Reoptimization Techniques Research Articles

Physical vs Virtual corporate power purchase agreements: Meeting renewable targets amid demand and price uncertainty

Power purchase agreements (PPAs) have become an important corporate procurement vehicle for renewable power, especially among companies that have committed to targets requiring a certain fraction of their power demand be met by renewables. PPAs are long-term contracts that provide renewable energy certificates (RECs) to the corporate buyer and take two main forms: Physical vs Virtual. Physical PPAs deliver power in addition to RECs, while virtual PPAs are financial contracts that hedge (at least partially) power price uncertainty. We compare procurement portfolios that sign physical PPAs with ones that sign virtual PPAs, focusing on fixed-volume contracts and emphasizing uncertainties in power demand and the prices of power and RECs. In particular, we first analyze a two-stage stochastic model to understand the behavior of procurement quantities and costs when using physical and virtual PPAs as well as variants that limit risk. We subsequently formulate a Markov decision process (MDP) that optimizes the multi-stage procurement of power to reach and sustain a renewable procurement target. By leveraging state-of-the-art reoptimization techniques, we solve this MDP on realistic instances to near optimality, and highlight the relative benefits of using PPA types to meet a renewable target. We underscore a trade-off between expected cost and cash flow variance that buyers should consider when choosing between physical and virtual PPAs. Moreover, advanced reoptimization techniques significantly impact the ability to manage this trade-off.

Reliable lifelong planning A*: Technique for re-optimizing reliable shortest paths when travel time distribution updating

Re-optimization technique is an efficient approach for solving the shortest path problem in dynamic deterministic networks, where link travel times are updated in real-time. However, existing re-optimization techniques, built on the assumption that link travel times are deterministic, cannot be used to solve reliable shortest path problems in real road networks with noticeable levels of travel time uncertainties. This study proposes a novel re-optimization technique, named reliable lifelong planning A* (RLPA*), for re-optimizing reliable shortest path finding results in dynamic stochastic networks, where link travel time distributions are updated in real-time. The proposed RLPA* technique can efficiently determine the optimal solution in dynamic stochastic networks by reusing path search results produced in the previous time instance. The proposed RLPA* technique is further utilized to solve the K reliable shortest paths problem, which is regarded as a series of reliable shortest path searches in a dynamic stochastic network. To validate the proposed algorithms, a comprehensive case study using real traffic data is conducted. The case study results demonstrated that the proposed algorithms significantly outperform the corresponding state-of-the-art algorithms on all testing networks.

Anatomic changes in head and neck intensity-modulated proton therapy: Comparison between robust optimization and online adaptation

Background/purposeSetup variations and anatomical changes can severely affect the quality of head and neck intensity-modulated proton therapy (IMPT) treatments. The impact of these changes can be alleviated by increasing the plan’s robustness a priori, or by adapting the plan online. This work compares these approaches in the context of head and neck IMPT. Materials/methodsA representative cohort of 10 head and neck squamous cell carcinoma (HNSCC) patients with daily cone-beam computed tomography (CBCT) was evaluated. For each patient, three IMPT plans were created: 1- a classical robust optimization (cRO) plan optimized on the planning CT, 2- an anatomical robust optimization (aRO) plan additionally including the two first daily CBCTs and 3- a plan optimized without robustness constraints, but online-adapted (OA) daily, using a constrained spot intensity re-optimization technique only. ResultsThe cumulative dose following OA fulfilled the clinical objective of both the high-risk and low-risk clinical target volumes (CTV) coverage in all 10 patients, compared to 8 for aRO and 4 for cRO. aRO did not significantly increase the dose to most organs at risk compared to cRO, although the integral dose was higher. OA significantly reduced the integral dose to healthy tissues compared to both robust methods, while providing equivalent or superior target coverage. ConclusionUsing a simple spot intensity re-optimization, daily OA can achieve superior target coverage and lower dose to organs at risk than robust optimization methods.

