An adaptive branching rule based branch-and-bound algorithm for generalized affine fractional programming

Efficient minimization of higher order submodular functions using monotonic Boolean functions

For applications that deal with large amounts of high dimensional multi-aspect data, it becomes natural to represent such data as tensors or multi-way arrays. Multi-linear algebraic computations such as tensor decompositions are performed for summarization and analysis of such data. Their use in real-world applications can span across domains such as signal processing, data mining, computer vision, and graph analysis. The major challenges with applying tensor decompositions in real-world applications are (1) dealing with large-scale high dimensional data and (2) dealing with sparse data. In this paper, we address these challenges in applying tensor decompositions in real data analytic applications. We describe new sparse tensor storage formats that provide storage benefits and are flexible and efficient for performing tensor computations. Further, we propose an optimization that improves data reuse and reduces redundant or unnecessary computations in tensor decomposition algorithms. Furthermore, we couple our data reuse optimization and the benefits of our sparse tensor storage formats to provide a memory-efficient scalable solution for handling large-scale sparse tensor computations. We demonstrate improved performance and address memory scalability using our techniques on both synthetic small data sets and large-scale sparse real data sets.

The aim of this paper is to suggest a solution procedure to fractional programming problem based on new ranking function (RF) with triangular fuzzy number (TFN) based on alpha cuts sets of fuzzy numbers. In the present procedure the linear fractional programming (LFP) problems is converted into linear programming problems. We concentrate on linear programming problem problems in which the coefficients of objective function are fuzzy numbers, the right- hand side are fuzzy numbers too, then solving these linear programming problems by using a new ranking function. The obtained linear programming problem can be solved using win QSB program (simplex method) which yields an optimal solution of the linear fractional programming problem. Illustrated examples and comparisons with previous approaches are included to evince the feasibility of the proposed approach.

In this paper a new Adaptive Full-order Observer (AFO) with an auxiliary variable is presented and compared with the classical one. This auxiliary variable introduced in the AFO state equations is related to the rotor time constant and is adapted together with the moto speed. Both adaptation rules are derived using Lyapunov theory. Based on the stability analysis it has been shown that the proposed estimator is stable in a full operating range on contrary to the classical solution, which have the unstable area in regenerating mode and requires application of a stability improvement method. This feature is validated by theoretical, simulation and experimental results, in full operating range, in open and closed-loop operation.

We formulate and study a one–dimensional single–species diffusive–delay population model. The time delay is the time taken from birth to maturity. Without diffusion, the delay differential model extends the well–known logistic differential equation by allowing delayed constant birth processes and instantaneous quadratically regulated death processes. This delayed model is known to have simple global dynamics similar to that of the logistic equation. Through the use of a sub/supersolution pair method, we show that the diffusive delay model continues to generate simple global dynamics. This has the important biological implication that quadratically regulated death processes dramatically simplify the growth dynamics. We also consider the possibility of travelling wavefront solutions of the scalar equation for the mature population, connecting the zero solution of that equation with the positive steady state. Our main finding here is that our fronts appear to be all monotone, regardless of the size of the delay. This is in sharp contrast to the frequently reported findings that delay causes a loss of monotonicity, with the front developing a prominent hump in some other delay models.

Depression filling is a critical step in distributed hydrological modeling using digital elevation models (DEMs). The traditional Priority‐Flood (PF) approach is widely used due to its relatively high efficiency when dealing with a small‐sized DEM. However, it seems inadequate and inefficient when dealing with large high‐resolution DEMs. In this work, we examined the relationship between the PF algorithm calculation process and the topographical characteristics of depressions, and found significant redundant calculations in the local micro‐relief areas in the conventional PF algorithm. As such calculations require more time when dealing with large DEMs, we thus propose a new variant of the PF algorithm, wherein redundant points and calculations are recognized and eliminated based on the local micro‐relief water‐flow characteristics of the depression‐filling process. In addition, depressions and flatlands were optimally processed by a quick queue to improve the efficiency of the process. The proposed method was applied and validated in eight case areas using the Shuttle Radar Topography Mission digital elevation model (SRTM‐DEM) with 1 arc‐second resolution. These selected areas have different data sizes. A comparative analysis among the proposed method, the Wang and Liu‐based PF, the improved Barnes‐based PF, the improved Zhou‐based PF, and the Planchon and Darboux (P&D) algorithms was conducted to evaluate the accuracy and efficiency of the proposed algorithm. The results showed that the proposed algorithm is 43.2% (maximum) faster than Wang and Liu's variant of the PF method, with an average of 31.8%. In addition, the proposed algorithm achieved similar performance to the improved Zhou‐based PF algorithm, though our algorithm has the advantage of being simpler. The optimal strategies using the proposed algorithm can be employed in various landforms with high efficiency. The proposed method can also achieve good depression filling, even with large amounts of DEM data.

Contributors

In this paper, we address the development of efficient global search methods for a sum of ratios (i.e. a fractional programming) problem. This is, in general, a nonconvex problem (with numerous local extremum) which belongs to a class of global optimization problems. We proved the reduction theorem for the fractional programming problem with the d.c. functions and one equation with the vector parameter that satisfy the nonnegativity assumption. This theorem allows a justified use of the Dinkelbach’s approach to solving fractional programming problems with the goal function given by d.c. functions.

