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The purpose of this paper is mainly to develop the adjoint method within the method of magnetic moment (MMM) and thus, to provide an efficient new way to solve topology optimization problems in magnetostatic to design 3D-magnetic circuits.

First, the MMM is recalled and the optimization design problem is reformulated as a partial derivative equation-constrained optimization problem where the constraint is the Maxwell equation in magnetostatic. From the Karush–Khun–Tucker optimality conditions, a new problem is derived which depends on a Lagrangian parameter. This problem is called the adjoint problem and the Lagrangian parameter is called the adjoint parameter. Thus, solving the direct and the adjoint problems, the values of the objective function as well as its gradient can be efficiently obtained. To obtain a topology optimization code, a semi isotropic material with penalization (SIMP) relaxed-penalization approach associated with an optimization based on gradient descent steps has been developed and used.

In this paper, the authors provide theoretical results which make it possible to compute the gradient via the continuous adjoint of the MMMs. A code was developed and it was validated by comparing it with a finite difference method. Thus, a topology optimization code associating this adjoint based gradient computations and SIMP penalization technique was developed and its efficiency was shown by solving a 3D design problem in magnetostatic.

This research is limited to the design of systems in magnetostatic using the linearity of the materials. The simple examples, the authors provided, are just done to validate our theoretical results and some extensions of our topology optimization code have to be done to solve more interesting design cases.

The problem of design is a 3D magnetic circuit. The 2D optimization problems are well known and several methods of resolution have been introduced, but rare are the problems using the adjoint method in 3D. Moreover, the association with the MMMs has never been treated yet. The authors show in this paper that this association could provide gains in CPU time.

This study aims to investigate the use of Artificial Intelligence (AI) applied to vertical farms to evaluate whether disrupting technology supports sustainability and increases strategic business model choices in the agricultural sector. The study responds through empirical analysis to the gap on the subject of AI-driven business models present in the growing sector literature.

The paper analyzes the case of “ZERO”, a company linked to the strategy innovation ecosystem of the Ca’ Foscari University of Venice, Italy. The empirical data were collected through a semi-structured questionnaire, interviews and the analysis of public news on the business model available in the analyzed case study. The research is empirical and uses exploratory, descriptive analysis to interpret the findings. The article focuses on the evaluation of AI impact on the agricultural sector and its potential to create new business models.

The study identified how AI can support the decision-making process leading to an increase in productivity, efficiency, product quality and cost reduction. AI helps increase these parameters through a continuous learning process and local production, and the possible decrease in prices directed toward the goal of zero km food with fresh products. AI is a winning technology to support the key elements of the vertical farm business model. However, it must be coupled with other devices, such as robots, sensors and drones, to collect enough data to enable continuous learning and improvement.

The research supports new research trends in AI applied to agriculture. The major implication is the construction of ecosystems between farms, technology providers, policymakers, universities, research centers and local consumer communities.

The ZERO case study underlines the potential of AI as a destructive technology that, especially in vertical farms, eliminates external conditions by increasing productivity, reducing costs and responding to production needs with adequate consumption of raw materials, boosting both environmental and social sustainability.

The study is original, as the current literature presents few empirical case studies on AI-supporting business models in agriculture. The study also favors valuable strategic implications for the policies to be adopted in favor of new business models in agriculture.