Cable tree wiring - benchmarking solvers on a real-world scheduling problem with a variety of precedence constraints

Abstract

Cable trees are used in industrial products to transmit energy and information between different product parts. To this date, they are mostly assembled by humans and only few automated manufacturing solutions exist using complex robotic machines. For these machines, the wiring plan has to be translated into a wiring sequence of cable plugging operations to be followed by the machine. In this paper, we study and formalize the problem of deriving the optimal wiring sequence for a given layout of a cable tree. We summarize our investigations to model this cable tree wiring problem (CTW). as a traveling salesman problem with atomic, soft atomic, and disjunctive precedence constraints as well as tour-dependent edge costs such that it can be solved by state-of-the-art constraint programming (CP), Optimization Modulo Theories (OMT), and mixed-integer programming (MIP). solvers. It is further shown, how the CTW problem can be viewed as a soft version of the coupled tasks scheduling problem. We discuss various modeling variants for the problem, prove its NP-hardness, and empirically compare CP, OMT, and MIP solvers on a benchmark set of 278 instances. The complete benchmark set with all models and instance data is available on github and was included in the MiniZinc challenge 2020.

Automatic constraint programming solver selection method based on machine learning for the cable tree wiring problem

“…To our knowledge, only one study has compared the performance of CP solvers on the CTW problem in practical scheduling scenarios involving various precedence constraints. Hence, within this chapter, we leveraged the primary experimental data provided by Koehler et al (2021) [1], systematically organizing and analyzing the datasets for our study.…”

“…Converting MiniZinc to FlatZinc is a unified interface for different solvers, allowing seamless switching between them to identify the optimal solution. This allows us to explore diverse solvers and determine the most effective resolution for the given problem [1,26].…”

“…Hence, within this chapter, we leveraged the primary experimental data provided by Koehler et al. (2021) [1], systematically organizing and analyzing the datasets for our study.…”

“…In our experiments, we adopted the model established by Koehler et al (2021) [1], which is based on a quadratic permutation representation of the traveling salesman problem (TSP) [27]. This model aims to formalize problem descriptions, serving as a foundational framework for empirical studies with various solvers.…”

“…Finding the optimal insertion sequence in a given fixed layout is called the cable tree wiring problem (CTW) [1]. The CTW problem commonly arises in industrial design, with cable tree wiring in automotive design being a critical challenge.…”