Suboptimal Search Algorithms Research Articles

K-Focal Search for Slow Learned Heuristics (Extended Abstract)

Learned heuristics, though inadmissible, can provide very good guidance for bounded-suboptimal search. Given a single search state s and a learned heuristic h, evaluating h(s) is typically very slow relative to expansion time, since state-of-the-art learned heuristics are implemented as neural networks. However, by using a Graphics Processing Unit (GPU), it is possible to compute heuristics using batched computation. Existing approaches to batched heuristic computation are specific to satisficing search and have not studied the problem in the context of bounded-suboptimal search. In this paper, we present K-Focal Search, a bounded suboptimal search algorithm that in each iteration expands K nodes from the FOCAL list and computes the learned heuristic values of the successors using a GPU. We experiment over the Rubik's Cube domain using DeepCubeA, a very effective inadmissible learned heuristic. Our results show that K-Focal Search benefits both from batched computation and from the diversity in the search introduced by its expansion strategy. Over standard FS, it improves runtime by a factor of 6, expansions by up to three orders of magnitude, and finds better solutions, keeping the theoretical guarantees of Focal Search.

Revisiting Suboptimal Search

Suboptimal search algorithms can often solve much larger problems than optimal search algorithms, and thus have broad practical use. This paper returns to early algorithms like WA*, A*_e and Optimistic search. It studies the commonalities between these approaches in order to build a new bounded-suboptimal algorithm. Combined with recent research on avoiding node re-expansions in bounded-optimal search, a new solution quality bound is developed, which often provides proof of the solution bound much earlier during the search. Put together, these ideas provide a new state-of-the-art in bounded-optimal search.

Bounded Suboptimal Search in Linear Space: New Results

Bounded suboptimal search algorithms are usually faster than optimal ones, but they can still run out of memory on large problems. This paper makes three contributions. First, we show how solution length estimates, used by the current state-of-the-art linear-space bounded suboptimal search algorithm Iterative Deepening EES, can be used to improve unbounded-space suboptimal search. Second, we convert one of these improved algorithms into a linear-space variant called Iterative Deepening A* epsilon, resulting in a new state of the art in linear-space bounded suboptimal search. Third, we show how Recursive Best-First Search can be used to create additional linear-space variants that have more stable performance. Taken together, these results significantly expand our armamentarium of bounded suboptimal search algorithms.

Bounded Suboptimal Heuristic Search in Linear Space

It is commonly appreciated that solving search problems optimally can overrun time and memory constraints. Bounded suboptimal search algorithms trade increased solution cost for reduced solving time and memory consumption. However, even suboptimal search can overrun memory on large problems. The conventional approach to this problem is to combine a weighted admissible heuristic with an optimal linear space algorithm, resulting in algorithms such as Weighted IDA* (wIDA*). However, wIDA* does not exploit distance-to-go estimates or inadmissible heuristics, which have recently been shown to be helpful for suboptimal search. In this paper, we present a linear space analogue of Explicit Estimation Search (EES), a recent algorithm specifically designed for bounded suboptimal search. We call our method Iterative Deepening EES (IDEES). In an empirical evaluation, we show that IDEES dramatically outperforms wIDA* on domains with non-uniform edge costs and can scale to problems that are out of reach for the original EES.

Speeding Up Search-Based Motion Planning using Expansion Delay Heuristics

Suboptimal search algorithms are a popular way to find solutions to planning problems faster by trading off solution optimality for search time. This is often achieved with the help of inadmissible heuristics. Prior work has explored ways to learn such inadmissible heuristics. However, it has focused on learning the heuristic value as an estimate of the cost to reach a goal. In this paper, we present a different approach that computes inadmissible heuristics by learning Expansion Delay for transitions in the state space. Expansion Delay is defined as the number of states expanded during the search between two consecutive states. Expansion Delay can be used as a measure of the depth of local minima regions i.e., regions where the heuristic(s) are weakly correlated with the true cost-to-goal (Vats, Narayanan and Likhachev 2017). Our key idea is to learn this measure in order to guide the search such that it reduces the total Expansion delay for reaching the goal and hence, avoid local minima regions in the state space. We analyze our method on 3D (x, y, theta) planning and Humanoid footstep planning. We find that the heuristics computed using our technique result in finding feasible plans faster.