Efficient algorithm for finding k shortest paths based on re-optimization technique

This study proposes an efficient deviation path algorithm for finding exactly k shortest simple paths without loops in road networks. The algorithm formulates the deviation path calculation process as repeated one-to-one searches for the shortest path in a dynamic network, where only a node and a link are restored at each search. Using this formulation, the proposed algorithm maintains and updates a single shortest path tree rooted at the destination. A re-optimization technique, lifelong planning A*, is incorporated into the algorithm to efficiently calculate each deviation path by reusing the shortest path tree generated at the previous search. To verify the efficiency of the proposed algorithm, computational experiments were conducted using several real road networks, and the results showed that the proposed algorithm performed significantly better than state-of-the-art algorithms.

Consolidation and coordination of routes in urban distribution

In this dissertation, two relevant aspects of routing in the urban environment are studied. In the first part of the thesis, the implications of considering release dates when planning for delivery from distribution centers are discussed. The routing problems with release dates are contextualized in the class of routing problems, and in particular, in the lass of routing problems in which timing decisions must be considered. The Traveling Salesman Problem with release dates and completion time minimization is studied. Properties are introduced for the problem and a formulation is proposed. Two variants of a heuristic algorithm are tested against the optimal solution and shown to provide high quality results. The benefits of considering release dates are assessed by comparing the results with those obtained disregarding the release dates and delivering the parcels as soon as they arrive to the distribution center. The study on routing problems with release dates is then expanded to consider the stochastic and dynamic nature of the release dates. A reoptimization technique is proposed to tackle the dynamic aspect of the problem. Three reoptimization policies are proposed, with increasing reoptimization frequency, together with two models for the solution of the problem. The first is a stochastic model, considering the entire probabilistic information available for the release dates, and the second is a deterministic model, where a point estimation is used. The stochastic model is shown to perform better than the deterministic model, at the expense of the computational time required to evaluate any of the solutions explored. The second part of the thesis is focused on the management of the loading and unloading areas in the city center. Urban distribution requires vehicles to temporarily stop to perform the last leg of the delivery by foot. If a spot is not available, vehicles resort to double parking which is a known cause of road congestion. Two booking management systems and the arising routing problems are presented. The solutions provided by the two systems are compared with the current state of the distribution.

A polynomial time algorithm for the minimum flow problem in time-varying networks

Flow variations over time generalize standard network flows by introducing an element of time. In contrast to the classical case of static flows, a flow over time in such a network specifies a flow rate entering an arc for each point in time. In this setting, the capacity of an arc limits the rate of flow into the arc at each point in time. Traditionally, flows over time are computed in time-expanded networks that contain one copy of the original network for each discrete time step. While this method makes available the whole algorithmic toolbox developed for static network flows, its drawback is the enormous size of the time-expanded network. In this paper, we extend the results about the minimum flow problem to network flows (with n nodes and m arcs) in which the time-varying lower bounds can involve both the source and the sink nodes (as in Fathabadi et al.) and also one additional node other than the source and the sink nodes. It is shown that this problem for the set \(\{0,1,\ldots ,T\}\) of time points can be solved by at most n minimum flow computations, by suitably extending the dynamic minimum flow algorithm and reoptimization techniques. The running time of the presented algorithm is \(O(n^2m)\).

Designing, Operating, and Reoptimizing Elastic Optical Networks

Emerging services and applications demanding high bitrate and stringent quality of service requirements are pushing telecom operators to upgrade their core networks based on wavelength-division multiplexing (WDM) to a more flexible technology for the more dynamic and variable traffic that is expected to be conveyed. Finally, academy- and industry-driven research on elastic optical networks (EON) has turned out into a mature enough technology ready to gradually upgrade WDM-based networks. Among others, key EON features include flexible spectrum allocation, connections beyond 100 Gb/s, advanced modulation formats, and elasticity against time-varying traffic. As a consequence of the variety of features involved, network design and algorithms for EONs are remarkably more complex than those for WDM networks. However, new opportunities for network operators to reduce costs arise by exploiting those features; in fact, the classical network life cycle based on fixed periodical planning cycles needs to be adapted to greatly reduce overprovisioning by applying reoptimization techniques to reconfigure the network while it is in operation and to efficiently manage new services, such as datacenter interconnection that will require provisioning multicast connections and elastic spectrum allocation for time-varying traffic. This paper reviews and extends mathematical models and algorithms to solve optimization problems related to the design, operation, and reoptimization of EONs. In addition, two use cases are presented as illustrative examples on how the network life cycle needs to be extended with in-operation planning and data analytics thus adding cognition to the network.

