Solving the volumetric modulated arc therapy (VMAT) problem using a sequential convex programming method

MEMPSODE: A global optimization software based on hybridization of population-based algorithms and local searches

This study focuses on the key challenge of achieving high-precision guidance for spacecraft: real-time trajectory optimization. The highly efficient sequential convex programming (SCP) is a potential method to address this issue, but its convergence is difficult to guarantee. To enhance the convergence performance of SCP, this paper proposes a high-dimensional merit-function-based SCP method. The main contribution of this paper is threefold. Firstly, the traditional one-dimensional penalty function used to ensure the convergence of SCP is extended to a high-dimensional merit function, which avoids using the penalty parameter that is difficult to determine in advance. Secondly, to match the high-dimensional merit function, a feasibility-then-optimality convergence strategy is proposed, which is essentially an application of the iterative direction descent property in higher dimensions. Finally, based on the high-dimensional merit function and the feasibility-then-optimality strategy, an iterative algorithm is developed, and its convergence analysis is provided under certain assumptions. In numerical simulations, the effectiveness and robustness of the proposed algorithm are validated using the reentry trajectory optimization problem of a lunar capsule.

Differential evolution with fusion of local and global search strategies

Comprehensive Dosimetric Evaluation of a Biology-Guided Radiotherapy Machine in Treatment Plans for Brain, Lung, Head and Neck, Esophagus, and Prostate Malignancies

Most of the existing evolutionary algorithms to deal with many-objective problems are based on the enhancing of selection strategy. Among them, the reference vector-guided evolutionary algorithm (RVEA) achieves excellent performance. In this paper, a new search engine is combined with RVEA to achieve further performance enhancement of the differential evolutionary (DE) algorithm. In the optimization process of differential evolution algorithm on many-objective problems, improving convergence and maintaining diversity are two different optimization directions, and it is usually difficult to maintain a balance between them. To solve this problem, a new search engine based on DE is proposed. The proposed search engine is implemented based on a cooperative scheme of local and global search strategies. In the local search, the population is divided into several sub-populations, each of which evolves independently using the proposed mutation strategy. The distance between the individuals in each sub-population is relatively close. Therefore, it has a strong exploitation capability, and will not make the population lose diversity. Meanwhile, the selection strategy of RVEA enables the population to maintain diversity, and the DE/rand/1 utilized in global search is sufficient to keep a strong exploration capability. Therefore, the proposed approach can achieve a good balance between exploration and exploitation. The experimental results show that the proposed algorithm performs well in many-objective optimizations up to more than 10 objectives.

Global and local game tree search

An important implementation issue in the design of hybrid evolutionary multiobjective optimization algorithms with local search (i.e., multiobjective memetic algorithms) is how to strike a balance between local search and global search. If local search is applied to all individuals at every generation, almost all computation time is spent by local search. As a result, global search ability of memetic algorithms is not well utilized. We can use three ideas for decreasing the computation load of local search. One idea is to apply local search to only a small number of individuals. This idea can be implemented by introducing a local search probability, which is used to choose only a small number of initial solutions for local search from the current population. Another idea is a periodical (i.e., intermittent) use of local search. This idea can be implemented by introducing a local search interval (e.g., every 10 generations), which is used to specify when local search is applied. The other idea is an early termination of local search. Local search for each initial solution is terminated after a small number of neighbors are examined. This idea can be implemented by introducing a local search length, which is the number of examined neighbors in a series of iterated local search from a single initial solution. In this paper, we discuss the use of these three ideas to strike a local-global search balance. Through computational experiments on a two-objective 500-item knapsack problem, we compare various settings of local search such as short local search from all individuals at every generation, long local search from only a few individuals at every generation, and periodical long local search from all individuals. Global search in this paper means genetic search by crossover and mutation in multiobjective memetic algorithms.

