Decomposable Structure Research Articles

Bamboo Structure and Its Impact on Mechanical Properties: A Case Study of Bambusa arundinaceae

Bamboo is a naturally occurring composite material, which exhibits a decomposable structure with varying composition. The distinct structural features of bamboo contribute to its exceptional strength and flexibility, making it an excellent choice for construction purposes. However, only a limited portion of bamboo species has been studied for its mechanical properties, and research on Bambusa arundinaceae has primarily focused on its pharmaceutical values. Therefore, we investigated the relationship between the structural characteristics of B. arundinaceae and its mechanical properties using axial compression experiments and tangential bending experiments. The results showed that the distribution density of vascular bundles (VBs) of B. arundinaceae ranged from 1.98 to 4.34 pcs/mm2,while the volume fraction of fiber sheaths (FSs) ranged from 35.82 to 42.58%. The average compressive strength, flexural strength, and flexural elasticity modulus were 113.99 MPa, 239.07 MPa, and 17.39 GPa, which were 97.56%, 64.07%, and 66.09% higher than those of moso bamboo (Phyllostachys edulis), respectively. The compressive strength, flexural strengths, and elasticity modulus of B. arundinaceae were positively correlated with both the distribution density of VBs and the volume fraction of FSs. These insights are crucial for the advancement of durable and efficient materials in diverse sectors including construction and manufacturing.

Two-Stage emergency material scheduling based on benders decomposition considering traffic congestion after a disaster

This study establishes a stochastic mixed integer nonlinear programming model for a two-stage emergency multiclass material scheduling problem considering traffic congestion with a Bureau of Public Roads (BPR) function. The generalized Benders decomposition (GBD) algorithm is used to solve the model on the basis of the characteristics of the decomposable structure and nonlinear convex function. To prove the effectiveness of the GBD algorithm, we set up a 30-node medium-scale case and a 50-node large-scale case for experimental demonstration and compared the GBD algorithm with the simple branch and bound (SBB) and discrete and continuous optimization solvers. Results show that for the medium-scale experiment, the gap between the solution results of the GBD algorithm and the ones of SBB or other solvers is less than 0.2%. The solution time of the GBD algorithm is only half of the time of SBB and other solvers. The large-scale case of 50 nodes cannot be solved by the SBB or other solvers, whereas the GBD algorithm can solve it normally, and the results are reasonable. In large-scale cases with more than 50 nodes, the GBD algorithm is more effective and efficient compared with SBB and other solvers. The sensitivity of the correlation coefficient α in the BPR function was analyzed. The actual expected total cost increases with the increase in the value of α. Its solving results are accurate and reasonable, proving that the results are more practical and applicable after adding the BPR function.

A new framework for analysing local participation in community energy initiatives

The Dutch Climate Agreement includes a 50 percent local ownership of energy production target. However, what is meant by “local,” “ownership” and “participation” is not strictly defined in the Agreement. Nevertheless, community energy initiatives are expected to be an integral part of the ‘local ownership’ goals listed in the Agreement. Consequently, there is a need for a robust framework which can capture local nuances, explain the role and degree of citizen participation in different contexts and areas of participation, and that will allow community energy initiatives to benchmark their participation levels in relation to ‘others’ and their own change over time. This paper proposes a new diagnostic framework which conceptualizes participation in the technical, political, and economic dimensions of local energy transitions and that can identify gaps and challenges in community energy initiatives in relation to local participation. We use the Socio-ecological Systems Framework (SESF) as a starting point and enrich the framework’s third and fourth tier variables using Arnstein’s ladder of participation along with other participatory literature. Our framework outlines the key variables for understanding the participatory environment in which participation occurs and links the environment to the levels of participation. The framework provides granularity and flexibility given its multi-tier and decomposable structure. Therefore, supporting gap analysis of local participation and comparison across diverse cases.

