Pareto Optimal Plans Research Articles

PO-0899: Dosimetric evaluation of deliverable and navigated Pareto optimal plans generated with MCO

PO-0899: Dosimetric evaluation of deliverable and navigated Pareto optimal plans generated with MCO

Hybrid QoS-Aware Web Service Composition Strategies for Group Pareto Optimal Plan

Group-oriented service composition is still challenging for big group and personalized QoS requirements. Therefore, this paper presents a Hybrid QoS-aware Web Service Composition Strategies for Group Pareto Optimal Plan (HOWSCS_GGOP) based on multi-attribute group decision making (MAGDM) theory. It includes five main steps: calculating group preference, clustering weighted cluster weights, constructing cluster weighted normalized decision-making matrix, determining the ideal solution, and evaluating alternatives for group synthetically. In addition, a hybrid Web service QoS model is introduced to describe QoS values with real numbers, interval numbers, triangular fuzzy numbers and intuitionistic fuzzy numbers. Experimental results show that the proposed algorithm can well solve the problem of Web service composition for big group and personalized QoS requirements.

General Theorem for a Pareto Optimal Plan - Generalization of the First Fundamental Theorem

Suppose that an economy has numerous feasible plans, one of which must be chosen. Suppose further that a “compensation” is adjusted such that all of the economy members prefer one feasible plan to other feasible plans. Then, this “unanimous feasible plan with compensation” is Pareto optimal, as will be proved in this paper. Expectedly, this “general theorem” can be applied to general equilibrium theory; (the allocation of) a general equilibrium is one of “unanimous feasible plans with compensation”. That is why (the allocation of) a general equilibrium is Pareto optimal. When technologies and/or preferences are not convex, however, “unanimous feasible plans with compensation” cannot always be supported by general equilibrium, which means that market economy can fail to be Pareto optimal. In these “market failures”, (the “general theorem” suggests that) we should leave “one price for one commodity” behind and use a more flexible “compensation” to find a “unanimous feasible plan with compensation”. The most important example is “innovation”; “benefit-based price” should be used for “innovative commodities”.

Multi-objective transmission expansion planning considering multiple generation scenarios

This paper shows a methodology for solving the Transmission Expansion Planning (TEP) problem when Multiple Generation Scenarios (MGS) are considered. MGS are a result of the multiple load flow patterns caused by realistic operation of the network, such as market rules, availability of generators, weather conditions or fuel prices. The solution to this problem is carried out by using multiobjective evolutionary strategies for the optimization process, implementing a new hybrid modified NSGA-II/Chu–Beasley algorithm and taking into account variable demand and generation. The proposed methodology is validated using the 6-bus Garver system and the IEEE-24 bus system. The TEP is based on the DC model of the network and non-linear interior point method is used to initialize the population.A set of Pareto optimal expansion plans with different levels of cost and load shedding is found for each system, showing the robustness of the proposed approach.

A DVH-guided IMRT optimization algorithm for automatic treatment planning and adaptive radiotherapy replanning.

To develop a novel algorithm that incorporates prior treatment knowledge into intensity modulated radiation therapy optimization to facilitate automatic treatment planning and adaptive radiotherapy (ART) replanning. The algorithm automatically creates a treatment plan guided by the DVH curves of a reference plan that contains information on the clinician-approved dose-volume trade-offs among different targets/organs and among different portions of a DVH curve for an organ. In ART, the reference plan is the initial plan for the same patient, while for automatic treatment planning the reference plan is selected from a library of clinically approved and delivered plans of previously treated patients with similar medical conditions and geometry. The proposed algorithm employs a voxel-based optimization model and navigates the large voxel-based Pareto surface. The voxel weights are iteratively adjusted to approach a plan that is similar to the reference plan in terms of the DVHs. If the reference plan is feasible but not Pareto optimal, the algorithm generates a Pareto optimal plan with the DVHs better than the reference ones. If the reference plan is too restricting for the new geometry, the algorithm generates a Pareto plan with DVHs close to the reference ones. In both cases, the new plans have similar DVH trade-offs as the reference plans. The algorithm was tested using three patient cases and found to be able to automatically adjust the voxel-weighting factors in order to generate a Pareto plan with similar DVH trade-offs as the reference plan. The algorithm has also been implemented on a GPU for high efficiency. A novel prior-knowledge-based optimization algorithm has been developed that automatically adjust the voxel weights and generate a clinical optimal plan at high efficiency. It is found that the new algorithm can significantly improve the plan quality and planning efficiency in ART replanning and automatic treatment planning.

