A multiobjective gradient-based algorithm has been developed for the purpose of dose distribution optimization in external beam conformal radiotherapy. This algorithm is based on the concept of gathering the values of all objectives into a single value. The weighting factors of the composite objective values are varied in different steps, allowing the reconstruction of the trade-off surfaces (three or more objectives) or curves (two objectives) which define the boundary between the feasible and non-feasible domain regions. The analysis of these curves allows the decision-maker to select the solution that best fits the clinical goals. In contrast to all the other algorithms, our method provides not a single solution but a sample of solutions representing all possible clinical importance factors (weights) for the objectives used. The application of this algorithm to two test cases shows that a correct selection for the importance factors to multiply the individual objectives in the global objective value is not trivial and that the location and shape of the boundary region between the feasible and non-feasible solution regions are case dependent. Provided that the individual objective functions are analytically differentiable and that the number of objectives is the range of two to three, the computation times are acceptable for clinical use. Furthermore, the optimization for a unique combination of importance factors within the aggregate objective function is performed in less than 1 min.

In high dose rate (HDR) brachytherapy, conventional dose optimization algorithms consider multiple objectives in the form of an aggregate function that transforms the multiobjective problem into a single-objective problem. As a result, there is a loss of information on the available alternative possible solutions. This method assumes that the treatment planner exactly understands the correlation between competing objectives and knows the physical constraints. This knowledge is provided by the Pareto trade-off set obtained by single-objective optimization algorithms with a repeated optimization with different importance vectors. A mapping technique avoids non-feasible solutions with negative dwell weights and allows the use of constraint free gradient-based deterministic algorithms. We compare various such algorithms and methods which could improve their performance. This finally allows us to generate a large number of solutions in a few minutes. We use objectives expressed in terms of dose variances obtained from a few hundred sampling points in the planning target volume (PTV) and in organs at risk (OAR). We compare two- to four-dimensional Pareto fronts obtained with the deterministic algorithms and with a fast-simulated annealing algorithm. For PTV-based objectives, due to the convex objective functions, the obtained solutions are global optimal. If OARs are included, then the solutions found are also global optimal, although local minima may be present as suggested.

We propose a hybrid multiobjective (MO) evolutionary optimization algorithm (MOEA) for intensity-modulated radiotherapy inverse planning and apply it to optimize the number of incident beams, their orientations and intensity profiles. The algorithm produces a set of efficient solutions, which represent different clinical trade-offs and contains information such as variety of dose distributions and dose-volume histograms. No importance factors are required and solutions can be obtained in regions not accessible by conventional weighted sum approaches. The application of the algorithm using a test case, a prostate and a head and neck tumour case is shown. The results are compared with MO inverse planning using a gradient-based optimization algorithm.

In conventional dose optimization algorithms, in brachytherapy, multiple objectives are expressed in terms of an aggregating function which combines individual objective values into a single utility value, making the problem single objective, prior to optimization. A multiobjective genetic algorithm (MOGA) was developed for dose optimization based on an a posteriori approach, leaving the decision-making process to a planner and offering a representative trade-off surface of the various objectives. The MOGA provides a flexible search engine which provides the maximum of information for a decision maker. Tests performed with various treatment plans in brachytherapy have shown that MOGA gives solutions which are superior to those of traditional dose optimization algorithms. Objectives were proposed in terms of the COIN distribution and differential volume histograms, taking into account patient anatomy in the optimization process.

Multiple objectives must be considered in anatomy-based dose optimization for high-dose-rate brachytherapy and a large number of parameters must be optimized to satisfy often competing objectives. For objectives expressed solely in terms of dose variances, deterministic gradient-based algorithms can be applied and a weighted sum approach is able to produce a representative set of non-dominated solutions. As the number of objectives increases, or non-convex objectives are used, local minima can be present and deterministic or stochastic algorithms such as simulated annealing either cannot be used or are not efficient. In this case we employ a modified hybrid version of the multi-objective optimization algorithm NSGA-II. This, in combination with the deterministic optimization algorithm, produces a representative sample of the Pareto set. This algorithm can be used with any kind of objectives, including non-convex, and does not require artificial importance factors. A representation of the trade-off surface can be obtained with more than 1000 non-dominated solutions in 2-5 min. An analysis of the solutions provides information on the possibilities available using these objectives. Simple decision making tools allow the selection of a solution that provides a best fit for the clinical goals. We show an example with a prostate implant and compare results obtained by variance and dose-volume histogram (DVH) based objectives.