Transition probabilities in generalized quantum search Hamiltonian evolutions

A relevant problem in quantum computing concerns how fast a source state can be driven into a target state according to Schrödinger’s quantum mechanical evolution specified by a suitable driving Hamiltonian. In this paper, we study in detail the computational aspects necessary to calculate the transition probability from a source state to a target state in a continuous time quantum search problem defined by a multiparameter generalized time-independent Hamiltonian. In particular, quantifying the performance of a quantum search in terms of speed (minimum search time) and fidelity (maximum success probability), we consider a variety of special cases that emerge from the generalized Hamiltonian. In the context of optimal quantum search, we find it is possible to outperform, in terms of minimum search time, the well-known Farhi–Gutmann analog quantum search algorithm. In the context of nearly optimal quantum search, instead, we show it is possible to identify sub-optimal search algorithms capable of outperforming optimal search algorithms if only a sufficiently high success probability is sought. Finally, we briefly discuss the relevance of a tradeoff between speed and fidelity with emphasis on issues of both theoretical and practical importance to quantum information processing.

Multi-level rate-constrained successive elimination algorithm tailored to suboptimal motion estimation in HEVC

In the context of motion estimation for video coding, successive elimination algorithms (SEAs) significantly reduce the number of candidates evaluated during motion estimation without altering the resulting optimal motion vector. Nevertheless, SEA is often only used in conjunction with exhaustive search algorithms (e.g., full search). In this paper, we combine the multi-level successive elimination algorithm (ML-SEA) and the rate-constrained successive elimination algorithm (RCSEA) and show that they can be advantageously applied to suboptimal search algorithms. We demonstrate that the savings brought about by the new multi-level RCSEA (ML-RCSEA) outweigh the pre-computational costs of this approach for the Test Zonal (TZ) Search algorithm found in the HM reference encoder. We propose a novel multi-level composition pattern for performing RCSEA on an asymmetric partitioning. We introduce a double-check mechanism for RCSEA, and show that on average, it avoids computing 71% of motion vector (MV) costs. We also apply the proposed ML-RCSEA to bi-predictive refinement search and leverage a cost-based search ordering to remove 56% of error metric computations, on average. When compared to the HM reference encoder, our experiments show that the proposed solution reduces the TZ Search time by approximately 45%, contributing to an average encoding time reduction of about 7%, without increasing the Bjøntegaard delta rate (BD-Rate).

Combination therapy design for maximizing sensitivity and minimizing toxicity

BackgroundDesign of personalized targeted therapies involve modeling of patient sensitivity to various drugs and drug combinations. Majority of studies evaluate the sensitivity of tumor cells to targeted drugs without modeling the effect of the drugs on normal cells. In this article, we consider the individual modeling of drug responses to tumor and normal cells and utilize them to design targeted combination therapies that maximize sensitivity over tumor cells and minimize toxicity over normal cells.ResultsThe problem is formulated as maximizing sensitivity over tumor cell models while maintaining sensitivity below a threshold over normal cell models. We utilize the constrained structure of tumor proliferation models to design an accelerated lexicographic search algorithm for generating the optimal solution. For comparison purposes, we also designed two suboptimal search algorithms based on evolutionary algorithms and hill-climbing based techniques. Results over synthetic models and models generated from Genomics of Drug Sensitivity in Cancer database shows the ability of the proposed algorithms to arrive at optimal or close to optimal solutions in significantly lower number of steps as compared to exhaustive search. We also present the theoretical analysis of the expected number of comparisons required for the proposed Lexicographic search that compare favorably with the observed number of computations.ConclusionsThe proposed algorithms provide a framework for design of combination therapy that tackles tumor heterogeneity while satisfying toxicity constraints.

An improvement on the Migrating Birds Optimization with a problem-specific neighboring function for the multi-objective task allocation problem

Allocating tasks to processors is a well-known NP-Hard problem in distributed computing systems. Due to the lack of practicable exact solutions, it has been attracted by the researchers working on heuristic-based suboptimal search algorithms. With the recent inclusion of multiple objectives such as minimizing the cost, maximizing the throughput and maximizing the reliability, the problem gets even more complex and an efficient approximate method becomes more valuable. In this work, I propose a new solution for the multi-objective task allocation problem. My solution consists in designing a problem-specific neighboring function for an existing metaheuristic algorithm that is proven to be successful in quadratic assignment problems. The neighboring function, namely greedy reassignment with maximum release (GR-MR), provides a dynamic mechanism to switch the preference of the search between the exploration and exploitation. The experiments validate both that the quality of the solutions are close to the optimal and the proposed method performs significantly better comparing to three other metaheuristic algorithms. Neighboring functions being the common reusable components of metaheuristic algorithms, GR-MR can also be utilized by other metaheuristic-based solutions in the future.

