Quadratic Unconstrained Binary optimization for the Automotive Paint Shop Problem

The Binary Paint Shop Problem (BPSP) is a combinatorial optimization problem which draws inspiration from the automotive paint shop. Its binary nature, making it a good fit for Quadratic Unconstrained Binary Optimization (QUBO) solvers, has been well studied but its industrial applications are limit...

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Vydané v:IEEE access Ročník 11; s. 1
Hlavní autori: Debevere, Pieter, Sugimura, Masahiko, Parizy, Matthieu
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Piscataway IEEE 01.01.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Automobiles
Automotive engineering
Automotive paint shop
Color
Combinatorial analysis
Constraints
evolutionary algorithms
Heuristic
Image color analysis
Industrial applications
Integers
k-hot constraints
Lower bounds
Mathematical models
Optimization
Paints
Quadratic programming
Quadratic unconstrained binary optimization
scatter search
Tabu search
ISSN:2169-3536, 2169-3536
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Abstract The Binary Paint Shop Problem (BPSP) is a combinatorial optimization problem which draws inspiration from the automotive paint shop. Its binary nature, making it a good fit for Quadratic Unconstrained Binary Optimization (QUBO) solvers, has been well studied but its industrial applications are limited. In this paper, in order to expand the industrial applications, QUBO formulations for two generalizations of the BPSP, which are the Multi-Car Paint Shop Problem (MCPSP) and the Multi-Car Multi-Color Paint Shop Problem (MCMCPSP), are proposed. Given the multiple colors, the MCMCPSP is no longer natively binary which increases the problem size and introduces additional constraint factors in the QUBO formulation. Resulting QUBOs are solved using Scatter Search (SS). Furthermore, extensions of the SS that can exploit k-hot constrained structures within the formulations are proposed to compensate the additional complexity introduced by formulating non-binary problems into QUBO. Since no public benchmark database currently exists, random problem instances are generated. Viability of the proposed QUBO solving methods for the MCPSP and MCMCPSP, is highlighted through comparison with an integer-based Random Parallel Multi-start Tabu Search (RPMTS) and a greedy heuristic for the problems. The greedy heuristic has negligible computational requirements and therefore serves as a lower bound on the desired performance. The results for both problems show that better results can be obtained than the greedy heuristic and integer-based RPMTS, by using the novel k-hot extensions of the SS to solve the problems as QUBO.
AbstractList The Binary Paint Shop Problem (BPSP) is a combinatorial optimization problem which draws inspiration from the automotive paint shop. Its binary nature, making it a good fit for Quadratic Unconstrained Binary Optimization (QUBO) solvers, has been well studied but its industrial applications are limited. In this paper, in order to expand the industrial applications, QUBO formulations for two generalizations of the BPSP, which are the Multi-Car Paint Shop Problem (MCPSP) and the Multi-Car Multi-Color Paint Shop Problem (MCMCPSP), are proposed. Given the multiple colors, the MCMCPSP is no longer natively binary which increases the problem size and introduces additional constraint factors in the QUBO formulation. Resulting QUBOs are solved using Scatter Search (SS). Furthermore, extensions of the SS that can exploit k-hot constrained structures within the formulations are proposed to compensate the additional complexity introduced by formulating non-binary problems into QUBO. Since no public benchmark database currently exists, random problem instances are generated. Viability of the proposed QUBO solving methods for the MCPSP and MCMCPSP, is highlighted through comparison with an integer-based Random Parallel Multi-start Tabu Search (RPMTS) and a greedy heuristic for the problems. The greedy heuristic has negligible computational requirements and therefore serves as a lower bound on the desired performance. The results for both problems show that better results can be obtained than the greedy heuristic and integer-based RPMTS, by using the novel k-hot extensions of the SS to solve the problems as QUBO.
Author Debevere, Pieter
Parizy, Matthieu
Sugimura, Masahiko
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SubjectTerms Automobiles
Automotive engineering
Automotive paint shop
Color
Combinatorial analysis
Constraints
evolutionary algorithms
Heuristic
Image color analysis
Industrial applications
Integers
k-hot constraints
Lower bounds
Mathematical models
Optimization
Paints
Quadratic programming
Quadratic unconstrained binary optimization
scatter search
Tabu search
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Title Quadratic Unconstrained Binary optimization for the Automotive Paint Shop Problem
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