Harmony search (HS) is a music-inspired algorithm (Geem et al., 2001) and has been applied to various optimization problems including music composition, Sudoku puzzle, magic square, timetabling, tour planning, logistics, web page clustering, text summarization, Internet routing, visual tracking, robotics, energy system dispatch, power system design, cell phone networking, structural design, water network design, dam scheduling, flood model calibration, groundwater management, soil stability analysis, ecological conservation, vehicle routing, heat exchanger design, satellite heat pipe design, offshore structure mooring, RNA structure prediction, medical imaging, medical physics, etc (Geem, 2009; 2010a). Recently, HS was also applied to astronomical data analysis, which was published in Nature (Deeg et al., 2010).
Each musician in music performance plays a musical note at a time, and those musical notes together make a harmony. Likewise, each variable in optimization has a value at a time, and those values together make a solution vector. Just like the music group improves their harmonies practice by practice, the algorithm improves its solution vectors iteration by iteration.
The HS algorithm basically has three operations, such as memory consideration, pitch adjustment, and random selection. Using memory consideration operation, HS chooses a value from harmony memory (HM); using pitch adjustment operation, HS chooses a value which is slightly modified from HM; and using random selection operation, HS chooses a value randomly from entire value range. These basic operations constitute a novel stochastic derivative (Geem, 2008), instead of traditional calculus-based derivative, in order to search for the right direction to the optimal solution.
For more advanced issues in HS, researchers have researched exploratory power (Das et al., 2010), multi-modal solution space (Gao et al., 2009), multi-objective optimization (Geem, 2010b), distributed memory (Pan et al., 2010), hybridization (Fesanghary et al., 2008), and adaptive theory (Geem and Sim, 2010). In addition, HS has a unique derivative which considers the relationship among variables (Geem, 2011).
References
Das, S., Mukhopadhyay, A., Roy, A., Abraham, A., & Panigrahi, B. K. (2010) Exploratory Power of the Harmony Search Algorithm: Analysis and Improvements for Global Numerical Optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics,
http://dx.doi.org/10.1109/TSMCB.2010.2046035
Deeg, H. J., Moutou, C., & Erikson A. et al. A transiting giant planet with a temperature between 250 K and 430 K. Nature, 464, 384-387.
Fesanghary, M., Mahdavi, M., Minary-Jolandan, M., Alizadeh, Y. (2008). Hybridizing harmony search algorithm with sequential quadratic programming for engineering optimization problems. Computer Methods in Applied Mechanics and Engineering, 197(33-40), 3080-3091.
Gao, X. Z., Wang, X., & Ovaska S. J. (2009) Uni-modal and Multi-modal Optimization Using Modified Harmony Search Methods. International Journal of Innovative Computing, Information and Control, 5(10A), 2985-2996.
Geem, Z. W. (2008). Novel Derivative of Harmony Search Algorithm for Discrete Design Variables. Applied Mathematics and Computation, 199(1), 223-230.
Geem, Z. W. (2009). Music-Inspired Harmony Search Algorithms: Theory and Applications. Berlin: Springer.
Geem, Z. W. (2010a). Recent Advances in Harmony Search Algorithm. Berlin: Springer.
Geem, Z. W. (2010b). Multiobjective Optimization of Time-Cost Trade-Off Using Harmony Search. ASCE Journal of Construction Engineering and Management, 136(6), 711-716.
Geem, Z. W. (2011). Stochastic Co-Derivative of Harmony Search Algorithm. International Journal of Mathematical Modelling and Numerical Optimisation, 2(1), 1-12.
Geem, Z. W., Kim, J. H., & Loganathan, G. V. (2001). A New Heuristic Optimization Algorithm: Harmony Search. Simulation, 76(2), 60-68.
Geem, Z.W., Sim, K.-B. (2010). Parameter-Setting-Free Harmony Search Algorithm. Applied Mathematics and Computation,
http://dx.doi.org/10.1016/j.amc.2010.09.049
Pan, Q.-K., Suganthan, P.N., Liang, J. J., Tasgetiren, M.F. (2010). A local-best harmony search algorithm with dynamic subpopulations. Engineering Optimization, 42(2), 101 - 117.