# Minimum Manhattan Distance Approach to Multiple Criteria Decision Making in Multiobjective Optimization Problems

arXiv: https://arxiv.org/abs/1705.01705 · HTML: https://mlsanity.com/paper/1705.01705/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2017.

## Built on by (most cited first, 5 of 5)

- [Towards Fairness-Aware Multi-Objective Optimization](https://mlsanity.com/paper/2207.12138/) (2022)
- [Uncertainty-Aware Multi-Objective Reinforcement Learning-Guided Diffusion Models for 3D De Novo Molecular Design](https://mlsanity.com/paper/2510.21153/) (2025)
- [Sharpness-Aware Minimization for Evolutionary Feature Construction in Regression](https://mlsanity.com/paper/2405.06869/) (2024)
- [Optimizing Prognostic Biomarker Discovery in Pancreatic Cancer Through Hybrid Ensemble Feature Selection and Multi-Omics Data](https://mlsanity.com/paper/2509.02648/) (2025)
- [Enhancing Generalization in Evolutionary Feature Construction for Symbolic Regression through Vicinal Jensen Gap Minimization](https://mlsanity.com/paper/2602.01510/) (2026)

## Abstract (arXiv)

A minimum Manhattan distance (MMD) approach to multiple criteria decision making in multiobjective optimization problems (MOPs) is proposed. The approach selects the final solution corresponding with a vector that has the MMD from a normalized ideal vector. This procedure is equivalent to the knee selection described by a divide and conquer approach that involves iterations of pairwise comparisons. Being able to systematically assign weighting coefficients to multiple criteria, the MMD approach is equivalent to a weighted-sum (WS) approach. Because of the equivalence, the MMD approach possesses rich geometric interpretations that are considered essential in the field of evolutionary computation. The MMD approach is elegant because all evaluations can be performed by efficient matrix calculations without iterations of comparisons. While the WS approach may encounter an indeterminate situation in which a few solutions yield almost the same WS, the MMD approach is able to determine the final solution discriminately. Since existing multiobjective evolutionary algorithms aim for a posteriori decision making, i.e., determining the final solution after a set of Pareto optimal solutions is available, the proposed MMD approach can be combined with them to form a powerful solution method of solving MOPs. Furthermore, the approach enables scalable definitions of the knee and knee solutions.