Scheduling unrelated parallel machines in semiconductor manufacturing by problem reduction and local search heuristics

We investigate a difficult scheduling problem in a semiconductor manufacturing process that seeks to minimize the number of tardy jobs and makespan with sequence-dependent setup time, release time, due dates and tool constraints. We propose a mixed integer programming (MIP) formulation which treats tardy jobs as soft constraints so that our objective seeks the minimum weighted sum of makespan and heavily penalized tardy jobs. Although our polynomial-sized MIP formulation can correctly model this scheduling problem, it is so difficult that even a feasible solution can not be calculated efficiently for small-scale problems. We then propose a technique to estimate the upper bound for the number of jobs processed by a machine, and use it to effectively reduce the size of the MIP formulation. In order to handle real-world large-scale scheduling problems, we propose an efficient dispatching rule that assigns a job of the earliest due date to a machine with least recipe changeover (EDDLC) and try to re-optimize the solution by local search heuristics which involves interchange, translocation and transposition between assigned jobs. Our computational experiments indicate that EDDLC and our proposed reoptimization techniques are very efficient and effective. In particular, our method usually gives solutions very close to the exact optimum for smaller scheduling problems, and calculates good solutions for scheduling up to 200 jobs on 40 machines within 10 min.

Minimum flow problem on network flows with time-varying bounds

In this paper, we consider the minimum flow problem on network flows in which the lower arc capacities vary with time. We will show that this problem for set {0,1,…,T} of time points can be solved by at most n minimum flow computations, by combining of preflow-pull algorithm and reoptimization techniques (no matter how many values of T are given). Running time of the presented algorithm is O(n2m).

New Reoptimization Techniques applied to Steiner Tree Problem

Abstract Given an instance of an optimization problem together with an optimal solution for it, a reoptimization problem asks for a solution for a locally modified input instance. In this paper we develop new reoptimization techniques and apply them to the Steiner Tree Problem. Our techniques significantly improve the previous results and apply to a variety of reoptimization problems.

Scheduling two-stage hybrid flow shops with parallel batch, release time, and machine eligibility constraints

This paper investigates a difficult scheduling problem on a specialized two-stage hybrid flow shop with multiple processors that appears in semiconductor manufacturing industry, where the first and second stages process serial jobs and parallel batches, respectively. The objective is to seek job-machine, job-batch, and batch-machine assignments such that makespan is minimized, while considering parallel batch, release time, and machine eligibility constraints. We first propose a mixed integer programming (MIP) formulation for this problem, then gives a heuristic approach for solving larger problems. In order to handle real world large-scale scheduling problems, we propose an efficient dispatching rule called BFIFO that assigns jobs or batches to machines based on first-in-first-out principle, and then give several reoptimization techniques using MIP and local search heuristics involving interchange, translocation and transposition among assigned jobs. Computational experiments indicate our proposed re-optimization techniques are efficient. In particular, our approaches can produce good solutions for scheduling up to 160 jobs on 40 machines at both stages within 10 min.

Reoptimization in Lagrangian methods for the 0–1 quadratic knapsack problem

The 0–1 quadratic knapsack problem consists of maximizing a quadratic objective function subject to a linear capacity constraint. To exactly solve large instances of this problem with a tree search algorithm (e.g., a branch and bound method), the knowledge of good lower and upper bounds is crucial for pruning the tree but also for fixing as many variables as possible in a preprocessing phase. The upper bounds used in the best known exact approaches are based on Lagrangian relaxation and decomposition. It appears that the computation of these Lagrangian dual bounds involves the resolution of numerous 0–1 linear knapsack subproblems. Thus, taking this huge number of resolutions into account, we propose to embed reoptimization techniques for improving the efficiency of the preprocessing phase of the 0–1 quadratic knapsack resolution. Namely, reoptimization is introduced to accelerate each independent sequence of 0–1 linear knapsack problems induced by the Lagrangian relaxation as well as the Lagrangian decomposition. Numerous numerical experiments validate the relevance of our approach.