Public Transport-Based Crowd-Shipping with Backup Transfers

With the rising urbanization and booming e-commerce, traditional last-mile delivery systems fail to satisfy the need for faster, cheaper, and more environmentally friendly deliveries. Several new approaches are put forward as an alternative to classical delivery systems in this regard, yet none of them offers the same level of flexibility, capacity, reliability, and managerial control by itself. This paper proposes a new last-mile delivery model that combines several new approaches and technologies to address this issue. More precisely, we suggest using public transit as a backbone network completed by automated service points, crowd-shipping, and backup transfers with zero-emission vehicles to provide a low-cost and environmentally friendly express delivery service. The design problem for the envisioned system is formulated as a two-stage stochastic program, and a branch-and-price (BP) algorithm is devised to solve it. Taking advantage of the nearly decomposable structure that would emerge in possible real-world applications, our study presents the first example of using decomposition branching in a BP framework to enhance computational efficiency. Extensive computational studies and simulations with real-world data reveal valuable managerial insights for the proposed system and attest to the efficacy of the suggested methodology. Funding: This work was supported by Türkiye Bilimsel ve Teknolojik Araştirma Kurumu [Grant 218M605] and Bilim Akademisi. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.1157 .

Joint berth allocation and ship loader scheduling under the rotary loading mode in coal export terminals

Due to nonmatching between the efficiency of ship deballasting and terminal loading, operations in modern coal export terminals (CETs) are frequently interrupted and significantly restricted by ship deballasting delays. This paper addresses a novel integrated problem of berth allocation and ship loader scheduling arising in CETs with new features, including the symmetrical berth layout-based rotary loading mode (SBLRLM) and deballasting restrictions. A mixed-integer programming (MIP) model is proposed to make joint decisions to minimize the total tardiness of all ships. By exploring the problem's decomposable structure, an exact method that relies on logic-based Benders decomposition (LBBD) is proposed to obtain optimal solutions. According to the problem features, the monolithic MIP formulation is decomposed into a new MIP (master problem) and a constraint programming (subproblem). Combinatorial valid inequalities are developed to enhance the master problem model and obtain a tighter lower bound. A Benders cut strengthening heuristic is developed to generate feasibility and optimality cuts to ensure efficient algorithm convergence. To evaluate the proposed method, computational experiments are conducted on a set of test instances generated based on real data collected from a major CET in northern China. The results indicate that the LBBD algorithm can optimally solve large-scale problem instances within a reasonable amount of time. The plan generated by the LBBD algorithm achieves a 51.9% reduction in ship tardiness, on average, compared to that of practical scheduling methods. By using the proposed method, the superiority of the SBLRLM in reducing deballasting delays becomes more significant as the problem scale increases. In addition, considering different working intensities, the results could also help port operators make decisions about the number of berths in the SBLRLM.

Approximate and Deployable Shortest Remaining Processing Time Scheduler

The scheduling policy installed on switches of datacenters plays a significant role on congestion control. Shortest-Remaining-Processing-Time (SRPT) achieves the near-optimal average message completion time (MCT) in various scenarios, but is difficult to deploy as viewed by the industry. The reasons are two-fold: 1) many commodity switches only provide FIFO queues, and 2) the information of remaining message size is not available. Recently, the idea of emulating SRPT using only a few FIFO queues and the original message size has been coined as the approximate and deployable SRPT (ADS) design. In this paper, we provide the first theoretical study on the optimal ADS design. Specifically, we first characterize a wide range of feasible ADS scheduling policies via a unified framework, and then derive the steady-state MCT, slowdown, and impoliteness in the M/G/1 setting. Hence we formulate the optimal ADS design as a non-linear combinatorial optimization problem, which aims to minimize the average MCT given the available FIFO queues. We also take into account the proportional fairness and temporal fairness constraints based on the maximal slowdown and impoliteness, respectively. The optimal ADS design problem is NP-hard in general, and does not exhibit monotonicity or sub-modularity. We leverage its decomposable structure and devise an efficient algorithm to solve the optimal ADS policy. We carry out extensive flow-level simulations and packet-level experiments to evaluate the proposed optimal ADS design. Results show that the optimal ADS policy installed on eight FIFO queues is capable of emulating the true SRPT.

