Strategies for Constrained Optimisation

The latest 6-man chess endgame results confirm that there are many deep forced mates beyond the 50-move rule. Players with potential wins near this limit naturally want to avoid a claim for a draw: optimal play to current metrics does not guarantee feasible wins or maximise the chances of winning against fallible opposition. A new metric and further strategies are defined which support players’ aspirations and improve their prospects of securing wins in the context of a k-move rule

A Feature-Based Comparison of Evolutionary Computing Techniques for Constrained Continuous Optimisation

Evolutionary algorithms have been frequently applied to constrained continuous optimisation problems. We carry out feature based comparisons of different types of evolutionary algorithms such as evolution strategies, differential evolution and particle swarm optimisation for constrained continuous optimisation. In our study, we examine how sets of constraints influence the difficulty of obtaining close to optimal solutions. Using a multi-objective approach, we evolve constrained continuous problems having a set of linear and/or quadratic constraints where the different evolutionary approaches show a significant difference in performance. Afterwards, we discuss the features of the constraints that exhibit a difference in performance of the different evolutionary approaches under consideration.Comment: 16 Pagesm 2 Figure

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

'On the Application of Hierarchical Coevolutionary Genetic Algorithms: Recombination and Evaluation Partners'

This paper examines the use of a hierarchical coevolutionary genetic algorithm under different partnering strategies. Cascading clusters of sub-populations are built from the bottom up, with higher-level sub-populations optimising larger parts of the problem. Hence higher-level sub-populations potentially search a larger search space with a lower resolution whilst lower-level sub-populations search a smaller search space with a higher resolution. The effects of different partner selection schemes amongst the sub-populations on solution quality are examined for two constrained optimisation problems. We examine a number of recombination partnering strategies in the construction of higher-level individuals and a number of related schemes for evaluating sub-solutions. It is shown that partnering strategies that exploit problem-specific knowledge are superior and can counter inappropriate (sub-) fitness measurements

A Robust Optimisation Strategy for Metal Forming Processes

Robustness, reliability, optimisation and Finite Element simulations are of major importance to improve product\ud quality and reduce costs in the metal forming industry. In this paper, we propose a robust optimisation strategy for metal\ud forming processes. The importance of including robustness during optimisation is demonstrated by applying the robust\ud optimisation strategy to an analytical test function and an industrial hydroforming process, and comparing it to deterministic\ud optimisation methods. Applying the robust optimisation strategy significantly reduces the scrap rate for both the analytical\ud test function and the hydroforming proces

Designing optimal urban transport strategies : the role of individual policy instruments and the impact of financial constraints

This paper presents a methodology for the design of optimal transport strategies and the case study results of the methodology for the City of Edinburgh, using the two multi-modal transport/land-use models MARS and TPM. First, a range of policy instruments are optimised in turn and their relative impacts explored. Second, optimisations with and without financial constraints are performed and compared. Although both models produce similar optimal policies, the relative contribution of the instruments differs between models as does the impact on outcome indicators. It is also shown that by careful design it is possible to identify a strategy which costs no more than the do-minimum but which can generate substantial additional benefits. The optimisation methodology is found to be robust, and is able to be used with different transport models, and with and without financial constraints

Project FATIMA Final Report: Part 1.

EXECUTIVE SUMMARY This Final Report covers the results of the EU-funded research project FATIMA (Financial Assistance for Transport Integration in Metropolitan Areas) which had the following objectives: (i) to identify the benefits to the private sector of optimal urban transport strategies, and the potential for obtaining private sector funding to reflect those benefits; (ii) to determine the differences between strategies optimised using public funds and those optimised within the constraints imposed by private funding initiatives; (iii) to propose mechanisms by which private sector funding can be provided so as to achieve appropriately optimal transport strategies while maintaining quality of operation; and (iv) to use the results to provide more general guidance on the role of private sector funding for urban transport in the EU. The project adopted an approach which involved the application of the same study method to nine cities, chosen to reflect a range of urban transport policy contexts in Europe: Edinburgh, Eisenstadt, Helsinki, Merseyside, Oslo, Salerno, Torino, Tromsø and Vienna. This method involved specifying appropriate policy objective functions against which transport strategies could be assessed, and finding the specific strategy that optimised each of these functions. The objective functions covered a range of differing regimes with respect to constraints on public finance and the involvement of the private sector. It was found that, in a majority of the case study cities, optimal socio-economic policies could be funded by road pricing or increased parking charges, considered over a 30 year time horizon. Such measures would typically be used to make it feasible to increase public transport frequency levels or decrease public transport fares. In general it was found to be important that the city transport planning authority had complete control over all transport measures, affecting both private and public transport. However, such strategies are likely to require significant levels of investment and, given current attitudes towards constraints on public spending, it might be politically awkward for the public sector to raise such finance. There is thus a potentially useful role for private finance to be used to help overcome such (short term) financing problems. However, it must be appreciated that the private sector will expect to make a profit on such investment. In cities where optimal policies are funded by travellers, the private sector can be reimbursed by travellers. In cities where it is unfeasible for travellers to fund all the costs of optimal policies, it will be necessary for the private sector to be reimbursed from public funds (raised from taxes). An important issue here is that the use of private finance should not be allowed to replace optimal policies with sub-optimal policies. Whether or not the private sector is involved in financing a strategy, there may be interest in private sector operation of the public transport service. However, evidence on the scale of benefits or losses from such operation is unclear. If, though, a city authority decides that private operation is beneficial, it should use, where legally possible, a franchising model in which it specifies optimal public transport service levels and fares. On the other hand, if a deregulation model is required (in order to comply with national law), private operators should not be given complete freedom to determine the operating conditions which meet their profitability target, even if the level of profitability is itself constrained as a result. There are typically a number of combinations (e.g. of fares and frequency) which achieve a given level of profitability, and not all will be equally effective in terms of public policy objectives

The robust optimisation of metal forming processes

Robustness, reliability, optimisation and Finite Element simulations are of major importance\ud to improve product quality and reduce costs in the metal forming industry. In this paper,\ud we review several possibilities for combining these techniques and propose a robust optimisation\ud strategy for metal forming processes. The importance of including robustness during optimisation\ud is demonstrated by applying the robust optimisation strategy to an analytical test function: for constrained\ud cases, deterministic optimisation will yield a scrap rate of about 50% whereas the robust\ud counterpart reduced this to the required 3 c reliability level