Cable Tree Wiring -- Benchmarking Solvers on a Real-World Scheduling Problem with a Variety of Precedence Constraints

TL;DR

This paper formalizes the cable tree wiring problem as a complex scheduling and routing challenge, benchmarking different solver approaches on a comprehensive set of real-world instances to identify effective solutions.

Contribution

It models the cable tree wiring problem as a TSP variant with precedence constraints, proves NP-hardness, and empirically compares CP, OMT, and MIP solvers on a large benchmark.

Findings

CP, OMT, and MIP solvers show varying performance on instances.

The problem is NP-hard, indicating computational complexity.

Benchmark dataset is publicly available for future research.

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 is accepted for inclusion in the MiniZinc challenge 2020.