A Convex Reformulation and an Outer Approximation for a Large Class of Binary Quadratic Programs

Binary Quadratic Program with Variable Partitioning Constraints The binary quadratic program with variable partitioning constraints is a very general class of optimization problems that is very difficult to solve because of the nonconvexity and integrality of the variables and is ubiquitous, among others, in network design, computer vision, and transportation and logistics. In their article, “A convex reformulation and an outer approximation for a large class of binary quadratic programs,” Rostami et al. show how to transform such a nonconvex challenging problem into a convex bilinear program with decomposable structure. The authors develop a branch-and-cut algorithm based on outer approximation cuts, in which the cuts are generated on the fly by efficiently solving separation subproblems. The results of their computational experiments on different problems confirm the efficacy of the solution methods in solving large-scale problem instances.

Data-Driven Aggregate Thermal Dynamic Model for Buildings: A Regression Approach

The thermal inertia of buildings brings considerable flexibility to the building heating and cooling loads, which is believed to be a promising demand response resource in energy systems. However, it is challenging to utilize the thermal inertia of buildings in the operation of energy systems because of the complicated thermal dynamics and high computational cost. This paper proposes a data-driven aggregate thermal dynamic model (ATDM) for the multi-zone building and building cluster, respectively, which offers an equivalent and low-complexity building model for the operation and control of energy systems. The ATDM consists of the aggregation equation and the state equation. The former projects the detailed real states of buildings into the characteristic state (i.e., aggregate state) using an affine function, and the latter describes the thermal dynamics of buildings using the aggregate state. The ATDM is formulated for two practical load control strategies for the building cluster, including direct load control and indirect load control. Then, the constrained nonlinear regression model is proposed to estimate the model parameters and occupant behavior, for which an efficient algorithm based on the block coordinate descent method is developed by exploiting the decomposable structure of the regression model. Simulation results based on real-world data show that the root mean square error and mean absolute percentage error for the multi-zone building (or building cluster) are below 0.72 °C and 1.44% (or 0.32°C and 1.39%), respectively, verifying the effectiveness of the proposed methods.

Ring hierarchical hub network design problem: Exact and heuristic solution methods

In this paper, we study the hierarchical hub network design problem with a ring-star-star structure. In this problem, the hubs are located in two layers. In the first layer, central hubs (main hubs) are located in a ring structure, and in the second layer, secondary hubs are located. Each secondary hub is allocated to a central hub. Other demand points can also be allocated to each of these hubs (central hubs or secondary hubs). The objective is to minimize transportation costs on the network. This problem applies to communication networks when establishing direct links between demand nodes is not cost-effective, and there are two levels of service for customers. Also, the ring structure is used to reduce costs associated with full communication between central hubs. We present a mixed-integer programming model for the problem and report the results of the problem solving for a numerical example on the CAB dataset. Also, we present three solution methods for the problem. First, by exploiting the decomposable structure of the proposed model, we introduce an accelerated Benders decomposition algorithm. Then, we present a hybrid genetic algorithm that uses the Dijkstra algorithm to evaluate solutions. Next, we present a hybrid variable neighborhood search algorithm that uses the Dijkstra algorithm to calculate the cost of each solution. Also, a relax-and-fix algorithm is proposed to find near-optimal feasible solutions for the problem. Computational results are presented on the USA423 dataset. The results show that the proposed relax-and-fix algorithm can solve instances with up to 100 nodes. Also, the proposed hybrid algorithms can solve instances with up to 423 nodes. The performance of the proposed hybrid variable neighborhood search is better than the proposed hybrid genetic algorithm in solving large-sized instances. • The paper formulates the hierarchical hub network using a ring structure for the central hubs. • Minimizing the total flow cost while satisfying the demands is considered. • The paper develops solution methodologies based on Accelerated Benders Decomposition, Hybrid Genetic Algorithm, and Hybrid Variable Neighborhood Search Algorithm. • The paper presents computational studies using CAB and USA423 datasets.

