This paper studies the following points: First, a new combined MOPT formulation for both energy and delay is developed. Second, numerical method based on KKT optimality conditions is used to find the optimal solution for the above formulation. Third, a sub-optimal solution using MOGA is calculated based on the MOPT formulation.
Numerical results generated using Newton-Raphson method, for the associated Lagrangian system of equations, are presented. We find a sub-optimal solution because of the high complexity to find the optimal solution. The effectiveness of the proposed formulation is evaluated using the average energy consumption and end-to-end delay. Unlike the optimal solution obtained using KKT analysis, a sub-optimal solution obtained using MOGA requires less complexity in terms of the
run time and the number of operations needed. The increase in the energy consumption and in the delay is not significant compared with the saving in the complexity.