The polynomial robust knapsack problem

Baldo, Alessandro; Boffa, Matteo; Cascioli, Lorenzo; Fadda, Edoardo; Lanza, Chiara; Ravera, Arianna

doi:10.1016/j.ejor.2022.06.029

Cited by 7 publications

(4 citation statements)

References 19 publications

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“…Therefore, we use as

{\hat{V}}_t^x\left[\cdotp \right]

a set of polynomial functions (one for each

t

). Interestingly, polynomial functions can be linearized since variables

{x}_v

are binary [4]. In fact, we can write the objective function (27), considering index

t

, as

\max \sum \limits_{v\in \mathcal{V}}-{c}_v{x}_v^t+\sum \limits_{A\in {2}^{\mid \mathcal{V}\mid }}{w}_A^t\prod \limits_{v\in A}{x}_v^t,

where

{w}_A^t

is the parameter that weighs the interactions obtained by influencing all the nodes in the subset

A

at time

t

.…”

Section: Solution Methodsmentioning

confidence: 99%

“…Therefore, we use as Vx t [⋅] a set of polynomial functions (one for each t). Interestingly, polynomial functions can be linearized since variables x v are binary [4]. In fact, we can write the objective function (27), considering index t, as max…”

mentioning

confidence: 99%

“…FIGURE4 Gap between TS and AVI on the left, and TS and GNNQL on the right for different values of budget B and time horizon T.…”

mentioning

confidence: 99%

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Math‐based reinforcement learning for the adaptive budgeted influence maximization problem

Fadda,

Corso,

Brusco

et al. 2023

Networks

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In social networks, the influence maximization problem requires selecting an initial set of nodes to influence so that the spread of influence can reach its maximum under certain diffusion models. Usually, the problem is formulated in a two‐stage un‐budgeted fashion: The decision maker selects a given number of nodes to influence and observes the results. In the adaptive version of the problem, it is possible to select the nodes at each time step of a given time interval. This allows the decision‐maker to exploit the observation of the propagation and to make better decisions. This paper considers the adaptive budgeted influence maximization problem, that is, the adaptive problem in which the decision maker has a finite budget to influence the nodes, and each node requires a cost to be influenced. We present two solution techniques: The first is an approximated value iteration leveraging mixed integer linear problems while the second exploits new concepts from graph neural networks. Extensive numerical experiments demonstrate the effectiveness of the proposed approaches.

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“…Therefore, we use as

{\hat{V}}_t^x\left[\cdotp \right]

a set of polynomial functions (one for each

t

). Interestingly, polynomial functions can be linearized since variables

{x}_v

are binary [4]. In fact, we can write the objective function (27), considering index

t

, as

\max \sum \limits_{v\in \mathcal{V}}-{c}_v{x}_v^t+\sum \limits_{A\in {2}^{\mid \mathcal{V}\mid }}{w}_A^t\prod \limits_{v\in A}{x}_v^t,

where

{w}_A^t

is the parameter that weighs the interactions obtained by influencing all the nodes in the subset

A

at time

t

.…”

Section: Solution Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Math‐based reinforcement learning for the adaptive budgeted influence maximization problem

Fadda,

Corso,

Brusco

et al. 2023

Networks

Self Cite

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“…The significance of wrapper-based selection techniques in feature selection optimizations cannot be overlooked [ 24 , 25 ]. These methods operate on the premise of treating feature selection as a black box, and employ meta-heuristic algorithms and classifiers to obtain the optimal subset [ 26 ].…”

Section: Related Workmentioning

confidence: 99%

IBGJO: Improved Binary Golden Jackal Optimization with Chaotic Tent Map and Cosine Similarity for Feature Selection

Zhang

Liu

Mei

et al. 2023

Entropy

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Feature selection is a crucial process in machine learning and data mining that identifies the most pertinent and valuable features in a dataset. It enhances the efficacy and precision of predictive models by efficiently reducing the number of features. This reduction improves classification accuracy, lessens the computational burden, and enhances overall performance. This study proposes the improved binary golden jackal optimization (IBGJO) algorithm, an extension of the conventional golden jackal optimization (GJO) algorithm. IBGJO serves as a search strategy for wrapper-based feature selection. It comprises three key factors: a population initialization process with a chaotic tent map (CTM) mechanism that enhances exploitation abilities and guarantees population diversity, an adaptive position update mechanism using cosine similarity to prevent premature convergence, and a binary mechanism well-suited for binary feature selection problems. We evaluated IBGJO on 28 classical datasets from the UC Irvine Machine Learning Repository. The results show that the CTM mechanism and the position update strategy based on cosine similarity proposed in IBGJO can significantly improve the Rate of convergence of the conventional GJO algorithm, and the accuracy is also significantly better than other algorithms. Additionally, we evaluate the effectiveness and performance of the enhanced factors. Our empirical results show that the proposed CTM mechanism and the position update strategy based on cosine similarity can help the conventional GJO algorithm converge faster.

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A machine learning optimization approach for last-mile delivery and third-party logistics

Bruni

Fadda

Fedorov

et al. 2023

Computers & Operations Research

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The polynomial robust knapsack problem

Cited by 7 publications

References 19 publications

Math‐based reinforcement learning for the adaptive budgeted influence maximization problem

Math‐based reinforcement learning for the adaptive budgeted influence maximization problem

IBGJO: Improved Binary Golden Jackal Optimization with Chaotic Tent Map and Cosine Similarity for Feature Selection

A machine learning optimization approach for last-mile delivery and third-party logistics

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