Insights into Weighted Sum Sampling Approaches for Multi-Criteria Decision Making Problems

Aled Williams; Yilun Cai

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arXiv · 2410.03931

Insights into Weighted Sum Sampling Approaches for Multi-Criteria Decision Making Problems

Aled Williams·Yilun Cai

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Abstract

In this paper we explore several approaches for sampling weight vectors in the context of weighted sum scalarisation approaches for solving multi-criteria decision making (MCDM) problems. This established method converts a multi-objective problem into a (single) scalar optimisation problem. It does so by assigning weights to each objective. We outline various methods to select these weights, with a focus on ensuring computational efficiency and avoiding redundancy. The challenges and computational complexity of these approaches are explored and numerical examples are provided. The theoretical results demonstrate the trade-offs between systematic and randomised weight generation techniques, highlighting their performance for different problem settings. These sampling approaches will be tested and compared computationally in an upcoming paper.

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Aled Williams, Yilun Cai. 2024-10-04. Insights into Weighted Sum Sampling Approaches for Multi-Criteria Decision Making Problems. https://arxiv.org/abs/2410.03931

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