A GRASP-based network re-optimization strategy for improving RWA in multi-constrained optical transport infrastructures

In wavelength-routed optical networks, end-to-end connection demands are dynamically routed according to the current network status. Naïve path selection schemes, the wavelength continuity constraint and the limited or inaccurate information available can cause the virtual topology resulting from the currently allocated lightpaths to become sub-optimal. We propose an efficient re-optimization technique based on a GRASP meta-heuristic. Our work is focused on a hybrid online–offline scenario: connections are ordinarily routed dynamically using one of the available algorithms for online routing, but occasionally, when reorganization of the current virtual topology is desirable, existing paths are re-routed in order to improve load balancing and hence the ability to efficiently accept further connections. Because global changes of the logical topology and/or routing scheme can be disruptive for the provided connection services, we used iterative stepwise approaches based on a sequence of small actions (i.e., single connection re-routing and on local search from a given configuration). Simulation results demonstrate that several network performance metrics – including connection blocking ratios and bandwidth gains – are significantly improved by such approach. In particular, we achieved to accept more connection requests in our re-optimized networks with respect to the same networks without re-optimization, thus lowering the blocking ratio. Besides, in all tests we measured a notable gain in the number of freed bandwidth OC-units thanks to our re-optimization approach.

Updating Network Flows Given Multiple, Heterogeneous Arc Attribute Changes

A dual ascent reoptimization technique is proposed for updating optimal flows for the minimum cost network flow problem (MCNFP) given any number of simultaneous, heterogeneous changes to the network attributes (i.e. supply at nodes, arc costs and arc capacities) and the optimal solutions to the prior primal and dual problems. Significant savings in computation time can be achieved through the use of reoptimization in place of solving a new MCNFP from scratch as each new problem instance (i.e. set of network attribute updates) arises. The proposed technique can be implemented with polynomial worst-case computational complexity. Extensive numerical experiments were designed and conducted to assess the computational benefits of employing the proposed reoptimization technique as compared with solution from scratch using comparable classic implementations of the original algorithms. This work was motivated by the need for the real-time provision of evacuation instructions to people seeking quick egress from a large sensor-equipped building that has come under attack by natural or terrorist forces, but has broad applicability.

Comparison of online IGRT techniques for prostate IMRT treatment: Adaptive vs repositioning correction

This study compares three online image guidance techniques (IGRT) for prostate IMRT treatment: bony-anatomy matching, soft-tissue matching, and online replanning. Six prostate IMRT patients were studied. Five daily CBCT scans from the first week were acquired for each patient to provide representative "snapshots" of anatomical variations during the course of treatment. Initial IMRT plans were designed for each patient with seven coplanar 15 MV beams on a Eclipse treatment planning system. Two plans were created, one with a PTV margin of 10 mm and another with a 5 mm PTV margin. Based on these plans, the delivered dose distributions to each CBCT anatomy was evaluated to compare bony-anatomy matching, soft-tissue matching, and online replanning. Matching based on bony anatomy was evaluated using the 10 mm PTV margin ("bone10"). Soft-tissue matching was evaluated using both the 10 mm ("soft10") and 5 mm ("soft5") PTV margins. Online reoptimization was evaluated using the 5 mm PTV margin ("adapt"). The replanning process utilized the original dose distribution as the basis and linear goal programming techniques for reoptimization. The reoptimized plans were finished in less than 2 min for all cases. Using each IGRT technique, the delivered dose distribution was evaluated on all 30 CBCT scans (6 patients x 5 CBCT/patient). The mean minimum dose (in percentage of prescription dose) to the CTV over five treatment fractions were in the ranges of 99%-100% (SD = 0.1%-0.8%), 65%-98% (SD = 0.4%-19.5%), 87%-99% (SD = 0.7%-23.3%), and 95%-99% (SD = 0.4%-10.4%) for the adapt, bone10, soft5, and soft10 techniques, respectively. Compared to patient position correction techniques, the online reoptimization technique also showed improvement in OAR sparing when organ motion/deformations were large. For bladder, the adapt technique had the best (minimum) D90, D50, and D30 values for 24, 17, and 15 fractions out of 30 total fractions, while it also had the best D90, D50, and D30 values for the rectum for 25, 16, and 19 fractions, respectively. For cases where the adapt plans did not score the best for OAR sparing, the gains of the OAR sparing in the repositioning-based plans were accompanied by an underdosage in the target volume. To further evaluate the fast online replanning technique, a gold-standard plan ("new" plan) was generated for each CBCT anatomy on the Eclipse treatment planning system. The OAR sparing from the online replanning technique was compared to the new plan. The differences in D90, D50, and D30 of the OARs between the adapt and the new plans were less than 5% in 3 patients and were between 5% and 10% for the remaining three. In summary, all IGRT techniques could be sufficient to correct simple geometrical variations. However, when a high degree of deformation or differential organ position displacement occurs, the online reoptimization technique is feasible with less than 2 min optimization time and provides improvements in both CTV coverage and OAR sparing over the position correction techniques. For these cases, the reoptimization technique can be a highly valuable online IGRT tool to correct daily treatment uncertainties, especially when hypofractionation scheme is applied and daily correction, rather than averaging over many fractions, is required to match the original plan.

