A Convex Optimization Framework for Resource Allocation in Smart Water Distribution Networks
Keywords:
Convex optimization; smart water distribution network; resource allocation; variational inequality; monotone operator theory; projection-based algorithm; mathematical optimization.Abstract
Resource allocation in smart water distribution systems is an intricate optimization task due to the correlation between water demands, flows allocation, energy usage, and limitations. This paper aims to develop a convex optimization approach for optimal resource allocation in a smart water distribution system by modeling the problem as a constrained convex minimization problem. In order to solve the problem, a closed convex feasible region, a convex cost function, and a variational inequality model are defined to investigate the optimality conditions in the optimization problem. A projection-type iterative algorithm is established by utilizing the theory of convex analysis and monotone operators to ensure feasibility, uniqueness, and convergence of the algorithm. Numerical experiments on a smart water distribution case study are carried out to test the convex optimization method. It is found that the convex optimization method converges to a convergence error of 0.001 after 200 iterations, which outperforms the gradient approach (0.028) and the genetic algorithm (0.072). In addition, the designed model also yields the least objective value of 112.8 through just 95 iterations, in comparison to 128.6 and 121.4 of conventional optimization techniques. It clearly indicates the enhanced stability of convergence, optimization performance, and preservation of constraints. The designed model offers an effective mathematical framework for smart management of water resources, including convex optimization, variational inequality, and a projection-based approach. Further, the model can be developed further by incorporating stochastic and distributed optimization approaches in future studies.
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