Plan averaging for multicriteria navigation of sliding window IMRT and VMAT

To describe a method for combining sliding window plans [intensity modulated radiation therapy (IMRT) or volumetric modulated arc therapy (VMAT)] for use in treatment plan averaging, which is needed for Pareto surface navigation based multicriteria treatment planning. The authors show that by taking an appropriately defined average of leaf trajectories of sliding window plans, the authors obtain a sliding window plan whose fluence map is the exact average of the fluence maps corresponding to the initial plans. In the case of static-beam IMRT, this also implies that the dose distribution of the averaged plan is the exact dosimetric average of the initial plans. In VMAT delivery, the dose distribution of the averaged plan is a close approximation of the dosimetric average of the initial plans. The authors demonstrate the method on three Pareto optimal VMAT plans created for a demanding paraspinal case, where the tumor surrounds the spinal cord. The results show that the leaf averaged plans yield dose distributions that approximate the dosimetric averages of the precomputed Pareto optimal plans well. The proposed method enables the navigation of deliverable Pareto optimal plans directly, i.e., interactive multicriteria exploration of deliverable sliding window IMRT and VMAT plans, eliminating the need for a sequencing step after navigation and hence the dose degradation that is caused by such a sequencing step.

A Bi-objective Optimization Framework for Heterogeneous CPU/GPU Query Plans

Graphics Processing Units (GPU) have significantly more applications than just rendering images. They are also used in general-purpose computing to solve problems that can benefit from massive parallel processing. However, there are tasks that either hardly suit GPU or fit GPU only partially. The latter class is the focus of this paper. We elaborate on hybrid CPU/GPU computation and build optimization methods that seek the equilibrium between these two computation platforms. The method is based on heuristic search for bi-objective Pareto optimal execution plans in presence of multiple concurrent queries. The underlying model mimics the commodity market where devices are producers and queries are consumers. The value of resources of computing devices is controlled by supply-and-demand laws. Our model of the optimization criteria allows finding solutions of problems not yet addressed in heterogeneous query processing. Furthermore, it also offers lower time complexity and higher accuracy than other methods.

A genetic algorithm based optimization framework to visualize, evaluate, and modify 3D space configurations in Desktop VR

This paper presents the design and implementation of a Desktop VR (Virtual Reality) framework for generating and evaluating Pareto-optimal alternate 3D spatial configurations using GA (genetic algorithms). The 3-tier framework involves the generation of the Pareto-optimal plans using GA which are subsequently visualized first using a Java-based 2D Interface and finally in the form of a 3D VR scene. The search spaces (function domains) are extremely large in today’s multifaceted interior design situations, and the optimization procedure involves conflicting objective functions, and limitations in the form of constraint functions. The interior space allocation problem is formulated and implemented as the “optimal configuration of artifacts”. When using GAs, a group of Pareto-optimal solutions (Pareto set) are available for the planners and decision-makers, wherefrom one solution ought to be picked. Therefore, this study applies a tool to not only visually evaluate the plans, but also to interact with those plans to develop them further if needed. Besides enabling the optimal spatial configuration of the scene elements, this framework also facilitates evaluation and interaction via the 3D VR worlds. The framework aids the proactive exploration, analysis, and finalization of design aspects such as color, size, lighting, etc. of the various elements prior to the actual construction. The results demonstrate the robust performance of the GA and the final 3D VR environment with dynamic interactive capabilities. This final interface facilitates “GA-Compliant” transformations and scene modifications thereby facilitating the exploration and examination of alternative scene configurations.

