Abstract
Abstract Mixed-variable optimization problems consist of the continuous, integer, and discrete variables generally used in various engineering optimization problems. These variables increase the computational cost and complexity of optimization problems due to the handling of variables. Moreover, there are few optimization algorithms that give a globally optimal solution for non-differential and non-convex objective functions. Initially, the Jaya algorithm has been developed for continuous variable optimization problems. In this paper, the Jaya algorithm is further extended for solving mixed-variable optimization problems. In the proposed algorithm, continuous variables remain in the continuous domain while continuous domains of discrete and integer variables are converted into discrete and integer domains applying bound constraint of the middle point of corresponding two consecutive values of discrete and integer variables. The effectiveness of the proposed algorithm is evaluated through examples of mixed-variable optimization problems taken from previous research works, and optimum solutions are validated with other mixed-variable optimization algorithms. The proposed algorithm is also applied to two-plane balancing of the unbalanced rigid threshing rotor, using the number of balance masses on plane 1 and plane 2. It is found that the proposed algorithm is computationally more efficient and easier to use than other mixed optimization techniques.
Highlights
Various optimization problems deal with integer, discrete, and continuous variables, known as mixedvariable optimization problems
The Jaya algorithm is further extended for solving mixed-variable optimization problems
Continuous variables remain in the continuous domain while continuous domains of discrete and integer variables are converted into discrete and integer domains applying bound constraint of the middle point of corresponding two consecutive values of discrete and integer variables
Summary
Various optimization problems deal with integer, discrete, and continuous variables, known as mixedvariable optimization problems. Classical techniques, such as sequential linear programming [24], branch and bound methods [5, 22, 40], a penalty function approach [14, 41], Lagrangian relaxation [15, 18], rounding-off techniques based on continuous variables, cutting plane techniques, and zero-one variable techniques (integer programming) [1] have been applied to mixed-variable optimization problems in order to find out the optimum design variables These methods include more computational cost, low efficiency, and low complexity due to the determination of derivatives and the Hessian matrix of the objective function [3].
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