<p>This dissertation investigates the dosimetric influence of mixed photon beams in volumetric modulated arc therapy (VMAT) for prostate cancer and presents new algorithmic frameworks for simultaneous optimization of mixed photon beams in VMAT.</p> <p>The potential scope of using mixed photon VMAT for prostate cancer was first studied by using a clinical treatment planning software. A significant reduction in doses to bladder (P < 0.05) and rectum (P < 0.05), and similar target dose conformity was achieved by mixed photon (6&15 MV) VMAT compared to single energy (6 or 15 MV) VMAT. Radiobiological effectiveness was evaluated through tumor control probability (TCP) and normal tissue complication probability (NTCP). Across four different parameter sets for grade ≥ 2 rectal bleeding, mixed energy reduced NTCP by 1.3%, 4.1%, 0.1% and 2.6%, respectively, compared to single energy (P < 0.05). For bladder, mixed energy reduced mean equivalent uniform dose by 2 Gy (P < 0.05). In this study, however, each energy plan had to be optimized separately followed by their summation in order to generate a mixed photon VMAT plan. From optimization standpoint, this approach limits the solution search space.</p> <p>With the aim of furthering current optimization approach, a comprehensive algorithmic framework was presented for simultaneous optimization of mixed photon beams (6 & 18 MV) in VMAT (MP-VMAT). This was solved heuristically in two steps, accounting for dosimetric and mechanical constraints. This novel proof of concept was tested for its practicality and dosimetric outcome on two prostate cancer cases. In both cases, the proposed approach was able to reduce doses to rectum and bladder while maintaining the target dose coverage. Overall results suggested the viability and dosimetric benefits of the proposed concept, compared to single energy approach, in VMAT planning.</p> <p>Next, the concept of MP-VMAT was expanded for a single-arc treatment, consisting of energy dependent partial arcs. To this end, the first formalism was presented to optimize mixed photon energy (6 & 18 MV) fluences along with corresponding arc locations and lengths over a full 360o gantry rotation. The radiobiological and dosimetric effectiveness of this framework was tested on prostate cases with varying body types. The proposed technique was able to reduce bladder and rectum complication by 14% and 7%, respectively, in large size patients compared to single energy VMAT.</p> <p>The novel concept of simultaneous optimization of multi-energy introduced in this dissertation can also be employed in learning based approach for beam angle optimization in intensity modulated radiation therapy treatments as well as in optimization of mixed modality treatments.</p>

This chapter is devoted to the parametrization of memetic algorithms and how to find a good balance between global and local search. This is one of the most pressing questions when designing a hybrid algorithm. The idea of hybridization is to combine the advantages of different components. But if one components dominates another one, hybridization may become more hindering than useful and computational effort may be wasted. For the case of memetic algorithms, if the effect of local search is too strong, the algorithm may quickly get stuck in local optima of bad quality.Moreover, the algorithm is likely to rediscover the same local optimum over and over again. Lastly, an excessive local search quickly leads to a loss of diversity within the population.

Purpose: Rotational IMRT delivery techniques, such as volumetric modulated arc therapy (VMAT), are alternatives to standard IMRT delivery, claiming faster delivery and equally good dose distributions. In reality there is a cost to faster delivery times. The purpose of this investigation is to understand the tradeoff between plan quality and treatment time in rotational delivery by use of optimization models. Method and Materials: We study a simplified VMAT model for a 2D phantom and construct an exact mixed integer optimization model for it. The model includes treatment time as a constraint, and otherwise does not specify how the delivery is to be done, allowing for either VMAT or IMRT solutions. The model is too large to solve, but we trap the optimal solution between tight upper and lower bounds with additional models. The lower bound solutions are used to warm start the upper bound solutions. We construct Pareto surfaces for the joint tradeoffs of treatment time, tumor maximum dose, and organ at risk mean dose. Results: Upper bounds are within 10% of lower bound solutions. This allows us to conclusively demonstrate that 1) the treatment time constraint becomes more important when high intensity modulation is required to achieve optimal dose distributions, and 2) finding a good feasible VMAT plan is benefitted (by ∼5% in objective value) by warmstarting using the fluence modulation required at each angular location. Conclusion: For problems where the optimal dose distribution has non‐convex iso‐dose lines (to avoid nearby critical structures), the high modulation necessary to achieve such plans translates into longer treatment times. In these cases, when allowed treatment time is small, the optimal solutions show fluence being delivered at every angle — VMAT. If treatment time is allowed to be larger, IMRT plans are found to be optimal.

Entry trajectory optimization for hypersonic vehicles has been formulated as constrained optimal control problems, which are difficult to solve because of the existing high nonlinearity and nonconvexity. In recent years, convex optimization has shown promise for real-time onboard applications with the state-of-the-art interior-point methods. In this paper, line-search and trust-region techniques are introduced to fundamentally improve the performance of the sequential convex programming method for entry trajectory optimization. Two improved algorithms are developed: line-search sequential convex programming and trust-region sequential convex programming. In addition, a new trajectory generation method is proposed by taking advantage of the predictor–corrector method to find an initial 3-D trajectory for the developed successive algorithms. As such, the convergence of the solution process is improved. To demonstrate the effectiveness and performance of the newly proposed algorithms, numerical simulations are presented for maximum-terminal-velocity and minimum-heat-load entry problems. Results show that these two problems are not well solved using the basic sequential convex programming algorithm. However, they can be efficiently solved by the two improved algorithms in a few seconds in MATLAB, showing a significant improvement over general-purpose solvers, such as GPOPS.

