This paper investigates using heuristic algorithms to solve Multi-Objective Optimization Problem (MOOP). The primary goal is to minimize the electricity cost for a set of air conditioners in residential or commercial buildings. The second objective is to minimize the discomfort factor. The algorithm, also, enhances the utilization of local renewable power. This allocation problem can be formulated using a static technique such as Mixed Integer Linear Programming (MILP), but solving MILP-based MOOP could be impracticable in heavy problems due to the hardness of the problem. Accordingly, a trade-off between cost and runtime is required. Our algorithm uses an MILP-based heuristic algorithm and LP relaxation and an innovative rounding technique called, Minimum Deviation Rounding (MDR) to get a sub-optimal solution. The result reveals that our algorithm can solve a massive problem in few seconds and gives a superb sub-optimal solution.