TH‐A‐116‐09: A Novel Prior‐Knowledge‐Based Optimization Algorithm for Automatic Treatment Planning and Adaptive Radiotherapy Re‐Planning

Purpose: To develop a novel algorithm that takes existing prior‐knowledge information into account in optimization to facilitate automatic treatment planning and adaptive radiotherapy (ART) re‐planning. Methods: We developed an algorithm to automatically create a treatment plan guided by the DVH curves of a reference plan that contains information on the clinician approved dose‐volume trade‐offs among different targets/organs and within the same organ. This method has applications in automatic treatment planning and ART re‐planning. In ART, the reference plan is the initial plan for the same patient, while for automatic treatment planning the reference plan is selected (based on patient similarity) from a library of clinically approved and delivered plans of previously treated patients with similar medical conditions. The proposed algorithm employs a voxel‐based optimization model and approximates the large voxel‐based Pareto surface iteratively. The voxel weights are iteratively adjusted to approach a plan that is similar to the reference plan in terms of the DVHs. If the reference plan is feasible but not Pareto optimal, the algorithm generates a Pareto optimal plan consistent with the reference DVHs. If the reference plan is too restricting, the algorithm generates a Pareto plan with DVHs close to the reference ones. Results: The algorithm was tested using a series of patient cases and found to be able to automatically adjust the voxel‐weighting factors automatically in order to generate a Pareto plan with DVHs similar to the reference plan. The algorithm has been implemented on GPU for high efficiency. Conclusion: A novel prior‐knowledge‐based optimization algorithm has been developed that uses the prior knowledge in optimization process to automatically adjust the voxel weights and generate a clinical optimal plan at high efficiency. It is found that the new algorithm can significantly improve the plan quality and planning efficiency in ART re‐planning and automatic treatment planning.

A moment-based approach for DVH-guided radiotherapy treatment plan optimization

The dose–volume histogram (DVH) is a clinically relevant criterion to evaluate the quality of a treatment plan. It is hence desirable to incorporate DVH constraints into treatment plan optimization for intensity modulated radiation therapy. Yet, the direct inclusion of the DVH constraints into a treatment plan optimization model typically leads to great computational difficulties due to the non-convex nature of these constraints. To overcome this critical limitation, we propose a new convex-moment-based optimization approach. Our main idea is to replace the non-convex DVH constraints by a set of convex moment constraints. In turn, the proposed approach is able to generate a Pareto-optimal plan whose DVHs are close to, or if possible even outperform, the desired DVHs. In particular, our experiment on a prostate cancer patient case demonstrates the effectiveness of this approach by employing two and three moment formulations to approximate the desired DVHs.

TH‐A‐213AB‐08: Robust Multi‐Criteria IMPT Optimization

Purpose: We present a method to include robustness in a multi‐criteria optimization (MCO) framework for intensity‐modulated proton therapy (IMPT). The approach allows one to simultaneously explore the trade‐off between different objectives including robustness and nominal plan quality. Methods: A database of plans each emphasizing different treatment planning objectives, is pre‐computed to approximate the Pareto surface. An IMPT treatment plan that strikes the best balance between the different objectives can be selected by navigating on the Pareto surface. We integrate robustness into MCO by adding robustified objectives and constraints. Uncertainties are modeled by pre‐calculated dose‐influence matrices for a nominal scenario and a number of pre‐defined error scenarios (shifted patient positions, proton beam undershoot and overshoot). A robustified objective represents the worst objective function value that can be realized for any of the error scenarios and thus provides a measure of plan robustness. The optimization method uses a linear projection solver and is capable of handling large problem sizes resulting from a fine dose grid resolution, many scenarios, and a large number of proton pencil beams. Results: A base‐of‐skull case is used to demonstrate that the robust optimization method reduces the sensitivity of the treatment plan to setup and range errors to a degree that is not achieved by a safety margin approach. A chordoma case is analyzed in more detail to demonstrate the involved trade‐offs between target underdose and brainstem sparing as well as robustness and nominal plan quality. The robust optimization for each Pareto optimal plan takes less than 5 min on a standard computer. Conclusions: The uncertainty pertinent to the IMPT procedure can be reduced during treatment planning by optimizing a database of plans that emphasize different treatment objectives, including robustness. The planner can then interactively explore all convex combinations of database plans to decide on the most‐preferred trade‐off.

