In this manuscript, a Combined Approach of Generalized Backtracking Regularized Adaptive Matching Pursuit Algorithm and Adaptive β-Hill Climbing Algorithm for Virtual Machine Allocation in Cloud Computing (BA-VMA-CC) is proposed. Generalized Backtracking Regularized Adaptive Matching Pursuit Algorithm (GBRAMP) is used for Virtual Machine (VM) Migration process and Adaptive β-Hill Climbing Algorithm is used to Virtual Machine Placement. These two tasks are essential elements of VM allocation. GBRAMP is used to minimize cost and energy for both cloud service providers and users with help of migration process and to save time and energy. Adaptive β-Hill Climbing Algorithm (AβHCA) is employed for maximizing efficiency, minimizing power consumption and resource wastage. By Combining both GBRAMPA-AβHCA VM is optimally allocated in PM with high efficiency by minimizing cost and energy consumptions. The proposed BA-VMA-CC is implemented in MATLAB platform. The performance of proposed method attains 23.84 %, 28.94 %, 33.94 % lower energy consumption, 28.94 %, 34.95 %, 25.36 % lower CPU utilization is analyzed with existing methods, such as sine cosine with ant lion optimization for VM allocation in Cloud Computing (SCA-ALO-VMA-CC), hybrid distinct multiple object whale optimization and multi-verse optimization for VM allocation in Cloud Computing (DMOWOA-MVO-VMA-CC) and Cuckoo search optimization algorithm and particle swarm optimization algorithm (CSO-PSO-VMA-CC) respectively.