Mathematics/software engineering internship (Non-Thesis): optimization with mixed integer programming

Introduction

Dies in spec (DIS) is one of the most crucial targets of edge placement error (EPE) optimization. Higher DIS of EPE brings higher yield, which has long been desired by our customers.

Theoretically, to maximize the DIS, the L0 norm of a loss function should be minimized. However, this task is challenging due to the nonlinear and nonconvex nature of the L0 norm. Instead, for the current optimization flow, the L1 norm is minimized as the approximation and solved by convex optimization. But this approximation leads to sub-optimal solutions and causes performance loss.

To improve the DIS performance of the current algorithm, a new method of maximizing DIS is proposed. Instead of minimizing L1 norm, the new method employs mixed integer programming (MIP) and big-M method to calculate the accurate solution of DIS. Rudimentary results show promising improvement: up to 3x DIS in certain cases.

Your Assignment

For this internship, the student is expected to:

• Further develop the current Python code to accommodate more use cases.

• Optimize the computational speed with High-performance computing (HPC).

• Collaborate with software engineers to maintain an Python-MATLAB interface for the code developed.

• Analyze the performance of the code using synthetic data.

Your profile

To be a match for this internship, you:

• Are a master student in the field of Mathematics, Statistics, Computer Science or a related technical field, looking for a non-thesis assignment.

• Have experience in the following topics: Python coding, algorithm development, quadratic optimization and data analysis

• Preferably have experience on optimization environment (such as Pyomo) and solvers (Gurobi and/or CLEX).

• Are able to conduct independent research, and are a team player.

• Have proficient communication skills in English, both written and verbally.

This is a master apprentice internship for a minimum of 3 months, for 4 to 5 days per week (at least 3 days onsite). The start date of this internship is as soon as possible (flexible).

Other requirements you need to meet

• You are enrolled at an educational institute for the entire duration of the internship;

• You are located in the Netherlands to perform your internship. In case you are currently living/studying outside of the Netherlands, your CV/motivation letter includes the willingness to relocate;

• If you are a non-EU citizen, studying in the Netherlands, your university is willing to sign the documents relevant for doing an internship (i.e., Nuffic agreement).

Diversity and inclusion

ASML is an Equal Opportunity Employer that values and respects the importance of a diverse and inclusive workforce. It is the policy of the company to recruit, hire, train and promote persons in all job titles without regard to race, color, religion, sex, age, national origin, veteran status, disability, sexual orientation, or gender identity. We recognize that diversity and inclusion is a driving force in the success of our company.

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