The dosimetric impact of leaf interdigitation and leaf width on VMAT treatment planning in Pinnacle: comparing Pareto fronts

To evaluate in an objective way the effect of leaf interdigitation and leaf width on volumetric modulated arc therapy plans in Pinnacle. Three multileaf collimators (MLCs) were modeled: two 10 mm leaf width MLCs, with and without interdigitating leafs, and a 5 mm leaf width MLC with interdigitating leafs. Three rectum patients and three prostate patients were used for the planning study. In order to compare treatment techniques in an objective way, a Pareto front comparison was carried out. 200 plans were generated in an automated way, per patient per MLC model, resulting in a total of 3600 plans. From these plans, Pareto-optimal plans were selected which were evaluated for various dosimetric variables. The capability of leaf interdigitation showed little dosimetric impact on the treatment plans, when comparing the 10 mm leaf width MLC with and without leaf interdigitation. When comparing the 10 mm leaf width MLC with the 5 mm leaf width MLC, both with interdigitating leafs, improvement in plan quality was observed. For both patient groups, the integral dose was reduced by 0.6 J for the thin MLC. For the prostate patients, the mean dose to the anal sphincter was reduced by 1.8 Gy and the conformity of the V95% was reduced by 0.02 using the thin MLC. The V65% of the rectum was reduced by 0.1% and the dose homogeneity with 1.5%. For rectum patients, the mean dose to the bowel was reduced by 1.4 Gy and the mean dose to the bladder with 0.8 Gy for the thin MLC. The conformity of the V95% was equivalent for the 10 and 5 mm leaf width MLCs for the rectum patients. We have objectively compared three types of MLCs in a planning study for prostate and rectum patients by analyzing Pareto-optimal plans which were generated in an automated way. Interdigitation of MLC leafs does not generate better plans using the SmartArc algorithm in Pinnacle. Changing the MLC leaf width from 10 to 5 mm generates better treatment plans although the clinical relevance remains to be proven.

ICycle: Integrated, multicriterial beam angle, and profile optimization for generation of coplanar and noncoplanar IMRT plans

To introduce iCycle, a novel algorithm for integrated, multicriterial optimization of beam angles, and intensity modulated radiotherapy (IMRT) profiles. A multicriterial plan optimization with iCycle is based on a prescription called wish-list, containing hard constraints and objectives with ascribed priorities. Priorities are ordinal parameters used for relative importance ranking of the objectives. The higher an objective priority is, the higher the probability that the corresponding objective will be met. Beam directions are selected from an input set of candidate directions. Input sets can be restricted, e.g., to allow only generation of coplanar plans, or to avoid collisions between patient/couch and the gantry in a noncoplanar setup. Obtaining clinically feasible calculation times was an important design criterium for development of iCycle. This could be realized by sequentially adding beams to the treatment plan in an iterative procedure. Each iteration loop starts with selection of the optimal direction to be added. Then, a Pareto-optimal IMRT plan is generated for the (fixed) beam setup that includes all so far selected directions, using a previously published algorithm for multicriterial optimization of fluence profiles for a fixed beam arrangement Breedveld et al. [Phys. Med. Biol. 54, 7199-7209 (2009)]. To select the next direction, each not yet selected candidate direction is temporarily added to the plan and an optimization problem, derived from the Lagrangian obtained from the just performed optimization for establishing the Pareto-optimal plan, is solved. For each patient, a single one-beam, two-beam, three-beam, etc. Pareto-optimal plan is generated until addition of beams does no longer result in significant plan quality improvement. Plan generation with iCycle is fully automated. Performance and characteristics of iCycle are demonstrated by generating plans for a maxillary sinus case, a cervical cancer patient, and a liver patient treated with SBRT. Plans generated with beam angle optimization did better meet the clinical goals than equiangular or manually selected configurations. For the maxillary sinus and liver cases, significant improvements for noncoplanar setups were seen. The cervix case showed that also in IMRT with coplanar setups, beam angle optimization with iCycle may improve plan quality. Computation times for coplanar plans were around 1-2 h and for noncoplanar plans 4-7 h, depending on the number of beams and the complexity of the site. Integrated beam angle and profile optimization with iCycle may result in significant improvements in treatment plan quality. Due to automation, the plan generation workload is minimal. Clinical application has started.

