Search Results For Beaming Fixed
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Search results for beaming
Purpose: The purpose of this article is to explore the use of the accelerated exhaustive search strategy for developing and validating methods for optimizing beam orientations for intensity-modulated radiation therapy (IMRT). Combining beam-angle optimization (BAO) with intensity distribution optimization is expected to improve the quality of IMRT treatment plans. However, BAO is one of the most difficult problems to solve adequately because of the huge hyperspace of possible beam configurations (e.g., selecting 7 of 36 uniformly spaced coplanar beams would require the intercomparison of 8,347,680 IMRT plans).
Methods and materials: An "influence vector" (IV) approximation technique for high-speed estimation of IMRT dose distributions was used in combination with a fast gradient search algorithm (Newton's method) for IMRT optimization. In the IV approximation, it is assumed that the change in intensity of a ray (or bixel) proportionately changes dose along the ray. Evidence is presented that the IV approximation is valid for BAO. The scatter contribution at points away from the ray is accounted for fully in IMRT optimization after the optimum beam orientation has been determined. IVs for all candidate beam angles are generated before the start of optimization. For all subsets of beams selected from a given pool of beams (e.g., 5 of 24 uniformly spaced beams), the distribution of planning scores for the best and the worst plans, optimum angle distributions, dose distributions, and dose-volume histograms (DVH) were analyzed for one prostate and two lung cancer cases. The results of the exhaustive search technique were used to develop a "multiresolution" search strategy. In this approach, a smaller number of beams (e.g., three) is first used to explore the hyperspace of solutions to determine the most preferred and the least preferred directions. The results of such exploration are then used as a starting point for determining an optimum configuration comprising a larger number of beams (e.g., seven). This two-step process is considerably faster than full exhaustive search. The question to be answered was whether the two methods lead to the same or similar solutions. The results of exhaustive search and multiresolution approaches were also compared with a previously published approach that used beam's-eye-view dosimetrics (BEVD).
Results: The relative ranks of plans optimized by an accurate dose calculation method were highly correlated with those of the plans optimized by the fast calculation method (i.e., using the IV approximation), which suggests that an approximate dose calculation algorithm can be used effectively for ranking of plans during BAO. We found that dose distributions and DVH of many beam configurations within a specified subset from a given pool of beams (e.g., 5 of 18) may be clinically indistinguishable and acceptable. Their optimized IMRT scores fall in a narrow range, although beam configurations and dose distributions may be different. We used the frequency distributions as a function of beam angles for the best 100 and the worst 100 plans to determine the most and the least preferred beam angles. We found that the most and the least preferred angle distributions for 3 of 18 configurations were very similar to those for 5, 6, 7, or 8 of 18 or 24 configurations, but the size of the search space was much smaller for the 3 of 18 case. Using fewer than three beams was discovered to be inadequate. This information was used to select the most preferred angles and eliminate the least preferred ones before searching for the optimum angles for the remaining beams. For the cases we studies, the multiresolution strategy produced very similar results to the full exhaustive search. Based on the observation that the worst plans had at least one parallel-opposed pair of beams and virtually all of the best plans had none, we were able to further reduce the size of the search space dramatically by using a pool of only nonparallel-opposed equispaced beams (i.e., 7 of 19 instead of 7 of 36). Another observation was that the probability of finding an optimum configuration in a smaller beam pool is substantially lower than in a larger pool (e.g., 5 of 18 vs. 5 of 24). The implication of this BAO is not very important when a large number of beams (nine or more) is used and vice versa. Our results showed that the plans with fewer but optimally placed beams could be as good as or better than plans using a larger number of unoptimized or uniformly placed beams.
Conclusion: Exhaustive search with fast IMRT algorithms provides a novel and realistic approach to study the characteristics of IMRT dose distributions as a function of beam angles and to design practical BAO strategies for IMRT planning.
