Efficient Problem Solving on Tree Decompositions Using Binary Decision Diagrams

Conjunctive queries ( CQ s) have been widely used in database systems in which acyclic CQ s can be computed efficiently, whereas cyclic CQ s may not. Here, a CQ is acyclic if its hypergraph representation H is acyclic. In order to find a class of CQ s that are "mildly cyclic", hypertree decompositions (HDs) have been studied. The quality of such HDs is by the so-called hypertree width. The class of acyclic queries is the queries whose hypertree width is 1, and a mildly cyclic CQ can be processed efficiently if its hypertree width is bounded. There are several HDs, such as tree decomposition (TD), generalized hypertree decomposition (GHD), fractional hypertree decomposition (FHD), as well as hypertree decomposition (HD). The minimum hypertree width by FHD is the smallest among all, and it is NP-complete to check if the minimum hypertree width by FHD exists for a given hypertree width at most k. In the literature, there is no dynamic programming ( DP ) algorithm or branch-&-bound algorithm reported to compute FHD. In this paper, we show that there is a DP algorithm for FHD, and we give a branch-&-bound algorithm based on our DP algorithm to compute FHD with upper/lower bounds. We confirm the effectiveness and efficiency of our algorithm by testing all 3,648 hypergraphs given in a benchmark for HDs, and we also confirm our approach in query evaluation in real database systems.

D-FLAT is a framework for developing algorithms that solve computational problems by dynamic programming on a tree decomposition of the problem instance. The dynamic programming algorithm is specified by means of Answer-Set Programming ASP, allowing for declarative and succinct specifications. D-FLAT traverses the tree decomposition and calls an ASP system with the provided specification at each tree decomposition node. It is thus crucial that the evaluation of the ASP program is done in an efficient way. As experiments have shown, problems that include weights or more involved arithmetics slow down this step significantly due to the grounding step in ASP, which yields large ground programs in these cases. To overcome this problem, we equip D-FLAT with built-in counters in order to shift certain computations from the ASP side to the internal part of D-FLAT. In this paper, we highlight this new feature and provide empirical benchmarks on weighted versions of the Dominating Set problem showing that our new version increases D-FLAT's robustness and efficiency.

Dynamic programming is widely used for exact computations based on tree decompositions of graphs. However, the space complexity is usually exponential in the treewidth. We study the problem of designing efficient dynamic programming algorithm based on tree decompositions in polynomial space. We show how to construct a tree decomposition and extend the algebraic techniques of Lokshtanov and Nederlof [18] such that the dynamic programming algorithm runs in time O *(2 h ), where h is the maximum number of vertices in the union of bags on the root to leaf paths on a given tree decomposition, which is a parameter closely related to the tree-depth of a graph [21]. We apply our algorithm to the problem of counting perfect matchings on grids and show that it outperforms other polynomial-space solutions. We also apply the algorithm to other set covering and partitioning problems.

We present a semantics for Probabilistic Description Logics that is based on the distribution semantics for Probabilistic Logic Programming. The semantics, called DISPONTE, allows to express assertional probabilistic statements. We also present two systems for computing the probability of queries to probabilistic knowledge bases: BUNDLE and TRILL. BUNDLE is based on the Pellet reasoner while TRILL exploits the declarative Prolog language. Both algorithms compute a propositional Boolean formula that represents the set of explanations to the query. BUNDLE builds a formula in Disjunctive Normal Form in which each disjunct corresponds to an explanation while TRILL computes a general Boolean pinpointing formula using the techniques proposed by Baader and Peñaloza. Both algorithms then build a Binary Decision Diagram (BDD) representing the formula and compute the probability from the BDD using a dynamic programming algorithm. We also present experiments comparing the performance of BUNDLE and TRILL.KeywordsProbabilistic DLBinary Decision Diagrams (BDD)Distributional SemanticsProbabilistic Knowledge BaseWeighted Model CountingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Recently, as the market share of electric vehicles (EVs) has increased, how to handle the increased electricity demand for EV charging in the power grid and how to use EV batteries from a grid-operating aspect have become more important. Also, from the perspective of individual EVs, Vehicle-to-Grid (V2G) technologies that reduce the cost for each vehicle’s charging in conjunction with the power grid are significant. In this paper, the V2G control problem at the individual vehicle level is studied using a Dynamic Programming (DP) algorithm that considers EVs’ charging efficiency. The DP algorithm is developed to generate an optimized charging/discharging power profile that minimizes electricity costs, while satisfying the constraints of the initial and final battery states of charge, for given a time-of-use electricity price. To show the effectiveness of the proposed algorithm, simulation is conducted for three different charging scenarios (unidirectional charging, bidirectional charging, and unidirectional charging with cost variations based on electricity usage), and the results showed that DP can achieve significant cost savings of about 30% compared to the normal charging method. Also, the result of DP is compared with that of Linear Programming, demonstrating that DP outperforms Linear Programming in cost savings for the V2G control problem.

