Multi-objective genetic algorithms for scheduling of radiotherapy treatments for categorised cancer patients

Abstract. This paper presents a multi-objective optimisation model and algorithms for scheduling of radiotherapy treatments for categorised cancer patients. The model is developed considering real life radiotherapy treatment processes at Arden Cancer Centre, in the UK. The scheduling model considers various real life constraints, such as doctors ’ rota, machine availability, patient’s category, waiting time targets, (i.e., the time when a patient should receive the first treatment fraction), and so on. Two objectives are defined: minimisation of the Average patient’s waiting time and minimisation of Average length of breaches of waiting time targets. Three Genetic Algorithms (GAs) are developed and implemented which treat radiotherapy patient categories, namely emergency, palliative and radical patients in different ways: (1) Standard-GA, which considers all patient categories equally, (2) KB-GA, which has an embedded knowledge on the scheduling of emergency patient category and (3) Weighted-GA, which operates with different weights given to the patient categories. The performance of schedules generated by using the three GAs is compared using the statistical analyses. The results show that KB-GA generated the schedules with best performance considering emergency patients and slightly outperforms the other two GAs when all patient categories are considered simultaneously. KB-GA and Standard-GA generated better performance schedules for emergency and palliative patient

Radiotherapy Patient Scheduling During Pandemics

With the Covid-19 outbreak happening worldwide, clinically vulnerable people should be of concern, as they are more likely to be exposed to the virus. Cancer patients with weak immune systems are a group of aforementioned people that often have to undergo radiotherapy treatment sessions every day for several weeks. Therefore, special measures are to take place for more protection. During the treatment process, they will be assigned to Linear Accelerator (LINAC) machines that are located in separate rooms of the radiotherapy center. During each visit, they are in close contact with other patients that are assigned to the same LINAC, but for different time slots. Our research focuses on scheduling radiotherapy patients, using two mixed-integer linear programming models, to minimize the total number of potential interactions between patients. A secondary objective is then proposed to choose among the set of optimal solutions, and the models' complexity growth is discussed. Then, we introduce a heuristic algorithm to increase the efficiency of the proposed model for large instances and use a visual step-by-step example to further elaborate the algorithm details. Finally, small numerical examples are used to demonstrate the effectiveness of the models, followed by larger instances from our partner clinic, the Grand River Regional Cancer Center (GRRCC). The results show that implementing the proposed model and the heuristic will decrease the number of interactions up to 75%, compared to the centre's original schedule

ROBUST RADIOTHERAPY APPOINTMENT SCHEDULING

Optimal scheduling of patients waiting for radiation treatments is a quite challenging operational problem in radiotherapy clinics. Long waiting times for radiotherapy treatments is mainly due to imbalanced supply and demand of radiotherapy services, which negatively affects the effectiveness and efficiency of the healthcare delivered. On the other hand, variations in the time required to set-up machines for each individual patient as well as patient treatment times make this problem even more involved. Efficient scheduling of patients on the waiting list is essential to reduce the waiting time and its possible adverse direct and indirect impacts on the patient. This research is focused on the problem of scheduling patients on a prioritized radiotherapy waiting list while the rescheduling of already booked patients is also possible. The aforementioned problem is formulated as a mixed-integer program that aims for maximizing the number of newly scheduled patients such that treatment time restrictions, scheduling of patients on consecutive days on the same machine, covering all required treatment sessions, as well as the capacity restriction of machines are satisfied. Afterwards, with the goal of protecting the schedule against treatment time perturbations, the problem is reformulated as a cardinality-constrained robust optimization model. This approach provides some insights into the adjustment of the level of robustness of the patients schedule over the planning horizon and protection against uncertainty. Further, three metaheuristics, namely Whale Optimization Algorithm, Particle Swarm Optimization, and Firefly Algorithm are proposed as alternative solution methods. Our numerical experiments are designed based on a case study inspired from a real radiotherapy clinic. The first goal of experiments is to analyze the performance of proposed robust radiotherapy appointment scheduling (ASP) model in terms of feasibility of schedule and the number of scheduled patients by the aid of Monte-Carlo simulation. Our second goal is to compare the solution quality and CPU time of the proposed metaheuristics with a commercial solver. Our experimental results indicate that by only considering half of patients treatment times as worst-case scenario, the schedule proposed by the robust RAS model is feasible in the presence of all randomly generated scenarios for this uncertain parameter. On the other hand, protecting the schedule against uncertainty at the aforementioned level would not significantly reduce the number of scheduled patients. Finally, our numerical results on the three metaheuristics indicate the high quality of their converged solution as well as the reduced CPU time comparing to a commercial solver