This work presents a method for fast volumetric modulated arc therapy (VMAT) adaptation in response to interfraction anatomical variations. Additionally, plan parameters extracted from the adapted plans are used to verify the quality of these plans. The methods were tested as a prostate class solution and compared to replanning and to their current clinical practice. The proposed VMAT adaptation is an extension of their previous intensity modulated radiotherapy (IMRT) adaptation. It follows a direct (forward) planning approach: the multileaf collimator (MLC) apertures are corrected in the beam's eye view (BEV) and the monitor units (MUs) are corrected using point dose calculations. All MLC and MU corrections are driven by the positions of four fiducial points only, without need for a full contour set. Quality assurance (QA) of the adapted plans is performed using plan parameters that can be calculated online and that have a relation to the delivered dose or the plan quality. Five potential parameters are studied for this purpose: the number of MU, the equivalent field size (EqFS), the modulation complexity score (MCS), and the components of the the aperture area variability (AAV) and the leaf sequence variability (LSV). The full adaptation and its separate steps were evaluated in simulation experiments involving a prostate phantom subjected to various interfraction transformations. The efficacy of the current VMAT adaptation was scored by target mean dose (CTVmean), conformity (CI95%), tumor control probability (TCP), and normal tissue complication probability (NTCP). The impact of the adaptation on the plan parameters (QA) was assessed by comparison with prediction intervals (PI) derived from a statistical model of the typical variation of these parameters in a population of VMAT prostate plans (n = 63). These prediction intervals are the adaptation equivalent of the tolerance tables for couch shifts in the current clinical practice. The proposed adaptation of a two-arc VMAT plan resulted in the intended CTVmean (Δ ≤ 3%) and TCP (ΔTCP ≤ 0.001). Moreover, the method assures the intended CI95% (Δ ≤ 11%) resulting in lowered rectal NTCP for all cases. Compared to replanning, their adaptation is faster (13 s vs 10 min) and more intuitive. Compared to the current clinical practice, it has a better protection of the healthy tissue. Compared to IMRT, VMAT is more robust to anatomical variations, but it is also less sensitive to the different correction steps. The observed variations of the plan parameters in their database included a linear dependence on the date of treatment planning and on the target radius. The MCS is not retained as QA metric due to a contrasting behavior of its components (LSV and AAV). If three out of four plan parameters (MU, EqFS, AAV, and LSV) need to lie inside a 50% prediction interval (3/4-50%PI), all adapted plans will be accepted. In contrast, all replanned plans do not meet this loose criterion, mainly because they have no connection to the initially optimized and verified plan. A direct (forward) VMAT adaptation performs equally well as (inverse) replanning but is faster and can be extended to real-time adaptation. The prediction intervals for the machine parameters are equivalent to the tolerance tables for couch shifts in the current clinical practice. A 3/4-50%PI QA criterion accepts all the adapted plans but rejects all the replanned plans.

Evolutionary multi-objective optimization algorithms are generally employed to generate Pareto optimal solutions by exploring the search space. To enhance the performance, exploration by global search can be complemented with exploitation by combining it with local search. In this paper, we address the issues in integrating local search with global search such as: how to select individuals for local search; how deep the local search is performed; how to combine multiple objectives into single objective for local search. We introduce a Preferential Local Search mechanism to fine tune the global optimal solutions further and an adaptive weight mechanism for combining multi-objectives together. These ideas have been integrated into NSGA-II to arrive at a new memetic algorithm for solving multi-objective optimization problems. The proposed algorithm has been applied on a set of constrained and unconstrained multi-objective benchmark test suite. The performance was analyzed by computing different metrics such as Generational distance, Spread, Max spread, and HyperVolume Ratio for the test suite functions. Statistical test applied on the results obtained suggests that the proposed algorithm outperforms the state-of-art multi-objective algorithms like NSGA-II and SPEA2. To study the performance of our algorithm on a real-world application, Economic Emission Load Dispatch was also taken up for validation. The performance was studied with the help of measures such as Hypervolume and Set Coverage Metrics. Experimental results substantiate that our algorithm has the capability to solve real-world problems like Economic Emission Load Dispatch and is able to produce better solutions, when compared with NSGA-II, SPEA2, and traditional memetic algorithms with fixed local search steps.

Optimization Solution Task is a typical and important task in many applications. Many optimization problems have been proved to be NP-hard problems, which cannot be solved by some predefined mathematic formulae. In this case, computer aided method is very helpful. While some local search algorithms are easily to fall into a local optimum solution. On contrast, the population based methods, such as Genetic Algorithms, Artificial Immune System, Autonomy Oriented Computing, are global search algorithms. However, they are not good at the local search. In this paper, an improved method is proposed by combining the local and global search ability, so as to improve the performance in terms of the convergence speed and the convergence reliability. We construct a generic form to deal with the common objective function space or the objective function with the partial derivative. In addition, we present an n-hold method in population based evolution method. The experiments indicate that our approach can effectively improve the convergence reliability, which is much concerned in some applications with the expensive executing expense.

This paper proposed an optimal time-varying proportional navigation guidance law based on sequential convex programming. The guidance law can achieve the desired impact angle and impact time with look angle and lateral acceleration constraints. By treating the multiconstraints’ guidance problem as an optimization problem and changing the independent variable to linearize the problem and constraints, the original nonlinear and nonconvex problem is transformed into a series of convex optimization problem so that it can be quickly solved by sequential convex programming. Numerical simulations compared to nonlinear programming and traditional analytical guidance law demonstrate the effectiveness and efficiency of the proposed algorithm. Finally, the proposed guidance law is verified to satisfy different impact time periods and impact angle constraints.