Multicriteria VMAT optimization

To make the planning of volumetric modulated arc therapy (VMAT) faster and to explore the tradeoffs between planning objectives and delivery efficiency. A convex multicriteria dose optimization problem is solved for an angular grid of 180 equi-spaced beams. This allows the planner to navigate the ideal dose distribution Pareto surface and select a plan of desired target coverage versus organ at risk sparing. The selected plan is then made VMAT deliverable by a fluence map merging and sequencing algorithm, which combines neighboring fluence maps based on a similarity score and then delivers the merged maps together, simplifying delivery. Successive merges are made as long as the dose distribution quality is maintained. The complete algorithm is called VMERGE. VMERGE is applied to three cases: a prostate, a pancreas, and a brain. In each case, the selected Pareto-optimal plan is matched almost exactly with the VMAT merging routine, resulting in a high quality plan delivered with a single arc in less than 5 min on average. VMERGE offers significant improvements over existing VMAT algorithms. The first is the multicriteria planning aspect, which greatly speeds up planning time and allows the user to select the plan, which represents the most desirable compromise between target coverage and organ at risk sparing. The second is the user-chosen epsilon-optimality guarantee of the final VMAT plan. Finally, the user can explore the tradeoff between delivery time and plan quality, which is a fundamental aspect of VMAT that cannot be easily investigated with current commercial planning systems.

Including robustness in multi-criteria optimization for intensity-modulated proton therapy

We present a method to include robustness in a multi-criteria optimization (MCO) framework for intensity-modulated proton therapy (IMPT). The approach allows one to simultaneously explore the trade-off between different objectives as well as the trade-off between robustness and nominal plan quality. In MCO, a database of plans each emphasizing different treatment planning objectives, is pre-computed to approximate the Pareto surface. An IMPT treatment plan that strikes the best balance between the different objectives can be selected by navigating on the Pareto surface. In our approach, robustness is integrated into MCO by adding robustified objectives and constraints to the MCO problem. Uncertainties (or errors) of the robust problem are modeled by pre-calculated dose-influence matrices for a nominal scenario and a number of pre-defined error scenarios (shifted patient positions, proton beam undershoot and overshoot). Objectives and constraints can be defined for the nominal scenario, thus characterizing nominal plan quality. A robustified objective represents the worst objective function value that can be realized for any of the error scenarios and thus provides a measure of plan robustness. The optimization method is based on a linear projection solver and is capable of handling large problem sizes resulting from a fine dose grid resolution, many scenarios, and a large number of proton pencil beams. A base-of-skull case is used to demonstrate the robust optimization method. It is demonstrated that the robust optimization method reduces the sensitivity of the treatment plan to setup and range errors to a degree that is not achieved by a safety margin approach. A chordoma case is analyzed in more detail to demonstrate the involved trade-offs between target underdose and brainstem sparing as well as robustness and nominal plan quality. The latter illustrates the advantage of MCO in the context of robust planning. For all cases examined, the robust optimization for each Pareto optimal plan takes less than 5 min on a standard computer, making a computationally friendly interface possible to the planner. In conclusion, the uncertainty pertinent to the IMPT procedure can be reduced during treatment planning by optimizing plans that emphasize different treatment objectives, including robustness, and then interactively seeking for a most-preferred one from the solution Pareto surface.

Feasibility of Identification of Gamma Knife Planning Strategies by Identification of Pareto Optimal Gamma Knife Plans

The use of conformity indices to optimize Gamma Knife planning is common, but does not address important tradeoffs between dose to tumor and normal tissue. Pareto analysis has been used for this purpose in other applications, but not for Gamma Knife (GK) planning. The goal of this work is to use computer models to show that Pareto analysis may be feasible for GK planning to identify dosimetric tradeoffs. We define a GK plan A to be Pareto dominant to B if the prescription isodose volume of A covers more tumor but not more normal tissue than B, or if A covers less normal tissue but not less tumor than B. A plan is Pareto optimal if it is not dominated by any other plan. Two different Pareto optimal plans represent different tradeoffs between dose to tumor and normal tissue, because neither plan dominates the other. ‘GK simulator’ software calculated dose distributions for GK plans, and was called repetitively by a genetic algorithm to calculate Pareto dominant plans. Three irregular tumor shapes were tested in 17 trials using various combinations of shots. The mean number of Pareto dominant plans/trial was 59 ± 17 (sd). Different planning strategies were identified by large differences in shot positions, and 70 of the 153 coordinate plots (46%) showed differences of 5mm or more. The Pareto dominant plans dominated other nearby plans. Pareto dominant plans represent different dosimetric tradeoffs and can be systematically calculated using genetic algorithms. Automatic identification of non-intuitive planning strategies may be feasible with these methods.

