Modelling, screening, and solving of optimisation problems: Application to industrial metal forming processes

Coupling Finite Element (FEM) simulations to mathematical optimisation techniques provides a high potential to improve industrial metal forming processes. In order to optimise these processes, all kind of optimisation problems need to be mathematically modelled and subsequently solved using an appropriate optimisation algorithm. Although the modelling part greatly determines the final outcome of optimisation, the main focus in most publications until now was on the solving part of mathematical optimisation, i.e. algorithm development. Modelling is generally performed in an arbitrary way. In this paper, we propose an optimisation strategy for metal forming processes using FEM. It consists of three stages: a structured methodology for modelling optimisation problems, screening for design variable reduction, and a generally applicable optimisation algorithm. The strategy is applied to solve manufacturing problems for an industrial deep drawing process

Computational optimisation of robust sheet forming processes

Mathematical optimisation consists of the modelling and solving of optimisation problems. Although both the modelling and the solving are essential for successfully optimising metal forming problems, much of the research published until now has focussed on the solving part, i.e. the development of a specific optimisation algorithm and its application to a specific optimisation problem for a specific metal forming process. We propose a generally applicable optimisation strategy which makes use of FEM simulations of metal forming processes. It consists of a methodology for modelling optimisation problems related to metal forming. Subsequently, screening is applied to reduce the size of the optimisation problem by selecting only the most important design variables. Finally, the reduced optimisation problem is solved by an efficient optimisation algorithm. However, the above strategy is deterministic, which implies that the robustness of the optimum solution is not taken into account. Robustness is a major item in the metal forming industry, hence the deterministic strategy is extended in order to include noise variables (e.g. material variation) in optimisation. This yields a robust optimisation strategy that enables to optimise to a robust solution of the problem, which contributes significantly to the industrial demand to design robust metal forming processes. Just as the deterministic optimisation strategy, it consists of a modelling, screening and solving stage. The deterministic and robust optimisation strategies are compared to each other by application to an analytical test function

Comparative study of different approaches to solve batch process scheduling and optimisation problems

Effective approaches are important to batch process scheduling problems, especially those with complex constraints. However, most research focus on improving optimisation techniques, and those concentrate on comparing their difference are inadequate. This study develops an optimisation model of batch process scheduling problems with complex constraints and investigates the performance of different optimisation techniques, such as Genetic Algorithm (GA) and Constraint Programming (CP). It finds that CP has a better capacity to handle batch process problems with complex constraints but it costs longer time

Population extremal optimisation for discrete multi-objective optimisation problems

The power to solve intractable optimisation problems is often found through population based evolutionary methods. These include, but are not limited to, genetic algorithms, particle swarm optimisation, differential evolution and ant colony optimisation. While showing much promise as an effective optimiser, extremal optimisation uses only a single solution in its canonical form – and there are no standard population mechanics. In this paper, two population models for extremal optimisation are proposed and applied to a multi-objective version of the generalised assignment problem. These models use novel intervention/interaction strategies as well as collective memory in order to allow individual population members to work together. Additionally, a general non-dominated local search algorithm is developed and tested. Overall, the results show that improved attainment surfaces can be produced using population based interactions over not using them. The new EO approach is also shown to be highly competitive with an implementation of NSGA-II.No Full Tex

Deterministic and robust optimisation strategies for metal forming proceesses

Product improvement and cost reduction have always been important goals in the metal forming industry. The rise of\ud Finite Element simulations for metal forming processes has contributed to these goals in a major way. More recently, coupling\ud FEM simulations to mathematical optimisation techniques has shown the potential to make a further contribution to product\ud improvement and cost reduction.\ud Mathematical optimisation consists of the modelling and solving of optimisation problems. Although both the\ud modelling and the solving are essential for successfully optimising metal forming problems, much of the research published until\ud now has focussed on the solving part, i.e. the development of a specific optimisation algorithm and its application to a specific\ud optimisation problem for a specific metal forming process.\ud In this paper, we propose a generally applicable optimisation strategy which makes use of FEM simulations of metal\ud forming processes. It consists of a structured methodology for modelling optimisation problems related to metal forming.\ud Subsequently, screening is applied to reduce the size of the optimisation problem by selecting only the most important design\ud variables. Screening is also utilised to select the best level of discrete variables, which are in such a way removed from the\ud optimisation problem. Finally, the reduced optimisation problem is solved by an efficient optimisation algorithm. The strategy is\ud generally applicable in a sense that it is not constrained to a certain type of metal forming problems, products or processes. Also\ud any FEM code may be included in the strategy.\ud However, the above strategy is deterministic, which implies that the robustness of the optimum solution is not taken\ud into account. Robustness is a major item in the metal forming industry, hence we extended the deterministic optimisation\ud strategy in order to be able to include noise variables (e.g. material variation) during optimisation. This yielded a robust\ud optimisation strategy that enables to optimise to a robust solution of the problem, which contributes significantly to the industrial\ud demand to design robust metal forming processes. Just as the deterministic optimisation strategy, it consists of a modelling,\ud screening and solving stage.\ud The deterministic and robust optimisation strategies are compared to each other by application to an analytical test\ud function. This application emphasises the need to take robustness into account during optimisation, especially in case of\ud constrained optimisation. Finally, both the deterministic and the robust optimisation strategies are demonstrated by application to\ud an industrial hydroforming example

Frameworks for logically classifying polynomial-time optimisation problems.

We show that a logical framework, based around a fragment of existential second-order logic formerly proposed by others so as to capture the class of polynomially-bounded P-optimisation problems, cannot hope to do so, under the assumption that P ≠ NP. We do this by exhibiting polynomially-bounded maximisation and minimisation problems that can be expressed in the framework but whose decision versions are NP-complete. We propose an alternative logical framework, based around inflationary fixed-point logic, and show that we can capture the above classes of optimisation problems. We use the inductive depth of an inflationary fixed-point as a means to describe the objective functions of the instances of our optimisation problems