Optimal Multi-Drug Chemotherapy Control Scheme for Cancer Treatment. Design and development of a multi-drug feedback control scheme for optimal chemotherapy treatment for cancer. Evolutionary multi-objective optimisation algorithms were used to achieve the optimal parameters of the controller for effective treatment of cancer with minimum side effects.

Cancer is a generic term for a large group of diseases where cells of the body lose their normal mechanisms for growth so that they grow in an uncontrolled way. One of the most common treatments of cancer is chemotherapy that aims to kill abnormal proliferating cells; however normal cells and other organs of the patients are also adversely affected. In practice, it¿s often difficult to maintain optimum chemotherapy doses that can maximise the abnormal cell killing as well as reducing side effects. The most chemotherapy drugs used in cancer treatment are toxic agents and usually have narrow therapeutic indices, dose levels in which these drugs significantly kill the cancerous cells are close to the levels which sometime cause harmful toxic side effects. To make the chemotherapeutic treatment effective, optimum drug scheduling is required to balance between the beneficial and toxic side effects of the cancer drugs. Conventional clinical methods very often fail to find drug doses that balance between these two due to their inherent conflicting nature. In this investigation, mathematical models for cancer chemotherapy are used to predict the number of tumour cells and control the tumour growth during treatment. A feedback control method is used so as to maintain certain level of drug concentrations at the tumour sites. Multi-objective Genetic Algorithm (MOGA) is then employed to find suitable solutions where drug resistances and drug concentrations are incorporated with cancer cell killing and toxic effects as design objectives. Several constraints and specific goal values were set for different design objectives in the optimisation process and a wide range of acceptable solutions were obtained trading off among different conflicting objectives. Abstract v In order to develop a multi-objective optimal control model, this study used proportional, integral and derivative (PID) and I-PD (modified PID with Integrator used as series) controllers based on Martin¿s growth model for optimum drug concentration to treat cancer. To the best of our knowledge, this is the first PID/I-PD based optimal chemotherapy control model used to investigate the cancer treatment. It has been observed that some solutions can reduce the cancer cells up to nearly 100% with much lower side effects and drug resistance during the whole period of treatment. The proposed strategy has been extended for more drugs and more design constraints and objectives.Libyan Ministry of Higher Educatio

An application of genetic algorithms to chemotherapy treatment.