Critical-Path-Search Logic-Based Benders Decomposition Approaches for Flexible Job Shop Scheduling

We solve the flexible job shop scheduling problems (F-JSSPs) to minimize makespan. First, we compare the constraint programming (CP) model with the mixed-integer programming (MIP) model for F-JSSPs. Second, we exploit the decomposable structure within the models and develop an efficient CP–logic-based Benders decomposition (CP-LBBD) technique that combines the complementary strengths of MIP and CP models. Using 193 instances from the literature, we demonstrate that MIP, CP, and CP-LBBD achieve average optimality gaps of 25.50%, 13.46%, and 0.37% and find optima in 49, 112, and 156 instances of the problem, respectively. We also compare the performance of the CP-LBBD with an efficient Greedy Randomized Adaptive Search Procedure (GRASP) algorithm, which has been appraised for finding 125 optima on 178 instances. CP-LBBD finds 143 optima on the same set of instances. We further examine the performance of the algorithms on 96 newly (and much larger) generated instances and demonstrate that the average optimality gap of the CP increases to 47.26%, whereas the average optimality of CP-LBBD remains around 1.44%. Finally, we conduct analytics on the performance of our models and algorithms and counterintuitively find out that as flexibility increases in data sets the performance CP-LBBD ameliorates, whereas that of the CP and MIP significantly deteriorates.

Branch-and-price for a class of nonconvex mixed-integer nonlinear programs

This work attempts to combine the strengths of two major technologies that have matured over the last three decades: global mixed-integer nonlinear optimization and branch-and-price. We consider a class of generally nonconvex mixed-integer nonlinear programs (MINLPs) with linear complicating constraints and integer linking variables. If the complicating constraints are removed, the problem becomes easy to solve, e.g. due to decomposable structure. Integrality of the linking variables allows us to apply a discretization approach to derive a Dantzig-Wolfe reformulation and solve the problem to global optimality using branch-andprice. It is a remarkably simple idea; but to our surprise, it has barely found any application in the literature. In this work, we show that many relevant problems directly fall or can be reformulated into this class of MINLPs. We present the branch-and-price algorithm and demonstrate its effectiveness (and sometimes ineffectiveness) in an extensive computational study considering multiple large-scale problems of practical relevance, showing that, in many cases, orders-of-magnitude reductions in solution time can be achieved.

Decomposition methods for solving Markov decision processes with multiple models of the parameters

We consider the problem of decision-making in Markov decision processes (MDPs) when the reward or transition probability parameters are not known with certainty. We study an approach in which the decision maker considers multiple models of the parameters for an MDP and wishes to find a policy that optimizes an objective function that considers the performance with respect to each model, such as maximizing the expected performance or maximizing worst-case performance. Existing solution methods rely on mixed-integer program (MIP) formulations, but have previously been limited to small instances, due to the computational complexity. In this article, we present branch-and-cut and policy-based branch-and-bound (PB-B&B) solution methods that leverage the decomposable structure of the problem and allow for the solution of MDPs that consider many models of the parameters. Numerical experiments show that a customized implementation of PB-B&B significantly outperforms the MIP-based solution methods and that the variance among model parameters can be an important factor in the value of solving these problems.

Stochastic joint homecare service and capacity planning with nested decomposition approaches

