# ATM-R: An Adaptive Tradeoff Model with Reference Points for Constrained Multiobjective Evolutionary Optimization

arXiv: https://arxiv.org/abs/2301.03317 · HTML: https://mlsanity.com/paper/2301.03317/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 73 references that are in the map.
- First posted on arXiv 9 Jan 2023.

## Builds on (most cited first, 9 of 9)

- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization](https://mlsanity.com/paper/1701.00879/) (2017)
- [A Bayesian approach to constrained single- and multi-objective optimization](https://mlsanity.com/paper/1510.00503/) (2015)
- [Two-Archive Evolutionary Algorithm for Constrained Multi-Objective Optimization](https://mlsanity.com/paper/1711.07907/) (2017)
- [Constrained Multi-Objective Optimization for Automated Machine Learning](https://mlsanity.com/paper/1908.04909/) (2019)
- [Push and Pull Search for Solving Constrained Multi-objective Optimization Problems](https://mlsanity.com/paper/1709.05915/) (2017)
- [Better call Surrogates: A hybrid Evolutionary Algorithm for Hyperparameter optimization](https://mlsanity.com/paper/2012.06453/) (2020)
- [Push and Pull Search Embedded in an M2M Framework for Solving Constrained Multi-objective Optimization Problems](https://mlsanity.com/paper/1906.00402/) (2019)
- [Memetic algorithms for Spatial Partitioning problems](https://mlsanity.com/paper/2208.02867/) (2022)

## Abstract (arXiv)

The goal of constrained multiobjective evolutionary optimization is to obtain a set of well-converged and welldistributed feasible solutions. To complete this goal, there should be a tradeoff among feasibility, diversity, and convergence. However, it is nontrivial to balance these three elements simultaneously by using a single tradeoff model since the importance of each element varies in different evolutionary phases. As an alternative, we adapt different tradeoff models in different phases and propose a novel algorithm called ATM-R. In the infeasible phase, ATM-R takes the tradeoff between diversity and feasibility into account, aiming to move the population toward feasible regions from diverse search directions. In the semi-feasible phase, ATM-R promotes the transition from "the tradeoff between feasibility and diversity" to "the tradeoff between diversity and convergence", which can facilitate the discovering of enough feasible regions and speed up the search for the feasible Pareto optima in succession. In the feasible phase, the tradeoff between diversity and convergence is considered to attain a set of well-converged and well-distributed feasible solutions. It is worth noting that the merits of reference points are leveraged in ATM-R to accomplish these tradeoff models. Also, in ATM-R, a multiphase mating selection strategy is developed to generate promising solutions beneficial to different evolutionary phases. Systemic experiments on a wide range of benchmark test functions demonstrate that ATM-R is effective and competitive, compared against five state-of-the-art constrained multiobjective optimization evolutionary algorithms.