The present work investigates methods for optimising cancer chemotherapy within the bounds of clinical acceptability and making this optimisation easily accessible to oncologists. Clinical oncologists wish to be able to improve existing treatment regimens in a systematic, effective and reliable way. In order to satisfy these requirements a novel approach to chemotherapy optimisation has been developed, which utilises Genetic Algorithms in an intelligent search process for good chemotherapy treatments. The following chapters consequently address various issues related to this approach. Chapter 1 gives some biomedical background to the problem of cancer and its treatment. The complexity of the cancer phenomenon, as well as the multi-variable and multi-constrained nature of chemotherapy treatment, strongly support the use of mathematical modelling for predicting and controlling the development of cancer. Some existing mathematical models, which describe the proliferation process of cancerous cells and the effect of anti-cancer drugs on this process, are presented in Chapter 2. Having mentioned the control of cancer development, the relevance of optimisation and optimal control theory becomes evident for achieving the optimal treatment outcome subject to the constraints of cancer chemotherapy. A survey of traditional optimisation methods applicable to the problem under investigation is given in Chapter 3 with the conclusion that the constraints imposed on cancer chemotherapy and general non-linearity of the optimisation functionals associated with the objectives of cancer treatment often make these methods of optimisation ineffective. Contrariwise, Genetic Algorithms (GAs), featuring the methods of evolutionary search and optimisation, have recently demonstrated in many practical situations an ability to quickly discover useful solutions to highly-constrained, irregular and discontinuous problems that have been difficult to solve by traditional optimisation methods. Chapter 4 presents the essence of Genetic Algorithms, as well as their salient features and properties, and prepares the ground for the utilisation of Genetic Algorithms for optimising cancer chemotherapy treatment. The particulars of chemotherapy optimisation using Genetic Algorithms are given in Chapter 5 and Chapter 6, which present the original work of this thesis. In Chapter 5 the optimisation problem of single-drug chemotherapy is formulated as a search task and solved by several numerical methods. The results obtained from different optimisation methods are used to assess the quality of the GA solution and the effectiveness of Genetic Algorithms as a whole. Also, in Chapter 5 a new approach to tuning GA factors is developed, whereby the optimisation performance of Genetic Algorithms can be significantly improved. This approach is based on statistical inference about the significance of GA factors and on regression analysis of the GA performance. Being less computationally intensive compared to the existing methods of GA factor adjusting, the newly developed approach often gives better tuning results. Chapter 6 deals with the optimisation of multi-drug chemotherapy, which is a more practical and challenging problem. Its practicality can be explained by oncologists' preferences to administer anti-cancer drugs in various combinations in order to better cope with the occurrence of drug resistant cells. However, the imposition of strict toxicity constraints on combining various anticancer drugs together, makes the optimisation problem of multi-drug chemotherapy very difficult to solve, especially when complex treatment objectives are considered. Nevertheless, the experimental results of Chapter 6 demonstrate that this problem is tractable to Genetic Algorithms, which are capable of finding good chemotherapeutic regimens in different treatment situations. On the basis of these results a decision has been made to encapsulate Genetic Algorithms into an independent optimisation module and to embed this module into a more general and user-oriented environment - the Oncology Workbench. The particulars of this encapsulation and embedding are also given in Chapter 6. Finally, Chapter 7 concludes the present work by summarising the contributions made to the knowledge of the subject treated and by outlining the directions for further investigations. The main contributions are: (1) a novel application of the Genetic Algorithm technique in the field of cancer chemotherapy optimisation, (2) the development of a statistical method for tuning the values of GA factors, and (3) the development of a robust and versatile optimisation utility for a clinically usable decision support system. The latter contribution of this thesis creates an opportunity to widen the application domain of Genetic Algorithms within the field of drug treatments and to allow more clinicians to benefit from utilising the GA optimisation

Novel approaches to radiotherapy treatment scheduling

Radiotherapy represents an important phase of treatment for a large number of cancer patients. It is essential that resources used to deliver this treatment are used efficiently. This thesis approaches the problem of scheduling treatments in a radiotherapy centre. Data about the daily intake of patients are collected and analysed. Several approaches are presented to create a schedule every day. The first presented are constructive approaches, developed due to their simplicity and low computational requirements. The approaches vary the preferred treatment start, machine utilisation reservation levels, and the frequency and number of days in advance with which schedules are created. An Integer Linear Programming (ILP) model is also presented for the problem and used in combination with approaches similar to the ones above. A generalisation of the constructive utilisation threshold approach is developed in order to vary the threshold level for each day according to how far it is from the current day. In addition, the model is evaluated for different sizes of the problem by increasing the rate of patient arrivals per day and the number of machines available. Different machine allocation policies are also evaluated. An exact method is introduced for finding a set of solutions representing the whole Pareto frontier for integer programming problems. It is combined with two robust approaches: the first considers known patients before they are ready to be scheduled, while the second considers sets of predicted patients who might arrive in the near future. A rescheduling approach is also suggested and implemented. A comparison is made amongst the best results from each group of approaches to identify the advantages and disadvantages of each. The robust approaches are found to be the best alternative of the set

A permutation flowshop model with time-lags and waiting time preferences of the patients

The permutation flowshop is a widely applied scheduling model. In many real-world applications of this model, a minimum and maximum time-lag must be considered between consecutive operations. We can apply this model to healthcare systems in which the minimum time-lag could be the transfer times, while the maximum time-lag could refer to the number of hours patients must wait. We have modeled a MILP and a constraint programming model and solved them using CPLEX to find exact solutions. Solution times for both methods are presented. We proposed two metaheuristic algorithms based on genetic algorithm and solved and compared them with each other. A sensitivity of analysis of how a change in minimum and maximum time-lags can impact waiting time and Cmax of the patients is performed. Results suggest that constraint programming is a more efficient method to find exact solutions and changes in the values of minimum and maximum time-lags can impact waiting times of the patients and Cmax significantly