In this paper, we study a joint service authorization and capacity planning problem for the home health care (HHC) system with demand uncertainty. We formulate the problem as a two-stage stochastic programming with recourse which maximizes the expected total revenue. The service authorization and capacity planning are the mixed binary-and-continuous first stage decisions, and the service hour (resource) allocation is modeled as the second-stage decision which adapts to the demand realizations. The resulting sample average approximation problem (of the stochastic program) could be a large scaled mixed integer linear program. To solve the model in a more scalable fashion, we propose a supergradient-based nested decomposition algorithm that exploits the nice decomposable structure of the problem to cope with the binary and continuous variables separately. The proposed nested decomposition scheme consists of two-layer of decomposition, where the outer decomposition solves for the authorization decision (binaries) with the supergradient cuts and each supergradient can be computed iteratively in the inner decomposition scheme. The proposed nested decomposition algorithm is feasibility-cut-free and is guaranteed to reach the exact optimality in finite steps. Furthermore, we extend our stochastic HHC planning model to a more general framework of Conditional Value-at-Risk (CV@R), and by model transformation with variable change we show that the CV@R model can actually be reformulated in a structure that the proposed nested decomposition scheme can be applied almost directly. Finally, a comprehensive computational study is performed which demonstrates the effectiveness of our model and the performance of the algorithm.

Public Transport-based Crowd-shipping with Backup Transfers

With the rising urbanization and booming e-commerce, traditional last-mile delivery systems fail to keep up with the exploding demand and to satisfy the need for faster, cheaper, and more environmentally friendly deliveries. Several new approaches are put forward as an alternative to classical delivery systems in this regard, yet none of them offers the same level of flexibility, capacity, reliability, and managerial control by itself. This paper proposes a new last-mile delivery model that combines several new approaches and technologies to address this issue. More precisely, we suggest using public transit as a backbone network completed by automated service points, crowd-shipping, and backup transfers with zero-emission vehicles to provide a low-cost and environmentally friendly express delivery service. Offering cheap, reliable, and fast transfers between any two locations in an urban area, such a delivery network can provide unique opportunities for small and medium-sized businesses to participate in the e-commerce ecosystem and help large e-tailers to lower their costs and improve service quality. The design problem for the envisioned system is formulated as a two-stage stochastic program, and a branch-and-price (BP) algorithm is devised to solve it. Taking advantage of the nearly decomposable structure that would emerge in possible real-world applications, our study presents the first example of using decomposition branching in a BP framework to enhance computational efficiency. Extensive computational studies on realistic problem instances reveal valuable managerial insights for the proposed system and attest to the efficacy of the suggested methodology.

Bayesian graph selection consistency under model misspecification.

Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously learn the covariance and the graph. There is a wide variety of model-based methods to learn the underlying graph assuming various forms of the graphical structure. Although for scalability of the Markov chain Monte Carlo algorithms, decomposability is commonly imposed on the graph space, its possible implication on the posterior distribution of the graph is not clear. An open problem in Bayesian decomposable structure learning is whether the posterior distribution is able to select a meaningful decomposable graph that is "close" to the true non-decomposable graph, when the dimension of the variables increases with the sample size. In this article, we explore specific conditions on the true precision matrix and the graph, which results in an affirmative answer to this question with a commonly used hyper-inverse Wishart prior on the covariance matrix and a suitable complexity prior on the graph space. In absence of structural sparsity assumptions, our strong selection consistency holds in a high-dimensional setting where p = O(nα ) for α < 1/3. We show when the true graph is non-decomposable, the posterior distribution concentrates on a set of graphs that are minimal triangulations of the true graph.

Special Issue “Nonsmooth Optimization in Honor of the 60th Birthday of Adil M. Bagirov”: Foreword by Guest Editors

Nonsmooth optimization refers to the general problem of minimizing (or maximizing) functions that have discontinuous gradients. This Special Issue contains six research articles that collect together the most recent techniques and applications in the area of nonsmooth optimization. These include novel techniques utilizing some decomposable structures in nonsmooth problems—for instance, the difference-of-convex (DC) structure—and interesting important practical problems, like multiple instance learning, hydrothermal unit-commitment problem, and scheduling the disposal of nuclear waste.