SU-E-T-470: Reducing the Uncertainties in Plan Evaluation for VMAT Treatment Planning by Choosing Different Collimator Angles

Purpose: To investigate how the uncertainties in plan evaluation can be reduced by simply choosing a suitable collimator angle for VMAT treatment planning and delivery. The plan quality deterioration due to the collimator angle is also examined. The plan quality is evaluated with a Pareto front based method and a quantitative measure called Pareto index. Methods: VMAT treatment plans with different collimator angles were generated and a QC measurement was performed for every collimator angle. The selected treatment site was the pelvic region. All the plans were generated and evaluated in Oncentra master plan, (Nucletron BV). The plans were created with different importance of the bowel. If a plan fulfilled the clinical protocol, apart from the bowel, it was contributing to a set of Pareto optimal plans. The Pareto set is displayed by plotting the mean dose to the bowel as a function of the under‐dosed PTV volume. The Pareto set for the different collimator angles were plotted in the same diagram to compare the plan quality. A quantitative metric for the Pareto set, called Pareto Index, was also calculated. Quality control measurements were performed using a Delta 4 diode array (Scandidos AB). 3D gamma evaluation was used to evaluate the QC results. The QC was used to evaluate the uncertainties in the plan. Results: The QC results for the 5˚ plans were about 99% and about 90% for the 35˚ plans. To achieve the same plan quality with 5˚, as the plans with 35˚, two arcs were needed. Conclusions: By choosing the right collimator angle the QC results can be improved thereby reducing the uncertainties in the plan evaluation. To achieve the same plan quality, however longer treatment times are necessary. On the other hand, the shorter plans are not as good as they seem in the TPS.

Conversion of helical tomotherapy plans to step-and-shoot IMRT plans-Pareto front evaluation of plans from a new treatment planning system

The resulting plans from a new type of treatment planning system called SharePlan have been studied. This software allows for the conversion of treatment plans generated in a TomoTherapy system for helical delivery, into plans deliverable on C-arm linear accelerators (linacs), which is of particular interest for clinics with a single TomoTherapy unit. The purpose of this work was to evaluate and compare the plans generated in the SharePlan system with the original TomoTherapy plans and with plans produced in our clinical treatment planning system for intensity-modulated radiation therapy (IMRT) on C-arm linacs. In addition, we have analyzed how the agreement between SharePlan and TomoTherapy plans depends on the number of beams and the total number of segments used in the optimization. Optimized plans were generated for three prostate and three head-and-neck (H&N) cases in the TomoTherapy system, and in our clinical treatment planning systems (TPS) used for IMRT planning with step-and-shoot delivery. The TomoTherapy plans were converted into step-and-shoot IMRT plans in SharePlan. For each case, a large number of Pareto optimal plans were created to compare plans generated in SharePlan with plans generated in the Tomotherapy system and in the clinical TPS. In addition, plans were generated in SharePlan for the three head-and-neck cases to evaluate how the plan quality varied with the number of beams used. Plans were also generated with different number of beams and segments for other patient cases. This allowed for an evaluation of how to minimize the number of required segments in the converted IMRT plans without compromising the agreement between them and the original TomoTherapy plans. The plans made in SharePlan were as good as or better than plans from our clinical system, but they were not as good as the original TomoTherapy plans. This was true for both the head-and-neck and the prostate cases, although the differences between the plans for the latter were small. The evaluation of the head-and-neck cases also showed that the plans generated in SharePlan were improved when more beams were used. The SharePlan Pareto front came close to the front for the TomoTherapy system when a sufficient number of beams were added. The results for plans generated with varied number of beams and segments demonstrated that the number of segments could be minimized with maintained agreement between SharePlan and TomoTherapy plans when 10-19 beams were used. This study showed (using Pareto front evaluation) that the plans generated in Share-Plan are comparable to plans generated in other TPSs. The evaluation also showed that the plans generated in SharePlan could be improved with the use of more beams. To minimize the number of segments needed in a plan with maintained agreement between the converted IMRT plans and the original TomoTherapy plans, 10-19 beams should be used, depending on target complexity. SharePlan has proved to be useful and should thereby be a time-saving complement as a backup system for clinics with a single TomoTherapy system installed alongside conventional C-arm linacs.

