A Comprehensive Review on Multi-objective Optimization Techniques: Past, Present and Future

Sharma, Shubhkirti; Kumar, Vijay

doi:10.1007/s11831-022-09778-9

Cited by 110 publications

(20 citation statements)

References 111 publications

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“…Population-based MOO methods [26] mainly include dominance-based [27], [28], decomposition-based [29], [30], indicator-based [31], [32], hybrid-based [33], [34], and modelbased methods [35]- [37]. Due to their easy scalability and gradient-free properties, these population-based methods are widely used in various machine learning problems, such as neuroevolution [38], [39], NAS [1], [40]- [42], feature selection [43], [44], reinforcement learning [45], federated learning [46], [47], MTL [48], and fairness learning [49].…”

Section: Moomentioning

confidence: 99%

Bi-Level Multiobjective Evolutionary Learning: A Case Study on Multitask Graph Neural Topology Search

Wang

Jiao

Zhao

et al. 2024

IEEE Trans. Evol. Computat.

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The construction of machine learning models involves many bi-level multi-objective optimization problems (BL-MOPs), where upper level (UL) candidate solutions must be evaluated via training weights of a model in the lower level (LL). Due to the Pareto optimality of sub-problems and the complex dependency across UL solutions and LL weights, an UL solution is feasible if and only if the LL weight is Pareto optimal. It is computationally expensive to determine which LL Pareto weight in the LL Pareto weight set is the most appropriate for each UL solution. This paper proposes a bi-level multi-objective learning framework (BLMOL), coupling the above decisionmaking process with the optimization process of the UL-MOP by introducing LL preference r. Specifically, the UL variable and r are simultaneously searched to minimize multiple UL objectives by evolutionary multi-objective algorithms. The LL weight with respect to r is trained to minimize multiple LL objectives via gradient-based preference multi-objective algorithms. In addition, the preference surrogate model is constructed to replace the expensive evaluation process of the UL-MOP. We consider a novel case study on multi-task graph neural topology search. It aims to find a set of Pareto topologies and their Pareto weights, representing different trade-offs across tasks at UL and LL, respectively. The found graph neural network is employed to solve multiple tasks simultaneously, including graph classification, node classification, and link prediction. Experimental results demonstrate that BLMOL can outperform some state-of-the-art algorithms and generate well-representative UL solutions and LL weights.

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Section: Moomentioning

confidence: 99%

Bi-Level Multiobjective Evolutionary Learning: A Case Study on Multitask Graph Neural Topology Search

Wang

Jiao

Zhao

et al. 2024

IEEE Trans. Evol. Computat.

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“…And conversely the increase in accuracy tends to generate an increase in the number of features. Based on the mathematical concept of Pareto dominance, among the solutions obtained, those which have a relation of dominance over the other solutions and none of them, constitute the Pareto optimal front [79,[82][83][84]. There are three main approaches for solving a multi-objective optimization problem including the participation of a decision maker [83,85,86] : A priori, A posteriori and Interactive.…”

Section: Mathematical Modeling Of the Wrapper Feature Selection In A ...mentioning

confidence: 99%

BHHO-EAS metaheuristic applied to the NP-Hard wrapper feature selection multi-objective optimization problem