Polynomial-size formulations and relaxations for the quadratic multiple knapsack problem

The Quadratic Multiple Knapsack Problem generalizes, simultaneously, two well-known combinatorial optimization problems that have been intensively studied in the literature: the (single) Quadratic Knapsack Problem and the Multiple Knapsack Problem. The only exact algorithm for its solution uses a formulation based on an exponential-size number of variables, that is solved via a Branch-and-Price algorithm. This work studies polynomial-size formulations and upper bounds. We derive linear models from classical reformulations of 0-1 quadratic programs and analyze theoretical properties and dominances among them. We define surrogate and Lagrangian relaxations, and we compare the effectiveness of the Lagrangian relaxation when applied to a quadratic formulation and to a Level 1 reformulation linearization that leads to a decomposable structure. The proposed methods are evaluated through extensive computational experiments.

Nutmeg: a MIP and CP Hybrid Solver Using Branch-and-Check

This paper describes the implementation of Nutmeg, a solver that hybridizes mixed integer linear programming and constraint programming using the branch-and-cut style of logic-based Benders decomposition known as branch-and-check. Given a high-level constraint programming model, Nutmeg automatically derives a mixed integer programming master problem that omits global constraints with weak linear relaxations, and a constraint programming subproblem identical to the original model. At every node in the branch-and-bound search tree, the linear relaxation computes dual bounds and proposes solutions, which are checked for feasibility of the omitted constraints in the constraint programming subproblem. In the case of infeasibility, conflict analysis generates Benders cuts, which are appended to the linear relaxation to cut off the candidate solution. Experimental results show that Nutmeg’s automatic decomposition outperforms pure constraint programming and pure mixed integer programming on problems known to have successful implementations of logic-based Benders decomposition, but performs poorly on general problems, which lack specific decomposable structure. Nonetheless, Nutmeg outperforms the standalone approaches on one problem with no known decomposable structure, providing preliminary indications that a hand-tailored decomposition for this problem could be worthwhile. On the whole, Nutmeg serves as a valuable tool for novice modelers to try hybrid solving and for expert modelers to quickly compare different logic-based Benders decompositions of their problems.

Dynamic optimization of fluid catalytic cracking unit using a nonconvex sensitivity-based generalized Benders decomposition

Fluid catalytic cracking unit, whose batch operations are operated in a multirate mode, is a typical continuous process with batch operations. The integrated optimization of this problem can be formulated as a hybrid parametric dynamic optimization. To obtain a high-quality solution, adaptive direct methods are usually required to solve the problem iteratively. By exploiting the decomposable structure, a novel framework is proposed in this paper, which can obtain an equivalent or better precision solution with relatively coarse discretization. In detail, by designating the batch operations as complicating variables, an optimal solution and sensitivity information about batch operations are obtained by a nonconvex sensitivity-based generalized Benders decomposition algorithm. Then the optimal continuous operations are implemented as extra closed-loop controllers by tracking the necessary conditions of optimality, while the optimal batch operations are improved by a line search method. The practical potential of the framework is demonstrated with several operation modes.

Template confined strategy for constructing nickel cobalt selenide nanoarrays for efficient oxygen evolution reaction

Developing high-efficient and earth-abundant metals for the oxygen evolution reaction catalyst is of significant and promising but still challenging. Prussian blue analogs (PBAs) show great potential for the dispersion and exposure of OER catalysts due to their adjustable element compositions and easily decomposable structures. Herein, bimetallic Ni–Co Prussian blue analogs grown on the conductive nickel foam supported by Ni(OH)2 nanosheets are designed and constructed. Firstly, the uniform dispersion of Ni–Co Prussian blue analogs has been realized on the surface of NF. By means of the confined decomposition of PBAs at calcination temperature, NiSe2/CoSe with the smaller particle size and good dispersion supported on NF can provide the more active sites when containing high electron transfer rate. The oxygen evolution reaction (OER) measurements show that the as-prepared NiSe2/CoSe/NF exhibits the very impressive OER activity with low overpotential of 270 mV to reach the current density of 100 mA/cm2. The special nanoarrays structure, abundant active sites and high intrinsic activity may contribute to the excellent performance. The synergistic effect of nickel-cobalt selenide and support enable superior stability toward OER. This confined decomposition strategy may provide a promising way to controlled assembly of transition metal-based electrocatalyst for OER.