Numerical Strategies for Mixed-Integer Optimization of Power-Split and Gear Selection in Hybrid Electric Vehicles

This paper presents numerical strategies for a computationally efficient energy management system that co-optimizes the power split and gear selection of a hybrid electric vehicle (HEV). We formulate a mixed-integer optimal control problem (MIOCP) that is transcribed using multiple-shooting into a mixed-integer nonlinear program (MINLP) and then solved by nonlinear model predictive control. We present two different numerical strategies, a Selective Relaxation Approach (SRA), which decomposes the MINLP into several subproblems, and a Round-n-Search Approach (RSA), which is an enhancement of the known ‘relax-n-round’ strategy. Subsequently, the resulting algorithmic performance and optimality of the solution of the proposed strategies are analyzed against two benchmark strategies; one using rule-based gear selection, which is typically used in production vehicles, and the other using dynamic programming (DP), which provides a global optimum of a quantized version of the MINLP. The results show that both SRA and RSA enable about\ua03.6%\ua0cost reduction compared to the rule-based strategy, while still being within\ua01%\ua0of the DP solution. Moreover, for the case studied RSA takes about\ua035%\ua0less mean computation time compared to SRA, while both SRA and RSA being about\ua099\ua0times faster than DP. Furthermore, both SRA and RSA were able to overcome the infeasibilities encountered by a typical rounding strategy under different drive cycles. The results show the computational benefit of the proposed strategies, as well as the energy saving possibility of co-optimization strategies in which actuator dynamics are explicitly included

Some mathematical aspects of price optimisation

Calculation of an optimal tariff is a principal challenge for pricing actuaries. In this contribution we are concerned with the renewal insurance business discussing various mathematical aspects of calculation of an optimal renewal tariff. Our motivation comes from two important actuarial tasks, namely a) construction of an optimal renewal tariff subject to business and technical constraints, and b) determination of an optimal allocation of certain premium loadings. We consider both continuous and discrete optimisation and then present several algorithmic sub-optimal solutions. Additionally, we explore some simulation techniques. Several illustrative examples show both the complexity and the importance of the optimisation approach

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

The intersection of machine learning with forecasting and optimisation: theory and applications

Forecasting and optimisation are two major fields of operations research that are widely used in practice. These methods have contributed to each other growth in several ways. However, the nature of the relationship between these two fields and integrating them have not been explored or understood enough. We advocate the integration of these two fields and explore several problems that require both forecasting and optimisation to deal with the uncertainties. We further investigate some of the methodologies that lie at the intersection of machine learning with prediction and optimisation to address real-world problems. Finally, we provide several research directions for those interested to work in this domain