Bi-objective parallel machines scheduling with sequence-dependent setup times using hybrid metaheuristics and weighted min–max technique

In the literature of multi-objective problem, there are different algorithms to solve different optimization problems. This paper presents a min–max multi-objective procedure for a dual-objective, namely make span, and sum of the earliness and tardiness of jobs in due window machine scheduling problems, simultaneously. In formulation of min–max method when this method is combined with the weighting method, the decision maker can have the flexibility of mixed use of weights and distance parameter to yield a set of Pareto-efficient solutions. This research extends the new hybrid metaheuristic (HMH) to solve parallel machines scheduling problems with sequence-dependent setup time that comprises three components: an initial population generation method based on an ant colony optimization (ACO), a simulated annealing (SA) as an evolutionary algorithm employs certain probability to avoid becoming trapped in a local optimum, and a variable neighborhood search (VNS) which involves three local search procedures to improve the population. In addition, two VNS-based HMHs, which are a combination of two methods, SA/VNS and ACO/VNS, are also proposed to solve the addressed scheduling problems. A design of experiments approach is employed to calibrate the parameters. The non-dominated sets obtained from HMH and two best existing bi-criteria scheduling algorithms are compared in terms of various indices and the computational results show that the proposed algorithm is capable of producing a number of high-quality Pareto optimal scheduling plans. Aside, an extensive computational experience is carried out to analyze the different parameters of the algorithm.

A hierarchical evolutionary algorithm for multiobjective optimization in IMRT

The current inverse planning methods for intensity modulated radiation therapy (IMRT) are limited because they are not designed to explore the trade-offs between the competing objectives of tumor and normal tissues. The goal was to develop an efficient multiobjective optimization algorithm that was flexible enough to handle any form of objective function and that resulted in a set of Pareto optimal plans. A hierarchical evolutionary multiobjective algorithm designed to quickly generate a small diverse Pareto optimal set of IMRT plans that meet all clinical constraints and reflect the optimal trade-offs in any radiation therapy plan was developed. The top level of the hierarchical algorithm is a multiobjective evolutionary algorithm (MOEA). The genes of the individuals generated in the MOEA are the parameters that define the penalty function minimized during an accelerated deterministic IMRT optimization that represents the bottom level of the hierarchy. The MOEA incorporates clinical criteria to restrict the search space through protocol objectives and then uses Pareto optimality among the fitness objectives to select individuals. The population size is not fixed, but a specialized niche effect, domination advantage, is used to control the population and plan diversity. The number of fitness objectives is kept to a minimum for greater selective pressure, but the number of genes is expanded for flexibility that allows a better approximation of the Pareto front. The MOEA improvements were evaluated for two example prostate cases with one target and two organs at risk (OARs). The population of plans generated by the modified MOEA was closer to the Pareto front than populations of plans generated using a standard genetic algorithm package. Statistical significance of the method was established by compiling the results of 25 multiobjective optimizations using each method. From these sets of 12-15 plans, any random plan selected from a MOEA population had a 11.3% +/- 0.7% chance of dominating any random plan selected by a standard genetic package with 0.04% +/- 0.02% chance of domination in reverse. By implementing domination advantage and protocol objectives, small and diverse populations of clinically acceptable plans that approximated the Pareto front could be generated in a fraction of 1 h. Acceleration techniques implemented on both levels of the hierarchical algorithm resulted in short, practical runtimes for multiobjective optimizations. The MOEA produces a diverse Pareto optimal set of plans that meet all dosimetric protocol criteria in a feasible amount of time. The final goal is to improve practical aspects of the algorithm and integrate it with a decision analysis tool or human interface for selection of the IMRT plan with the best possible balance of successful treatment of the target with low OAR dose and low risk of complication for any specific patient situation.