SASSI,

CHELOUAH

2024

Preprint

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Faced with the increase in high-dimensional Big Data creating more volume and complexity, the feature selection process became an essential phase in the preprocessing workflow upstream of the design of systems based on deep learning. This paper is a concrete and first application of the new metaheuristic Harris Hawk Optimization Encirclement-Attack-Synergy (HHO-EAS) in solving the NP-Hard wrapper feature selection multi-objective optimization problem. This problem combines two contradictory objectives: maximizing the accuracy of a classifier while minimizing the number of the most relevant and non-redundant selected features. To do this we hybridized HHO-EAS to create the new metaheuristic Binary HHO-EAS (BHHO-EAS). We combined HHO-EAS to the sixteen transfer functions most used in the literature structured in a balanced way among the four main categories including S-Shaped, V-Shaped, Q-Shaped and U-Shaped. This wide range of transfer function allows us to analyze the evolution of BHHO-EAS’s skills according to the assigned transfer function and to determine which of them offer the best performances. We applied wrapper feature selection to the well-known NSL-KDD dataset with the deep learning Multi Layer Perceptron (MLP) classifier. We put BHHO-EAS in competition with three other well-known population based binary metaheuristics, BPSO, BBA and BHHO. The analysis of the experimental results, compared to the three other binary metaheuristics, demonstrated that BHHO-EAS obtained the best performance on 100% of the transfer functions. This is more particularly highlighted by the U-Shaped transfer functions, which give an acceptable compromise for the two objectives of the problem with an average accuracy of 96,4% and an average size of selected features of 20.

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“…This mathematical model provides a comprehensive approach to decisionmaking by simultaneously considering multiple conflicting objectives. This generates a set of solutions, also known as the Pareto optimal solutions [27,28]. These solutions present different options, where improving one objective may result in a tradeoff with another objective [29][30][31].…”

Section: Multiobjective Optimization Modelmentioning

confidence: 99%

Logistical Assessment of Deep-Sea Polymetallic Nodules Transport from an Offshore to an Onshore Location Using a Multiobjective Optimization Approach

2023

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The increasing growth in the global population has led to a substantial demand for low-carbon energy infrastructure, metals, and minerals. This has put more pressure on land-based deposits, which have been unsustainably exploited over the years. As a result, attention has shifted towards exploring minerals in sea-based environments. Currently, industry and researchers have identified potentially commercially viable locations for the exploration of these nodules. However, significant knowledge gaps remain in the sustainable, efficient, and effective recovery and transportation of the nodules to onshore locations. To address these gaps, the study develops a logistics and cost model embedded in a multiobjective optimization (MOO) approach. This model considers several parameters, such as the production targets, port distance and location, storage capacity, vessel characteristics, transportation options, and cost inputs. By incorporating these parameters, the study analyzes different combinations of vessel classes and onshore locations and provides insights into optimizing offshore–onshore logistics and transportation options. The findings reveal that small and medium-sized vessels require lower storage capacity because they can complete more trips. Furthermore, the analysis reveals the cost of deploying additional vessels outweighs the benefits of reduced storage space for long-distance transport; therefore, smaller and medium-sized vessels are more suitable for locations closer to the offshore production site. Additionally, proximity to the onshore location is important, as it reduces transport costs and simplifies logistics operations. Subsequently, there is a need to have a reasonable buffer rate as this reduces the impact of potential disruptions during transport. From a managerial viewpoint, the study highlights the need to carefully consider vessel types based on transport requirements and journey characteristics. The analysis further identifies the benefits of having an onshore location close to the offshore production site. This will lead to optimized transport and logistics operations. Based on this, the study contributes to the body of knowledge in offshore logistics by developing a multiobjective optimization model for offshore–onshore transport logistics and cost analysis. This model provides a practical tool for informed decision-making and provides insight into vessel size and location considerations. Finally, the study establishes how simultaneous consideration of multiple factors in transport operations can lead to optimized and informed decision-making.

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A Comprehensive Review on Multi-objective Optimization Techniques: Past, Present and Future

Cited by 110 publications

References 111 publications

Bi-Level Multiobjective Evolutionary Learning: A Case Study on Multitask Graph Neural Topology Search

Bi-Level Multiobjective Evolutionary Learning: A Case Study on Multitask Graph Neural Topology Search

BHHO-EAS metaheuristic applied to the NP-Hard wrapper feature selection multi-objective optimization problem

Logistical Assessment of Deep-Sea Polymetallic Nodules Transport from an Offshore to an Onshore Location Using a Multiobjective Optimization Approach

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