Dynamic programming (DP) is a fundamental tool used to obtain exact, optimal solutions for many combinatorial optimization problems. Among these problems, important ones including the knapsack problems and the computation of edit distances between string pairs can be solved with a kind of DP that corresponds to solving the shortest path problem on a directed acyclic graph (DAG). These problems can be solved efficiently with DP, however, in practical situations, we want to solve the customized problems made by adding logical constraints to the original problems. Developing an algorithm specifically for each combination of a problem and a constraint set is unrealistic. The proposed method, BDD-Constrained Search (BCS), exploits a Binary Decision Diagram (BDD) that represents the logical constraints in combination with the DAG that represents the problem. The BCS runs DP on the DAG while using the BDD to check the equivalence and the validity of intermediate solutions to efficiently solve the problem. The important feature of BCS is that it can be applied to problems with various types of logical constraints in a unified way once we represent the constraints as a BDD. We give a theoretical analysis on the time complexity of BCS and also conduct experiments to compare its performance to that of a state-of-the-art integer linear programming solver.

In this paper, a dynamic programming (DP) algorithm is proposed to compute the maximum a posteriori probability (MAP) estimate of the random location of multiple sources by passive sensor array. Based on the principle of optimality, the multivariate MAP decision problem can be transformed into a multistage one‐dimensional maximization problem. By a recursive computation and backward optimum searching technique, the MAP solution can be obtained. The computational complexity is much less than that of the direct MAP searching method, especially when the number of sensors and/or the number of sources is large. In addition, the DP computation technique is equally applicable both in the case of correlated sources and the case of uncorrelated sources.

In this work, we study dynamic programming (DP) algorithms for partially observable Markov decision processes with jointly continuous and discrete state-spaces. We consider a class of stochastic systems which have coupled discrete and continuous systems, where only the continuous state is observable. Such a family of systems includes many realworld systems, for example, Markovian jump linear systems and physical systems interacting with humans. A finite history of observations is used as a new information state, and the convergence of the corresponding DP algorithms is proved. In particular, we prove that the DP iterations converge to a certain bounded set around an optimal solution. Although deterministic DP algorithms are studied in this paper, it is expected that this fundamental work lays foundations for advanced studies on reinforcement learning algorithms under the same family of systems.

Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical dynamic programming (DP) algorithms guarantee optimal solutions, but scale badly with the problem size. We propose Deep Policy Dynamic Programming (DPDP), which aims to combine the strengths of learned neural heuristics with those of DP algorithms. DPDP prioritizes and restricts the DP state space using a policy derived from a deep neural network, which is trained to predict edges from example solutions. We evaluate our framework on the travelling salesman problem (TSP), the vehicle routing problem (VRP) and TSP with time windows (TSPTW) and show that the neural policy improves the performance of (restricted) DP algorithms, making them competitive to strong alternatives such as LKH, while also outperforming most other ‘neural approaches’ for solving TSPs, VRPs and TSPTWs with 100 nodes.KeywordsDynamic ProgrammingDeep LearningVehicle Routing

The powertrain model of the series-parallel plug-in hybrid electric vehicles (PHEVs) is more complicated, compared with series PHEVs and parallel PHEVs. Using the traditional dynamic programming (DP) algorithm or Pontryagin minimum principle (PMP) algorithm to solve the global-optimization-based energy management strategies of the series-parallel PHEVs is not ideal, as the solution time is too long or even impossible to solve. Chief engineers of hybrid system urgently require a handy tool to quickly solve global-optimization-based energy management strategies. Therefore, this paper proposed to use the Radau pseudospectral knotting method (RPKM) to solve the global-optimization-based energy management strategy of the series-parallel PHEVs to improve computational efficiency. Simulation results showed that compared with the DP algorithm, the global-optimization-based energy management strategy based on the RPKM improves the computational efficiency by 1806 times with a relative error of only 0.12%. On this basis, a bi-level nested component-sizing method combining the genetic algorithm and RPKM was developed. By applying the global-optimization-based energy management strategy based on RPKM to the actual development, the feasibility and superiority of RPKM applied to the global-optimization-based energy management strategy of the series-parallel PHEVs were further verified.

