Efficient Greedy Algorithm for Multi-Objective Sensor Placement Optimization
Abstract
The sensor placement problem is a complex combinatorial optimization challenge, where greedy selection provides performance guarantees for submodular objective functions, yielding suboptimal yet efficient solutions. Multi-objective optimization addresses the trade-offs among individual objectives, often requiring solutions on the Pareto Front. This paper introduces two multi-objective optimization functions based on optimal experimental design, incorporating normalization and weight update strategies. Leveraging the definition of submodularity, we revalidate that the non-negative linear combination of submodular functions preserves submodularity, applicable to one of the proposed functions. The effectiveness of the methods is validated across four datasets, demonstrating superior performance in sensor placement tasks. Notably, for bi-objective optimization involving A-optimality and D-optimality, adaptive-weight greedy solutions not only provide performance guarantees but also dominate most fixed-weight greedy solutions and lie on the Pareto Front.