2002) used another metaheuristic algorithm, simulated annealing (SA), to solve the dam operation problem.
Although several metaheuristic algorithms have been already applied to the dam scheduling problem, the recently-developed HS algorithm was not applied to the problem before. Thus, this article deals with the HS algorithm’s pioneering application to the problem.Top
Harmony Search Model And Application
This article presents two major parts. The first part explains the structure of the HS model; and the second part applies the HS model to a bench-mark problem.
Key Terms in this Chapter
Evolutionary Computation: Solution approach guided by biological evolution, which begins with potential solution models, then iteratively applies algorithms to find the fittest models from the set to serve as inputs to the next iteration, ultimately leading to a model that best represents the data
Soft Computing: Collection of computational techniques in computer science, especially in artificial intelligence, such as fuzzy logic, neural networks, chaos theory, and evolutionary algorithms
Metaheuristics: Technique to find solutions by combining black-box procedures (heuristics). Here, ‘meta’ means ‘beyond’, and ‘heuristic’ means ‘to find’
Multiple Dam Scheduling: Process of developing individual dam schedule in multiple dam system. The schedule contains water release amount at each time period while satisfying release limit, storage limit, and continuity conditions
Optimization: Process of seeking to optimize (minimize or maximize) an objective function while satisfying all problem constraints by choosing the values of continuous or discrete variables.
Genetic Algorithm: Technique to search exact or approximate solutions of optimization or search problem by using evolution-inspired phenomena such as selection, crossover, and mutation. Genetic algorithm is classified as global search algorithm
Harmony Search: Technique to search exact or approximate solutions of optimization or search problem by using music-inspired phenomenon (improvisation). Harmony search has three major operations such as random selection, memory consideration, and pitch adjustment. Harmony search is classified as global search algorithm