Comparison of various online IGRT strategies: The benefits of online treatment plan re-optimization

Purpose To compare the dosimetric differences of various online IGRT strategies and to predict potential benefits of online re-optimization techniques in prostate cancer radiation treatments. Materials and methods Nine prostate patients were recruited in this study. Each patient has one treatment planning CT images and 10-treatment day CT images. Five different online IGRT strategies were evaluated which include 3D conformal with bone alignment, 3D conformal re-planning via aperture changes, intensity modulated radiation treatment (IMRT) with bone alignment, IMRT with target alignment and IMRT daily re-optimization. Treatment planning and virtual treatment delivery were performed. The delivered doses were obtained using in-house deformable dose mapping software. The results were analyzed using equivalent uniform dose (EUD). Results With the same margin, rectum and bladder doses in IMRT plans were about 10% and 5% less than those in CRT plans, respectively. Rectum and bladder doses were reduced as much as 20% if motion margin is reduced by 1 cm. IMRT is more sensitive to organ motion. Large discrepancies of bladder and rectum doses were observed compared to the actual delivered dose with treatment plan predication. The therapeutic ratio can be improved by 14% and 25% for rectum and bladder, respectively, if IMRT online re-planning is employed compared to the IMRT bone alignment approach. The improvement of target alignment approach is similar with 11% and 21% dose reduction to rectum and bladder, respectively. However, underdosing in seminal vesicles was observed on certain patients. Conclusions Online treatment plan re-optimization may significantly improve therapeutic ratio in prostate cancer treatments mostly due to the reduction of PTV margin. However, for low risk patient with only prostate involved, online target alignment IMRT treatment would achieve similar results as online re-planning. For all IGRT approaches, the delivered organ-at-risk doses may be significantly different from treatment planning prediction.

On-line re-optimization of prostate IMRT plans for adaptive radiation therapy**Abstract and preliminary data presented at 49th AAPM Annual Meeting, Minneapolis, MN, USA, July 2007.

For intermediate and high risk prostate cancer, both the prostate gland and seminal vesicles are included in the clinical target volume. Internal motion patterns of these two organs vary, presenting a challenge for adaptive treatment. Adaptive techniques such as isocenter repositioning and soft tissue alignment are effective when tumor volumes only exhibit translational shift, while direct re-optimization of the intensity-modulated radiation therapy (IMRT) plan maybe more desirable when extreme deformation or differential positioning changes of the organs occur. Currently, direct re-optimization of the IMRT plan using beamlet (or fluence map) has not been reported. In this study, we report a novel on-line re-optimization technique that can accomplish plan adjustment on-line. Deformable image registration is used to provide position variation information on each voxel along the three dimensions. The original planned dose distribution is used as the ‘goal’ dose distribution for adaptation and to ensure planning quality. Fluence maps are re-optimized via linear programming, and a plan solution can be achieved within 2 min. The feasibility of this technique is demonstrated with a clinical case with large deformation. Such on-line ART process can be highly valuable with hypo-fractionated prostate IMRT treatment.