If the goal is to obtain the most likely sequence, we may consider usingexhaustive search: exhaustively enumerate all the possible outputsequences with their conditional probabilities, and then output the onethat scores the highest predicted probability.
You could view sequence decoding strategies as lying on a spectrum, withbeam search striking a compromise between the efficiency of greedysearch and the optimality of exhaustive search. The most straightforwardversion of beam search is characterized by a single hyperparameter, thebeam size, \(k\). At time step 1, we select the \(k\) tokenswith the highest predicted probabilities. Each of them will be the firsttoken of \(k\) candidate output sequences, respectively. At eachsubsequent time step, based on the \(k\) candidate output sequencesat the previous time step, we continue to select \(k\) candidateoutput sequences with the highest predicted probabilities from\(k\left\mathcalY\right\) possible choices.
The computational cost of beam search is\(\mathcalO(k\left\mathcalY\rightT')\). This result is inbetween that of greedy search and that of exhaustive search. Greedysearch can be treated as a special case of beam search arising when thebeam size is set to 1.
Sequence searching strategies include greedy search, exhaustive search,and beam search. Beam search provides a tradeoff between accuracy versuscomputational cost via its flexible choice of the beam size.
In computer science, beam search is a heuristic search algorithm that explores a graph by expanding the most promising node in a limited set. Beam search is an optimization of best-first search that reduces its memory requirements. Best-first search is a graph search which orders all partial solutions (states) according to some heuristic. But in beam search, only a predetermined number of best partial solutions are kept as candidates.[1] It is thus a greedy algorithm.
Beam search uses breadth-first search to build its search tree. At each level of the tree, it generates all successors of the states at the current level, sorting them in increasing order of heuristic cost.[3] However, it only stores a predetermined number, β \displaystyle \beta , of best states at each level (called the beam width). Only those states are expanded next. The greater the beam width, the fewer states are pruned. With an infinite beam width, no states are pruned and beam search is identical to breadth-first search. The beam width bounds the memory required to perform the search. Since a goal state could potentially be pruned, beam search sacrifices completeness (the guarantee that an algorithm will terminate with a solution, if one exists). Beam search is not optimal (that is, there is no guarantee that it will find the best solution).[4]
A beam search is most often used to maintain tractability in large systems with insufficient amount of memory to store the entire search tree.[5] For example, it has been used in many machine translation systems.[6] (The state of the art now primarily uses neural machine translation based methods.) To select the best translation, each part is processed, and many different ways of translating the words appear. The top best translations according to their sentence structures are kept, and the rest are discarded. The translator then evaluates the translations according to a given criterion, choosing the translation which best keeps the goals. The first use of a beam search was in the Harpy Speech Recognition System, CMU 1976.[7]
Beam search has been made complete by combining it with depth-first search, resulting in beam stack search[8] and depth-first beam search,[5] and with limited discrepancy search,[5] resulting in beam search using limited discrepancy backtracking[5] (BULB). The resulting search algorithms are anytime algorithms that find good but likely sub-optimal solutions quickly, like beam search, then backtrack and continue to find improved solutions until convergence to an optimal solution.
In the context of a local search, we call local beam search a specific algorithm that begins selecting β \displaystyle \beta randomly generated states and then, for each level of the search tree, it always considers β \displaystyle \beta new states among all the possible successors of the current ones, until it reaches a goal.[9][10]
Since local beam search often ends up on local maxima, a common solution is to choose the next β \displaystyle \beta states in a random way, with a probability dependent from the heuristic evaluation of the states. This kind of search is called stochastic beam search.[11]
Beam search is an algorithm used in many NLP and speech recognition models as a final decision making layer to choose the best output given target variables like maximum probability or next output character. First used for speech recognition in 1976, beam search is used often in models that have encoders and decoders with LSTM or Gated Recurrent Unit modules built in. To understand where this algorithm is used a little more let's take a look at how NLP models generate output, to see where Beam search comes into play. 041b061a72