A robust-CVaR optimization approach with application to breast cancer therapy

Operational research techniques applied throughout cancer care services: a review

“…Importantly, the tumour should receive enough radiation, called target coverage, while normal tissues and surrounding organs should receive as little as possible, called organ sparing. For example, some models minimise the "conditional value-at-risk", which is the average dose that is received in the parts of an organ that receive the highest dose (Chan et al, 2014;Mahmoudzadeh et al, 2016). Different optimisation, heuristic and simulation methods have been used on these problems.…”

“…Some of these address the fluence map optimisation problem (Cabrera, Ehrgott, Mason, & Philpott, 2014;Chan, Mahmoudzadeh, & Purdie, 2014;Mahmoudzadeh, Purdie, & Chan, 2016;Van Haveren et al, 2017). Chan and Mišić (2013) and Aleman, Wallgren, Romeijn, and Dempsey (2014) optimise fluence maps over the whole series of treatment sessions, called fractions.…”

“…Jalalimanesh et al (2017) develop an agent-based simulation of tumour growth and use the Q-learning algorithm, a type of reinforcement learning, to optimise. A series of papers use robust optimisation to capture the uncertainty in patients' breathing patterns (Chan & Mišić, 2013;Chan et al, 2014;Mahmoudzadeh et al, 2016). Chan and Mišić (2013) update what is known about a patient's breathing each treatment to help with planning the next treatment.…”

“…This is modelled as a series of linear programs. Mahmoudzadeh et al (2016) use constraint generation (a decomposition method) to solve the robust optimisation first presented by Chan et al (2014).…”

Minimizing Risk Exposure When the Choice of a Risk Measure Is Ambiguous

“…In addition, Artzner et al (1999) introduced positive homogeneity and Kusuoka (2001) formally addressed the property of law invariance, which together naturally lead to the use of a measure known as conditional value at risk (CVaR) (see Artzner et al 1999, Rockafellar andUryasev 2000). Although the CVaR measure is now being used in a wide range of applications such as healthcare (see Chan et al 2014), supply chain (see Carneiro et al 2010), network design (see Babazadeh et al 2011), vehicle routing (see Toumazis and Kwon 2013), energy (see Jabr 2005), etc., there is still some resistance toward adopting such a measure as a gold standard. Perhaps one of the most important issues is that the class of CVaR measures can only capture a limited spectrum of risk attitudes and thus might not be able to accurately represent the risk aversion of some coherent decision or policy makers.…”