SU-DD-A3-04: On-Line Re-Optimization of Prostate IMRT Plans for Image Guided Adaptive Radiation Therapy

Purpose: This study proposes a novel on-line adaptive planning technique for the prostate treatment by directly re-optimizing the IMRT plan based on both the “anatomy-of-the-day” and the original plan information. Method & Materials: Using a commercial treatment planning system, an initial IMRT plan for prostate cancer treatment was optimized using seven coplanar 15-MV beams based on the structures of interest (SOIs) delineated in the planning CT. Then, the optimized plan with both intensity fluence maps and dose distributions was exported to an in-house adaptive planning platform. To correct for target variations, a set of on-board cone-beam CT (CBCT) images were acquired prior to treatment and the daily SOIs (“anatomy-of-the-day”) were identified. The original planning SOIs and daily SOIs were registered using a thin-plate-spline based deformable registration algorithm. The optimal dose distribution was then deformed to match the “anatomy-of-the-day” and served as the “prescription dose distribution” for the re-optimization process. Linear programming algorithm was used for re-optimization and could reach a solution in seconds. The algorithm also used the original IMRT plan information as the initial solution. Both hard and soft constraints were used to differentiate the priorities of meeting the prescription dose distribution. A proof-of-concept case using an IMRT prostate plan was presented. The dose-volume histograms from the original, the uncorrected and re-optimized plans were compared. Results: The proposed re-optimization technique reached solutions within 1minute on a desktop PC. The D95(min/max) doses to the GTV were 99.3%(90.0%/104.1%), 83%(57.6%/104.1%) and 98.3%(90.0%/103.8%), for the original, uncorrected and re-optimized plans, respectively. The median doses to the rectum and bladder were comparable for the original and re-optimized plans (41.0% vs. 45.0%, and 14.0% vs. 16.4%, respectively). Conclusion: It is technically feasible to perform on-line re-optimization based on the “anatomy-of-the-day” and to achieve results similar to the original dose distribution.

An algorithm for ranking assignments using reoptimization

We consider the problem of ranking assignments according to cost in the classical linear assignment problem. An algorithm partitioning the set of possible assignments, as suggested by Murty, is presented where, for each partition, the optimal assignment is calculated using a new reoptimization technique. Its computational performance is compared with all available implementations of algorithms with the same time complexity. The results are encouraging.

Adaptive rank-aware query optimization in relational databases

Rank-aware query processing has emerged as a key requirement in modern applications. In these applications, efficient and adaptive evaluation of top- k queries is an integral part of the application semantics. In this article, we introduce a rank-aware query optimization framework that fully integrates rank-join operators into relational query engines. The framework is based on extending the System R dynamic programming algorithm in both enumeration and pruning. We define ranking as an interesting physical property that triggers the generation of rank-aware query plans. Unlike traditional join operators, optimizing for rank-join operators depends on estimating the input cardinality of these operators. We introduce a probabilistic model for estimating the input cardinality, and hence the cost of a rank-join operator. To our knowledge, this is the first effort in estimating the needed input size for optimal rank aggregation algorithms. Costing ranking plans is key to the full integration of rank-join operators in real-world query processing engines.Since optimal execution strategies picked by static query optimizers lose their optimality due to estimation errors and unexpected changes in the computing environment, we introduce several adaptive execution strategies for top- k queries that respond to these unexpected changes and costing errors. Our reactive reoptimization techniques change the execution plan at runtime to significantly enhance the performance of running queries. Since top- k query plans are usually pipelined and maintain a complex ranking state, altering the execution strategy of a running ranking query is an important and challenging task.We conduct an extensive experimental study to evaluate the performance of the proposed framework. The experimental results are twofold: (1) we show the effectiveness of our cost-based approach of integrating ranking plans in dynamic programming cost-based optimizers; and (2) we show a significant speedup (up to 300%) when using our adaptive execution of ranking plans over the state-of-the-art mid-query reoptimization strategies.