What's Hot in Heuristic Search

Search in general, and heuristic search in particular, is at the heart of many Artificial Intelligence algorithms and applications. There is now a growing and active community devoted to the empirical and theoretical study of heuristic search algorithms, thanks to the successful application of search-based algorithms to areas such as robotics, domain-independent planning, optimization, and computer games. In this extended abstract we highlight recent efforts in understanding suboptimal search algorithms, as well as ensembles of heuristics and algorithms. The result of these efforts are meta-reasoning methods which are applied to orchestrate the different components of modern search algorithms. Finally, we mention recent innovative applications of search that demonstrate the relevance of the field to general AI.

HARQ Rate Selection Schemes in a Multihop Relay Network With a Delay Constraint

We investigate rate selection methods to maximize a utility function of a multihop relay network adopting a Chase combining-type hybrid automatic repeat request scheme. For supporting delay-limited applications, we consider the following two constraints: 1) The number of (re)transmissions used in the whole hops is limited to L, and 2) the information-theoretic outage probability should be less than or equal to ε. We formulate an optimization problem to maximize the long-term average transmission rate of an M-hop relay network by finding the optimal round transmission rate [b/s/Hz] of each hop while satisfying those two constraints. We also consider two reformulated problems and, as the solutions to those problems, propose suboptimal search algorithms, which significantly reduce the complexity, compared with that of the optimal search algorithm corresponding to the solution of the original optimization problem. While the original optimization problem always requires M-dimensional exhaustive search, the first reformulated problem requires M-dimensional exhaustive search only in a specific condition, and it obtains a closed-form solution otherwise. The second reformulated problem requires 1-D numerical search only in a specific condition, and it obtains a closed-form solution otherwise. We also show that the relative loss of the solution of the first reformulated problem is upper bounded by 2ε.

Simpler Bounded Suboptimal Search

It is commonly appreciated that solving search problems optimally can take too long. Bounded suboptimal search algorithms trade increased solution cost for reduced solving time. Explicit Estimation Search (EES) is a recent state-of-the-art algorithm specifically designed for bounded suboptimal search. Although it tends to expand fewer nodes than alternative algorithms, such as weighted A* (WA*), its per-node expansion overhead is higher, causing it to sometimes take longer. In this paper, we present simplified variants of EES (SEES) and an earlier algorithm, A*epsilon (SA*epsilon), that use different implementations of the same motivating ideas to significantly reduce search overhead and implementation complexity. In an empirical evaluation, we find that SEES, like EES, outperforms classic bounded suboptimal search algorithms, such as WA*, on domains tested where distance-to-go estimates enable better search guidance. We also confirm that, while SEES and SA*epsilon expand roughly the same number of nodes as their progenitors, they solve problems significantly faster and are much easier to implement. This work widens the applicability of state-of the-art bounded suboptimal search by making it easier to deploy.

Learning Inadmissible Heuristics During Search

Suboptimal search algorithms offer shorter solving times by sacrificing guaranteed solution optimality. While optimal searchalgorithms like A* and IDA* require admissible heuristics, suboptimalsearch algorithms need not constrain their guidance in this way. Previous work has explored using off-line training to transform admissible heuristics into more effective inadmissible ones. In this paper we demonstrate that this transformation can be performed on-line, during search. In addition to not requiring training instances and extensive pre-computation, an on-line approach allows the learned heuristic to be tailored to a specific problem instance. We evaluate our techniques in four different benchmark domains using both greedy best-first search and bounded suboptimal search. We find that heuristics learned on-line result in both faster search andbetter solutions while relying only on information readily available in any best-first search.

Finding Acceptable Solutions Faster Using Inadmissible Information

Bounded suboptimal search algorithms attempt to find a solution quickly while guaranteeing that the cost does not exceed optimal by more than a desired factor. These algorithms generally use a single admissible heuristic both for guidance and guaranteeing solution quality. We present a new approach to bounded suboptimal search that separates these roles, consulting multiple sources of potentially inadmissible information to determine search order and using admissible information to guarantee quality. An empirical evaluation across six benchmark domains shows the new approach has better overall performance.

