A First Runtime Analysis of the NSGA-II on a Multimodal Problem

Doerr, Benjamin; Qu, Zhongdi

doi:10.1109/tevc.2023.3250552

Cited by 35 publications

(15 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A similar result was proven for the multimodal DLTB problem [33] recently. The first lower bounds for the NSGA-II [34] show that the previous results for ONEMINMAX [19] and ONE-JUMPZEROJUMP [32] are asymptotically tight, even for larger population sizes. This implies that using a population size asymptotically larger than the minimum required size leads to asymptotic performance losses.…”

mentioning

confidence: 64%

“…This is particularly interesting in that here a uniform random choice was successful, whereas most previous works using random parameter choices employ power-law distributions, see, e.g., [14], [29]- [31]. The first mathematical runtime analysis on a multimodal problem, the ONEJUMPZEROJUMP benchmark from [14], was conducted in [32]. It shows that when the population size is at least 4 times the Pareto front size, then the NSGA-II with the right population size is as effective as the GSEMO on this benchmark.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Approximation Guarantees for the Non-Dominated Sorting Genetic Algorithm II (NSGA-II)

Zheng,

Doerr

2024

IEEE Trans. Evol. Computat.

View full text Add to dashboard Cite

mentioning

confidence: 64%

mentioning

confidence: 99%

Approximation Guarantees for the Non-Dominated Sorting Genetic Algorithm II (NSGA-II)

Zheng,

Doerr

2024

IEEE Trans. Evol. Computat.

View full text Add to dashboard Cite

“…This mechanism explores the less-crowded zone in the current archive to obtain more non-dominated solutions nearby (as depicted in the below figure). Interested readers can refer to Doerr and Qu (2023) for more information.…”

Section: Solution Algorithmsmentioning

confidence: 99%

A multi-objective optimization model of truck scheduling problem using cross-dock in supply chain management: NSGA-II and NRGA

Haghgoei,

Irajpour,

Hamidi

2024

JM2

View full text Add to dashboard Cite

Purpose This paper aims to develop a multi-objective problem for scheduling the operations of trucks entering and exiting cross-docks where the number of unloaded or loaded products by trucks is fuzzy logistic. The first objective function minimizes the maximum time to receive the products. The second objective function minimizes the emission cost of trucks. Finally, the third objective function minimizes the number of trucks assigned to the entrance and exit doors. Design/methodology/approach Two steps are implemented to validate and modify the proposed model. In the first step, two random numerical examples in small dimensions were solved by GAMS software with min-max objective function as well as genetic algorithms (GA) and particle swarm optimization. In the second step, due to the increasing dimensions of the problem and computational complexity, the problem in question is part of the NP-Hard problem, and therefore multi-objective meta-heuristic algorithms are used along with validation and parameter adjustment. Findings Therefore, non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are used to solve 30 random problems in high dimensions. Then, the algorithms were ranked using the TOPSIS method for each problem according to the results obtained from the evaluation criteria. The analysis of the results confirms the applicability of the proposed model and solution methods. Originality/value This paper proposes mathematical model of truck scheduling for a real problem, including cross-docks that play an essential role in supply chains, as they could reduce order delivery time, inventory holding costs and shipping costs. To solve the proposed multi-objective mathematical model, as the problem is NP-hard, multi-objective meta-heuristic algorithms are used along with validation and parameter adjustment. Therefore, NSGA-II and NRGA are used to solve 30 random problems in high dimensions.

show abstract

“…This mechanism explores the less-crowded zone in the current archive in order to obtain more non-dominated solutions nearby (as depicted in the below figure). Interested readers can refer to Doerr, B., & Qu (2023) for obtaining more information.…”

Section: Nsgaiimentioning

confidence: 99%

Multi-objective Optimization Model of Truck Scheduling Problem using Cross-Dock in Supply Chain Management: NSGA-II & NRGA

Haqhgoie,

Irajpour,

Hamidi

2023

Preprint

View full text Add to dashboard Cite

A large percentage of the cost of most products is related to shipping and distribution costs. By the proper design of the product distribution network, as an important part of the supply chain, these costs can be reduced in the logistic activities. The use of cross-docks between suppliers and customers is a solution utilized in supply chain management to reduce costs. Cross-docks are one of the most important options for reducing time in the supply chain. Accordingly, this paper develops a multi-objective problem of scheduling the operations of trucks entering and exiting cross-docks by considering that the number of products that are unloaded or loaded by trucks is fuzzy logistic. The first objective function minimizes the maximum time to receive the products. The second objective function minimizes the emission cost of trucks. Finally, the third objective function minimizes the number of trucks assigned to the entrance and exit doors. Then, two steps are implemented to validate and modify the proposed model. In the first step, two random numerical examples in small dimensions were solved by GAMS software with min-max objective function as well as Genetic Algorithms (GA) and Particle Swarm Optimization (PSO). In the second step, due to the increasing dimensions of the problem and computational complexity, the problem in question is part of the NP-Hard problem and therefore multi-objective meta-heuristic algorithms are utilized along with validation and parameter adjustment. Therefore, non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NSGA) are employed to solve 30 random problems in high dimensions. Then, the algorithms were ranked using the TOPSIS method for each problem according to the results obtained from the evaluation criteria. The analysis of the results confirms the applicability of the proposed model and solution methods.

show abstract

A First Runtime Analysis of the NSGA-II on a Multimodal Problem

Cited by 35 publications

References 50 publications

Approximation Guarantees for the Non-Dominated Sorting Genetic Algorithm II (NSGA-II)

Approximation Guarantees for the Non-Dominated Sorting Genetic Algorithm II (NSGA-II)

A multi-objective optimization model of truck scheduling problem using cross-dock in supply chain management: NSGA-II and NRGA

Multi-objective Optimization Model of Truck Scheduling Problem using Cross-Dock in Supply Chain Management: NSGA-II & NRGA

Contact Info

Product

Resources

About

A First Runtime Analysis of the NSGA-II on a Multimodal Problem

Cited by 35 publications

References 50 publications

Approximation Guarantees for the Non-Dominated Sorting Genetic Algorithm II (NSGA-II)

Approximation Guarantees for the Non-Dominated Sorting Genetic Algorithm II (NSGA-II)

A multi-objective optimization model of truck scheduling problem using cross-dock in supply chain management: NSGA-II and NRGA

Multi-objective Optimization Model of Truck Scheduling Problem using Cross-Dock in Supply Chain Management: NSGA-II &amp; NRGA

Contact Info

Product

Resources

About

Multi-objective Optimization Model of Truck Scheduling Problem using Cross-Dock in Supply Chain Management: NSGA-II & NRGA