Multi‐objective optimization for cost‐efficient and resilient machining under tool wear

Tucker

2022

Sci Rep

Mixed-Integer Linear Programming (MILP) plays an important role across a range of scientific disciplines and within areas of strategic importance to society. The MILP problems, however, suffer from combinatorial complexity. Because of integer decision variables, as the problem size increases, the number of possible solutions increases super-linearly thereby leading to a drastic increase in the computational effort. To efficiently solve MILP problems, a “price-based” decomposition and coordination approach is developed to exploit 1. the super-linear reduction of complexity upon the decomposition and 2. the geometric convergence potential inherent to Polyak’s stepsizing formula for the fastest coordination possible to obtain near-optimal solutions in a computationally efficient manner. Unlike all previous methods to set stepsizes heuristically by adjusting hyperparameters, the key novel way to obtain stepsizes is purely decision-based: a novel “auxiliary” constraint satisfaction problem is solved, from which the appropriate stepsizes are inferred. Testing results for large-scale Generalized Assignment Problems demonstrate that for the majority of instances, certifiably optimal solutions are obtained. For stochastic job-shop scheduling as well as for pharmaceutical scheduling, computational results demonstrate the two orders of magnitude speedup as compared to Branch-and-Cut. The new method has a major impact on the efficient resolution of complex Mixed-Integer Programming problems arising within a variety of scientific fields.

Section: Demonstration Of Convergence Of Multipliers Based On a Small...mentioning

confidence: 99%

Surrogate “Level-Based” Lagrangian Relaxation for mixed-integer linear programming

Tucker

2022

Sci Rep

“…Such model is commonly used in reliability analysis of equipment failures. [43] In practice, tool wear x increases as more parts are processed by the tool before it is replaced. Without loss of generality, it is assumed in this paper that the tool wear of a new tool is zero and that a tool is replaced for every N parts processed.…”

Section: Process-level Model and Controlmentioning

confidence: 99%

A simulation‐based integrated virtual testbed for dynamic optimization in smart manufacturing systems

Sun

et al. 2022

J Adv Manuf & Process

In a manufacturing system, production control-related decision-making activities occur at different levels. At the process level, one of the main control activities is to tune the parameters of individual manufacturing equipment. At the system level, the main activity is to coordinate production resources and to route parts to appropriate workstations based on their processing requirement, priority indices, and control policy. At the factory level, the goal is to plan and schedule the processing of parts at different operations for the entire system in order to optimize certain objectives. Note that the results of such activities at different levels are closely coupled and affect the overall performance of the manufacturing system as a whole. Therefore, it is important to systematically integrate these control and optimization activities into one unified platform to ensure the goal of each individual activity is aligned with the overall performance of the system. In this paper, we develop a simulation-based virtual testbed that implements dynamic optimization, automatic information exchange, and decision-making from the process-level, system-level, and factory-level of a manufacturing system into an integrated computation environment. This is demonstrated by connecting a Python-based numerical computation program, discrete-event simulation software (Simul8), and an optimization solver (CPLEX) via a third-party master program. The application of this simulation-based virtual testbed is illustrated by a case study in a machining shop.

“…Limited machine capacity brings a layer of difficulty since multiple "individual-job" subproblem are considered together competing for limited resources (machines). Another difficulty arises because of uncertainties, including processing times [23][24][25][26][27][28] and scrap [29][30][31].…”

Section: Example 2: Stochastic Job-shop Scheduling With the Considera...mentioning

confidence: 99%

Surrogate "Level-Based" Lagrangian Relaxation for Mixed-Integer Linear Programming

Tucker

2022

Preprint

Mixed-Integer Linear Programming (MILP) plays an important role across a range of scientific disciplines and within areas of strategic importance to society. The MILP problems, however, suffer from combinatorial complexity. Because of integer decision variables, as the problem size increases, the number of possible solutions increases super-linearly thereby leading to a drastic increase in the computational effort. To efficiently solve MILP problems, a “price-based” decomposition and coordination approach is developed to exploit 1. the super-linear reduction of complexity upon the decomposition and 2. the geometric convergence potential inherent to Polyak’s step-sizing formula for the fastest coordination possible to obtain near-optimal solutions in a computationally efficient manner. Unlike all previous methods to set step-sizes heuristically by adjusting hyper-parameters, the key novel way to obtain step-sizes is purely decision-based: a novel “auxiliary” constraint satisfaction problem is solved, from which the appropriate step-sizes are inferred. Testing results for large-scale Generalized Assignment Problems (GAP) demonstrate that for the majority of instances, certifiably optimal solutions are obtained. For stochastic job-shop scheduling as well as for pharmaceutical scheduling, computational results demonstrate the two orders of magnitude speedup as compared to frequently used Branch-and-Cut (B&C). SLBLR has a major impact on the efficient resolution of complex Mixed-Integer Programming (MIP) problems arising within a variety of scientific fields.