Comparison of Dynamic Programming and Genetic Algorithm Approaches for Solving Subset Sum Problems

Author(s):  
Konjeti Harsha Saketh ◽  
G. Jeyakumar
2020 ◽  
Vol 25 (4) ◽  
pp. 10-15
Author(s):  
Alexander Nikolaevich Rybalov

Generic-case approach to algorithmic problems was suggested by A. Miasnikov, I. Kapovich, P. Schupp and V. Shpilrain in 2003. This approach studies behavior of an algo-rithm on typical (almost all) inputs and ignores the rest of inputs. In this paper, we prove that the subset sum problems for the monoid of integer positive unimodular matrices of the second order, the special linear group of the second order, and the modular group are generically solvable in polynomial time.


Water ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 1392 ◽  
Author(s):  
Iram Parvez ◽  
JianJian Shen ◽  
Mehran Khan ◽  
Chuntian Cheng

The hydro generation scheduling problem has a unit commitment sub-problem which deals with start-up/shut-down costs related hydropower units. Hydro power is the only renewable energy source for many countries, so there is a need to find better methods which give optimal hydro scheduling. In this paper, the different optimization techniques like lagrange relaxation, augmented lagrange relaxation, mixed integer programming methods, heuristic methods like genetic algorithm, fuzzy logics, nonlinear approach, stochastic programming and dynamic programming techniques are discussed. The lagrange relaxation approach deals with constraints of pumped storage hydro plants and gives efficient results. Dynamic programming handles simple constraints and it is easily adaptable but its major drawback is curse of dimensionality. However, the mixed integer nonlinear programming, mixed integer linear programming, sequential lagrange and non-linear approach deals with network constraints and head sensitive cascaded hydropower plants. The stochastic programming, fuzzy logics and simulated annealing is helpful in satisfying the ramping rate, spinning reserve and power balance constraints. Genetic algorithm has the ability to obtain the results in a short interval. Fuzzy logic never needs a mathematical formulation but it is very complex. Future work is also suggested.


Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1526 ◽  
Author(s):  
Seung-Ju Lee ◽  
Yourim Yoon

Recently, energy storage systems (ESSs) are becoming more important as renewable and microgrid technologies advance. ESSs can act as a buffer between generation and load and enable commercial and industrial end users to reduce their electricity expenses by controlling the charge/discharge amount. In this paper, to derive efficient charge/discharge schedules of ESSs based on time-of-use pricing with renewable energy, a combination of genetic algorithm and dynamic programming is proposed. The performance of the combined method is improved by adjusting the size of the base units of dynamic programming. We show the effectiveness of the proposed method by simulating experiments with load and generation profiles of various commercial electricity consumers.


2014 ◽  
Vol 519-520 ◽  
pp. 1468-1471
Author(s):  
Jun Quan Gong ◽  
Xiao Hong Qin

Enterprise often face to limit financial resources but also have to consider how to invest effectively on a number of projects in the various factors of the risks and benefits in different periods. In order to assure the optimal investment results of capital investment, this paper has established dynamic programming model which is multi-dimensional and multi-objective and fuzzy optimization, dynamic programming and genetic algorithm is combination to solve investment decision of enterprise. At last, this paper through an example to verify the validity of dynamic programming model.


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