A Fast Block Matching Algorithm Based on Motion Vector Correlation and Integral Projections

The block based motion estimation technique is adopted by various video coding standards to reduce the temporal redundancy in video sequences. The core of that technique is the search algorithm implementedto find the location of the best matched block. Indeed, the full search algorithm is the most straightforward and optimal but computationally demanding search algorithm. Consequently, many fast and suboptimal search algorithms have been proposed. Reduction of the number of location being searched is the approach used to decrease the computational load of full search. In this paper, hybridization between an adaptive search algorithm and the full search algorithm is proposed. The adaptive search algorithm benefits from the correlation within spatial and temporal adjacent blocks. At the same time, a feature domain based matching criteria is used to reduce the complexity resulting from applying the pixel based conventional criteria. It is shown that the proposed algorithm produces good quality performance and requires less computational time compared with popular block matching algorithms.

Foveation image coding with fuzzy-based joint parameter selection

This paper presents a novel method of the foveation image coding based on the fuzzy-based joint parameter selection. Our objective is to maximize foveated wavelet image quality index (FWQI) of the reconstructed image. With the foveated visual sensitivity model, image regions are first prioritized. The image regions close to foveation points have higher priorities than those far away from the foveation points. The discrete wavelet transform (DWT) is utilized to transform the considering image to the wavelet domain. The wavelet coefficients from different image regions are weighted using the foveated visual sensitivity model and then scaled down before entropy encoding. To achieve the objective, we use a fuzzy logic system and an iterative search to select image coding parameters under the bit budget constraint. The coding parameters consist of a number of weighted wavelet coefficients in the list significant pixel (LSP) of the SPIHT codec [A. Said, W.A. Pearlman, A new, fast, and efficient image codec based on set partitioning in hierarchical trees, IEEE Trans. Circuits Syst. Video Technol. 6 (3) (1996) 243–250], represented as N LSP, and a scaling down factor ( QP). There are two inputs and one output in the proposed fuzzy logic system. The inputs are N LSP and targeted bit per pixel used to encode an image. The output is an interval of QP. The QP value corresponding to the input N LSP giving the highest FWQI is selected from the derived interval. We iteratively search for the values of N LSP and QP providing the highest FWQI. Then, the SPIHT codec is used to generate a scalable bitstream of the discrete wavelet coefficients with the optimal pair of N LSP and QP. The sub-optimal search algorithm to compute both N LSP and QP with low complexity is also proposed. Our simulation results show that the proposed scheme provides a better reconstructed image quality comparing to previous work in both objective and subjective qualities.

Variable selection procedures and efficient suboptimal mask search algorithms in fuzzy inductive reasoning

This paper describes two new suboptimal mask search algorithms for Fuzzy inductive reasoning (FIR), a technique for modelling dynamic systems from observations of their input/output behaviour. Inductive modelling is by its very nature an optimisation problem. Modelling large-scale systems in this fashion involves solving a high-dimensional optimisation problem, a task that invariably carries a high computational cost. Suboptimal search algorithms are therefore important. One of the two proposed algorithms is a new variant of a directed hill-climbing method. The other algorithm is a statistical technique based on spectral coherence functions. The utility of the two techniques is demonstrated by means of an industrial example. A garbage incinerator process is inductively modelled from observations of 20 variable trajectories. Both suboptimal search algorithms lead to similarly good models. Each of the algorithms carries a computational cost that is in the order of a few percent of the cost of solving the complete optimisation problem. Both algorithms can also be used to filter out variables of lesser importance, i.e. they can be used as variable selection tools.

Fractal model of a one-dimensional discrete signal and its implementation

An extended iterated-function-system (IFS) interpolation method is presented for modelling for a given discrete signal. To reduce the computing complexity a suboptimal search algorithm with a robust technique for estimating the IFS affine-map parameters is introduced. Simulation results show that the IFS approach achieves a higher signal-to-noise ratio than does an existing approach based on autoregressive modelling.

Near merging of paths in suboptimal tree searching (Corresp.)

The near merging of paths in tree searching is explored. This near merging can degrade coding performance when a suboptimal search algorithm is used. The problem is first identified and then a feasible solution is presented. Some examples from image source coding using the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(M, L)</tex> algorithm are given.