This study mainly analyses the fuel consumption of plug-in hybrid vehicles during operation. A new control method for automobiles based on energy management strategy and dynamic programming algorithm is proposed. The new method plans and analyses the minimum electricity consumption, and then uses dynamic programming algorithms to analyse this parameter. The research results indicated that the vehicle state was constantly changing with the variation of SOC value during driving. The energy mobilization of the vehicle was more obvious after adding dynamic programming strategy. The efficiency of the vehicle was relatively high in driving state 1, with a minimum value of 70%, which was about 20% higher than in driving state 4. The average fuel consumption in driving state 2 was 1.8L higher than in other driving states. The overall efficiency of automobiles after incorporating dynamic programming was improved, with a shorter time to reach the lowest efficiency point compared with not incorporating dynamic programming algorithms. The highest efficiency value was 7.86% higher than that of not incorporating dynamic programming models. The new control method can reduce energy consumption and improve the energy management and control effect. The study provides a better research direction for energy management and control of hybrid electric vehicles in the future.

Dynamic Programming (DP) technique is an effective algorithm to find the global optimum. However when applying DP for finite state problems, if the state variables are discretized, it increases the cumulative errors and leads to suboptimal results. In this paper we develop and present a new DP algorithm that overcomes the above problem by eliminating the need to discretize the state space by the use of sets. We show that the proposed DP leads to a globally optimal solution for a discrete time system by minimizing a cost function at each time step. To show the efficacy of the proposed DP, we apply it to optimize the fuel economy of the series and parallel Hybrid Electric Vehicle (HEV) architectures and the case study of Chevrolet Volt 2012 and the Honda Civic 2012 for the series and parallel HEV’s respectively are considered. Simulations are performed over predefined drive cycles and the results of the proposed DP are compared to previous DP algorithm (DPdis). The proposed DP showed an average improvement of 2.45% and 21.29% over the DPdis algorithm for the series and the parallel HEV case respectively over the drive cycles considered. We also propose a real time control strategy (RTCS) for online implementation based on the concept of Preview Control. The RTCS proposed is applied for the series and parallel HEV’s over the drive cycles and the results obtained are discussed.

Dynamic programming is used infrequently by APL programmers, in spite of its ability to reduce the computational effort required to solve many problems. This paper uses the String Shuffle problem as the basis for a comparison of brute force, recursive, and dynamic programming algorithms. Simple algorithms for each of these approaches are designed and evaluated, then individually optimized and re-evaluated, to show the benefits of dynamic programming. The dynamic programming algorithm is then recast to use flow control structures recently introduced into ISI J and APL*PLUS III. Use of control structures in conjunction with dynamic programming results in orders of magnitude performance improvement over brute force and naive recursive algorithms. APL*PLUS III control structures are shown to provide a performance improvement of up to 30% over GOTO-based loops.

The improvement in Integrated Circuits density increases the fault occurrence probability. To ensure proper operation of critical systems, circuits testing becomes a task of extreme importance. Over the years, several methods have been proposed to optimize ATPGs (Automatic Test Pattern Generation). The optimization in test pattern generation aims to reduce the set of test vectors to be applied to circuits. Several techniques explore the concept of equivalent faults (Fault Collapsing). BDDs (Binary Decision Diagram) are one of the data structures explored to solve the problem. With a low capacity to handle large circuits, many extensions and modifications in BDDs have been proposed in the literature. This work aims to review Fault Collapsing concepts and investigate the efficiency of the BDDs proposed in the literature. A case study is done to compare classic techniques with BDDs extensions.

Purpose. To develop a new approach to the design of mining production processes with limited resources. Methods. Combinatorial optimisation methods were used to develop a new approach. The problem of designing technological processes can be solved by interpreting the problem “knapsack problem” with a private solution “backpack 0-1”. Dynamic programming algorithms are used to find the optimal solution. Findings. A new approach to the design of mining production management processes with limited resources has been developed. If the target goal is to obtain the maximum effect at minimum costs, then the direct run method is used. If there are restrictions on bandwidth, energy characteristics, specific cost, then the reverse run method is used. In the final part of the study, the proposed approach was verified. The task consisted in the development of recommendations regarding the choice of the structure of the technological chain of the cleaning pit under the given technological and mining-geological development parameters. The amount of specific production cost was imposed as a limitation. As a result of solving the design problem by the reverse run method, recommendations for replacing the cleaning equipment were developed. This made it possible to ensure the specified level of productivity and reduce the unit cost by 10.6%. The use of combinatorial optimisation methods made it possible to obtain an optimal solution in the field of given parameters. Originality. The scientific novelty of the work consists in establishing regularities in the formation of the efficiency of mineral deposit development processes. For the first time, combinatorial optimization methods were used to design the processes that accompany the development of mineral deposits, and the scope of their application was determined, as well as a number of dynamic programming tasks and algorithms were formalised: backtracking, spanning tree. Practical implication. Verification of the developed approach was carried out in relation to the design of mining production processes with limited resources. The obtained approach makes it possible to find optimal solutions under the constraints set at the design stage. As limitations can be: throughput capacity of the transport chain, energy characteristics of technological processes accompanying mining, specific cost of mining, etc. The design problem can be solved in a direct order – if the objective function is to maximise the parameter, or in the opposite way – if there are restrictions.