The global Riemann problem for a nonstrictly hyperbolic system of conservation laws modeling polymer flooding is solved. In particular, the system contains a term that models adsorption effects.

Dynamic Heterogeneous GNNs (DyHGNNs) are increasingly employed to model the complex relationships between various types of vertices and edges in real-world applications. When performing DyHGNN inference, existing software/hardware solutions adopt the snapshot-by-snapshot execution approach, and suffer from frequent and irregular access to identical neighbors for the same vertex across multiple snapshots, leading to redundant computations and irregular memory accesses. To address these challenges, we propose an efficient cross-snapshot hardware accelerator, i.e., COSH, which facilitates high-performance execution of DyHGNN inference. Specifically, we integrate a redundancy-aware asynchronous Filter-Load-Aggregate-Gather (FLAG) execution model into the accelerator design to minimize redundant computation and off-chip memory accesses. FLAG traverses the neighbors of the same vertex across different snapshots to identify all involved vertices and filter out changes in neighbors between consecutive snapshots. Then, it computes intermediate aggregation features for all encountered neighbors and incrementally calculates the results for the vertices in each snapshot, eliminating redundant computations and regularizing memory accesses. To minimize redundant accesses for vertex features, we also design a hierarchical data loading mechanism to provide a parallelized cross-snapshot filter to enhance the efficiency of processing graph structures. Besides, a coordinated feature aggregator is also proposed to synchronize feature aggregation and gathering, ensuring the timely utilization and management of generated intermediate features to boost computational parallelism. Our experimental results demonstrate that, compared to state-of-the-art software and hardware solutions, COSH achieves performance improvements of 27.1x and 3.6x on average, and also energy efficiency gains of 29.5x and 3.7x on average, respectively.

Graph processing has become a central concern for many real-world applications and is well-known for its low compute-to-communication ratios and poor data locality. By integrating computing logic into memory, resistive random access memory (ReRAM) tackles the demand for high memory bandwidth in graph processing. Despite the years’ research efforts, existing ReRAM-based graph processing approaches still face the challenges of redundant computation overhead . It is because the vertices of many subgraphs are ineffectively and repeatedly processed over the ReRAM crossbars for lots of iterations so as to update their states according to the vertices of other subgraphs regardless of the dependencies among the subgraphs. In this article, we propose ASGraph , a dependency-aware ReRAM-based graph processing accelerator that overcomes the aforementioned performance bottlenecks. Specifically, ASGraph dynamically constructs the subgraph based on the dependencies between vertices’ states and then detects constructed subgraph that owns high value (it is likely that it has accumulated many state propagations from its neighbors and is able to affect more other neighbors) to be preferentially processed. In this way, it makes the vertex states propagate along the dependencies between vertices as much as possible to reduce the redundant computation. Besides, ASGraph employs a hybrid processing scheme to accelerate the state propagations of the tightly connected subgraph, thereby minimizing the redundant computations. Experimental results show that ASGraph achieves 25.5× and 4.8× speedup and 70.8× and 2.2× energy saving on average compared with the state-of-the-art ReRAM-based graph processing accelerators, that is, GraphR and GaaS-X, respectively.

PurposeThe paper aims to introduce a novel concept to solve the bi-level multi-criteria nonlinear fractional programming (BL-MCNFP) problems. Bi-level programming problem (BLPP) is rigorously flourished and studied by several researchers, which deals with decentralized decisions by comprising a sequence of two optimization problems, namely upper and lower-level problems. However, on the other hand, many real-world decision-making problems involve multiple objectives with fraction aspects, called fractional programming problems that reflect technical and economic performance.Design/methodology/approachThis paper introduces a VIKOR (“VlseKriterijumska Optimizacija I Kompromisno Resenje”) approach to solve the BL-MCNFP problem. In this approach, an aggregating function based on LP metrics is formulated on the basis of the “closeness” scheme from the “ideal” solution. The three steps perform the solution process: First, a new concept is attempted to minimize and maximize of the numerators and denominators from their respective ideal solutions and anti-ideal values simultaneously. Second, for each level, the K-dimensional objective space of each level is converted to a one-dimensional space by an aggregating function. Third, to obtain the final solution, all levels are combined into single-level model where the decision variables of upper levels are interrelated with other levels through fuzzy strategy-based linear and nonlinear membership functions.FindingsThe effectiveness of the proposed VIKOR is demonstrated by numerical examples, where the reported results affirm that the extended VIKOR method provides superior results in comparison with the same methods in the literature, and it is a good alternative to BL-MCNFP problems.Originality/valueIn terms of the assistance-based right decision, a parametric analysis for the weight of the majority is provided to exhibit a wide range of compromise solutions for the decision-maker.

A proposed model for solving fuzzy linear fractional programming problem: Numerical Point of View

A new approach to obtaining the optimality conditions for fractional mathematical programming problems involving one objective ratio in the objective function is considered. Using this approach, an equivalent optimization problem is constructed by a modification of the single-ratio objective function in the fractional programming problem. Furthermore, an η-Lagrange function is introduced for a constructed optimization problem and modified saddle-point results are presented.

Fuzed fiber optic plates