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A Constructive Cooperative Coevolutionary Algorithm Applied to Press Line Optimisation A Constructive Cooperative Coevolutionary Algorithm Applied to Press Line Optimisation Emile Glorieux1*, Bo Svensson1, Fredrik Danielsson1, and Bengt Lennartson1,2 * Corresponding author: Tel.: +46 520 22 32 69; Fax: +46 520 22 30 99; Email: emile.glorieux@hv.se 1Department of Engineering Science, University West, Trollhättan, Sweden 2Department of Signals and Systems, Chalmers University of Technology, Gothenburg, Sweden ABSTRACT Simulationbased optimisation often considers computationally expensive problems. Successfully optimising such large scale and complex problems within a practical timeframe is a challenging task. Optimisation techniques to fulfil this need to be developed. A technique to address this involves decomposing the considered problem into smaller subproblems. These subproblems are then optimised separately. In this paper, an efficient algorithm for simulationbased optimisation is proposed. The proposed algorithm extends the cooperative coevolutionary algorithm, which optimises subproblems separately. To optimise the subproblems, the proposed algorithm enables using a deterministic algorithm, next to stochastic genetic algorithms, getting the flexibility of using either type. It also includes a constructive heuristic that creates good initial feasible solutions to reduce the number of fitness calculations. The extension enables solving complex, computationally expensive problems efficiently. The proposed algorithm has been applied on automated sheet metal press lines from the automotive industry. This is a highly complex optimisation problem due to its nonlinearity and high dimensionality. The optimisation problem is to find control parameters that maximises the line’s production rate. These control parameters determine velocities, time constants, and cam values for critical interactions between components. A simulation model is used for the fitness calculation during the optimisation. The results show that the proposed algorithm manages to solve the press line optimisation problem efficiently. This is a step forward in press line optimisation since this is to the authors’ knowledge the first time a press line has been optimised efficiently in this way. 1. INTRODUCTION Practical optimisation problems often have high dimensionality and the fitness calculations are computationally expensive [1], e.g. in the case of simulationbased optimisation. The “curseofdimensionality” for optimisation problems states that high dimensionality results in an exponential difficulty [2]. An increase in difficulty is even more pronounced if there are nonlinear parameter interactions and a multimodal search space [3]. All this makes it very hard to find optimal solutions efficiently, within a practical timeframe. In engineering optimisation applications, the critical limitation for applying optimisation techniques on problems that are represented by computer simulation models, is the computational expense of the fitness calculations [4]. In this work, the considered engineering optimisation application is a sheet metal tandem press line. The optimisation problem is to find optimal values for the control system parameters [5]. The control system manages, among other things, the speed, the robot paths and the start/stop signals of the motions of the material handling robots and the presses in the press line. Nowadays, these process control parameters are determined online, manually, by trial and error. This approach is time consuming, not without risk of damaging the robot grippers or/and the press dies, and relatively unreliable since it is highly dependent on the experience of the operator. By using simulationbased optimisation techniques, optimal process control parameters can be determined more efficiently and reliably, and nearly without risks of damaging the equipment. The press line problem is subject to the curseofdimensionality. Due to its complexity, multimodality and nonlinearity, finding a near optimal solution might exceed the human’s cognitive capabilities. There are over a hundred different parameters in the control system of an automated sheet metal press line. It is not practical to model it into a set of mathematical expressions. Instead, it was represented by a computer simulation model. The optimisation software works in concert with the simulation model to perform the fitness calculations. The simulation model provides the robots and presses motion profiles to calculate the fitness value for the trial solutions generated by the optimiser. Because of the high dimensionality and the computationally expensive fitness calculations, selecting a suitable optimisation algorithm or search procedure is challenging. It must be able to handle the high number of dimensions, while keeping the number of fitness calculations limited to solve it within the practical timeframe.
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Transcript  A Constructive Cooperative Coevolutionary Algorithm Applied to Press Line Optimisation A Constructive Cooperative Coevolutionary Algorithm Applied to Press Line Optimisation Emile Glorieux1*, Bo Svensson1, Fredrik Danielsson1, and Bengt Lennartson1,2 * Corresponding author: Tel.: +46 520 22 32 69; Fax: +46 520 22 30 99; Email: emile.glorieux@hv.se 1Department of Engineering Science, University West, Trollhättan, Sweden 2Department of Signals and Systems, Chalmers University of Technology, Gothenburg, Sweden ABSTRACT Simulationbased optimisation often considers computationally expensive problems. Successfully optimising such large scale and complex problems within a practical timeframe is a challenging task. Optimisation techniques to fulfil this need to be developed. A technique to address this involves decomposing the considered problem into smaller subproblems. These subproblems are then optimised separately. In this paper, an efficient algorithm for simulationbased optimisation is proposed. The proposed algorithm extends the cooperative coevolutionary algorithm, which optimises subproblems separately. To optimise the subproblems, the proposed algorithm enables using a deterministic algorithm, next to stochastic genetic algorithms, getting the flexibility of using either type. It also includes a constructive heuristic that creates good initial feasible solutions to reduce the number of fitness calculations. The extension enables solving complex, computationally expensive problems efficiently. The proposed algorithm has been applied on automated sheet metal press lines from the automotive industry. This is a highly complex optimisation problem due to its nonlinearity and high dimensionality. The optimisation problem is to find control parameters that maximises the line’s production rate. These control parameters determine velocities, time constants, and cam values for critical interactions between components. A simulation model is used for the fitness calculation during the optimisation. The results show that the proposed algorithm manages to solve the press line optimisation problem efficiently. This is a step forward in press line optimisation since this is to the authors’ knowledge the first time a press line has been optimised efficiently in this way. 1. INTRODUCTION Practical optimisation problems often have high dimensionality and the fitness calculations are computationally expensive [1], e.g. in the case of simulationbased optimisation. The “curseofdimensionality” for optimisation problems states that high dimensionality results in an exponential difficulty [2]. An increase in difficulty is even more pronounced if there are nonlinear parameter interactions and a multimodal search space [3]. All this makes it very hard to find optimal solutions efficiently, within a practical timeframe. In engineering optimisation applications, the critical limitation for applying optimisation techniques on problems that are represented by computer simulation models, is the computational expense of the fitness calculations [4]. In this work, the considered engineering optimisation application is a sheet metal tandem press line. The optimisation problem is to find optimal values for the control system parameters [5]. The control system manages, among other things, the speed, the robot paths and the start/stop signals of the motions of the material handling robots and the presses in the press line. Nowadays, these process control parameters are determined online, manually, by trial and error. This approach is time consuming, not without risk of damaging the robot grippers or/and the press dies, and relatively unreliable since it is highly dependent on the experience of the operator. By using simulationbased optimisation techniques, optimal process control parameters can be determined more efficiently and reliably, and nearly without risks of damaging the equipment. The press line problem is subject to the curseofdimensionality. Due to its complexity, multimodality and nonlinearity, finding a near optimal solution might exceed the human’s cognitive capabilities. There are over a hundred different parameters in the control system of an automated sheet metal press line. It is not practical to model it into a set of mathematical expressions. Instead, it was represented by a computer simulation model. The optimisation software works in concert with the simulation model to perform the fitness calculations. The simulation model provides the robots and presses motion profiles to calculate the fitness value for the trial solutions generated by the optimiser. Because of the high dimensionality and the computationally expensive fitness calculations, selecting a suitable optimisation algorithm or search procedure is challenging. It must be able to handle the high number of dimensions, while keeping the number of fitness calculations limited to solve it within the practical timeframe. 