A Radial Boundary Intersection aided interior point method for multi-objective optimization

Datta, Siddhartha; Ghosh, A.; Sanyal, Krishnendu; Das, Swagatam

doi:10.1016/j.ins.2016.09.062

Cited by 23 publications

(7 citation statements)

References 23 publications

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“…In future work, it would be prudent to improve and develop MOBO using vector-valued GPs with high noise observations and the weight adaptation method to accommodate complex PF shapes. Regarding the performance metrics in cases of complex PF shapes, we think that in addition to Loss and IGD metrics, various metrics [12] need to more precisely quantify the performance of algorithms [9]. In addition, real experiments would be desirable to confirm the effectiveness of combining random scalarizations and vector-valued GPs in materials discovery.…”

Section: Discussionmentioning

confidence: 99%

“…In this section, as a real application for evaluating the weight adaptation, material search experiments were conducted on one hydrogen storage material database 9 . The objectives were maximizing the (negated) temperature and weight percent of hydrogen storage materials, which are the quantities corresponding to the evaluation criteria for promising storage materials [30].…”

Section: Experiments For Hydrogen Storage Materials Databasementioning

confidence: 99%

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Analysis of Multi-objective Bayesian Optimization Using Random Scalarizations for Correlated Observations

Ohno

2021

SN COMPUT. SCI.

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Bayesian optimization (BO) has been used for a wide range of applications. However, multi-objectives (e.g., time and cost of moving people and/or products) are often found in practical situations, and thus, multi-objective optimization is often required. In addition, correlated observations are found in various applications, e.g., materials discovery. To deal with such situations effectively, random scalarizations and vector-valued Gaussian processes (GPs) are adopted. For multi-objective BO (MOBO) using random scalarizations (linear and Tchebychev schemes) and vector-valued GPs, regret bounds are analyzed. In terms of Tchebychev scalarizations, these are sub-linear in the number of rounds. Bayes risk decomposition of the GP upper confidence bound (UCB) is utilized for theoretical analysis. In addition, a weight distribution for scalarizing objective functions is estimated by nonstationary Thompson sampling where the Dirichlet distribution is a prior, thereby achieving automatic weight adaptations according to the progress of optimization. Experimental results generated from 10 benchmark functions and one real application (a hydrogen storage material database) testify to the effectiveness of using vector-valued GPs compared to real-valued GPs and the weight adaptations. Moreover, under very noisy observations in the experimental settings, real-valued GPs are found to work better than vector-valued GPs in the context of MOBO convergence. This is because of random fluctuation in posterior variance caused by noisy observations in the UCB.

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Section: Discussionmentioning

confidence: 99%

Section: Experiments For Hydrogen Storage Materials Databasementioning

confidence: 99%

Analysis of Multi-objective Bayesian Optimization Using Random Scalarizations for Correlated Observations

Ohno

2021

SN COMPUT. SCI.

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“…Kelner et al [31] proposed a hybrid optimization technology by combining genetic algorithm with local search strategy based on interior point method. Datta et al [103] proposed a new multiobjective optimization technology, which combines an interior point method with the nonconvex radial boundary intersection. The radial boundary intersection decomposes the multiobjective optimization problem into several subproblems, which find the solutions of the nearest reference point radially outward along equidistant lines.…”

Section: E Hybrid Methodsmentioning

confidence: 99%

A Survey on Evolutionary Constrained Multiobjective Optimization

Liang

Ban

et al. 2023

IEEE Trans. Evol. Computat.

163

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Handling constrained multi-objective optimization problems (CMOPs) is extremely challenging, since multiple conflicting objectives subject to various constraints require to be simultaneously optimized. To deal with CMOPs, numerous constrained multi-objective evolutionary algorithms (CMOEAs) have been proposed in recent years, and they have achieved promising performance. However, there has been few literature on the systematic review of the related studies currently. This article provides a comprehensive survey for evolutionary constrained multi-objective optimization. We first review a large number of CMOEAs through categorization, and analyze their advantages and drawbacks in each category. Then, we summarize the benchmark test problems and investigate the performance of different constraint handling techniques and different algorithms, followed by some emerging and representative applications of CMOEAs. Finally, we discuss some new challenges and point out some directions of the future research in the field of evolutionary constrained multi-objective optimization.

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“…The SAA‐EVM model can be solved by a well‐established constrained minimization algorithm such as the interior point (IP) method. [ 36 ] In 1984, Karmarkar developed an improved IP method, [ 37 ] demonstrating that it was characterized by polynomial complexity. The computational complexity of the IP method is

O ((), n^{3 - 5} L^{2})

.…”

Section: Introductionmentioning

confidence: 99%

A two‐layer chance‐constrained optimization model for a thickening‐dewatering process with uncertain variables

Zhang

Wang

et al. 2021

Can J Chem Eng

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The feed mass and the filter‐press mass per cabinet (FMP) are uncertain variables in the thickening‐dewatering (TD) process. These uncertain variables must be considered for the optimization; otherwise, the energy economic index (EEI) and the safety risks will increase. Therefore, in this paper, a two‐layer chance‐constrained optimization model for the TD process with uncertain variables is proposed. The optimization model is a sample average approximate‐expected value model (SAA‐EVM), and scenarios are generated by Monte‐Carlo simulation. To reduce the computational time, the optimization model is divided into a two‐layer chance‐constrained optimization model. The computational time is reduced by reducing the dimensions of the decision variables. Simulation results show that this two‐layer chance‐constrained optimization model can reduce the EEI and safety risks and improve the stability of the process, while the computational time meets the requirements of mineral processing plants.

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A Radial Boundary Intersection aided interior point method for multi-objective optimization

Cited by 23 publications

References 23 publications

Analysis of Multi-objective Bayesian Optimization Using Random Scalarizations for Correlated Observations

Analysis of Multi-objective Bayesian Optimization Using Random Scalarizations for Correlated Observations

A Survey on Evolutionary Constrained Multiobjective Optimization

A two‐layer chance‐constrained optimization model for a thickening‐dewatering process with uncertain variables

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