Constraint Decomposition Research Articles

DivideMerge: A multi-vessel optimization approach for cooperative operation and maintenance scheduling in offshore wind farm

The optimization of maintenance scheduling and routing in offshore wind farms is crucial for the intelligent operation and maintenance of offshore wind energy. It involves determining the optimal timing, assigning vessels, planning routes, and efficiently completing maintenance tasks with maximum efficiency and minimal cost. Traditional branch-and-bound search methods, often used in multi-vessel cooperative maintenance scheduling models, face limitations in finding optimal solutions efficiently, while classic heuristic methods may compromise on global optimality. This paper introduces DivideMerge, a high-performance hybrid algorithm that synergizes heuristic and exact algorithms to address large-scale multi-vessel cooperative maintenance scheduling challenges in offshore wind farms. Initially, a maintenance task constraint decomposition heuristic method is utilized to break down the collaborative optimization scheduling problem into individual vessel scheduling sub-problems, ensuring adherence to the constraints of the original problem. Subsequently, the CP-SAT solver is employed to sequentially solve these sub-problems rapidly. The solutions for individual vessel scheduling are then merged to form a comprehensive solution for the multi-vessel cooperative maintenance scheduling problem. Computational results validate the effectiveness and robustness of DivideMerge, demonstrating a solution speed nearly 1000 times faster than the commercial Gurobi solver, thus offering a significant advancement in the field of offshore wind farm maintenance optimization.

Data-Driven Dynamic Optimization for Real-Time Parking Reservation Considering Parking Unpunctuality

This paper examines a real-time parking reservation service that dynamically allocates a limited number of parking slots (which can be reused) to serve parking requests in a crowded area. The study takes into account two stochastic factors: (i) random arrivals of parking requests and (ii) driver parking unpunctuality, which are seldom simultaneously considered in the existing literature. This study formulates the dynamic parking resource allocation problem as a joint chance-constrained model to maximize the expected total revenue over a finite horizon. Due to the complex nature of the model considering the two stochastic factors, the study proposes a data-driven approach using joint chance constraint decomposition and sample average approximation to approximate the model to a deterministic mixed-integer programming model. Furthermore, a stratified ranked set sampling method is introduced to construct a high-quality sample set as the input to the deterministic model, and valid inequalities are designed to accelerate the solution process. Numerical experiments based on real-world data are conducted to validate the performance of the proposed approach under multiple parking scenarios and provide findings.

ALESQP: An Augmented Lagrangian Equality-Constrained SQP Method for Optimization with General Constraints

We present a new algorithm for infinite-dimensional optimization with general constraints, called ALESQP. In short, ALESQP is an augmented Lagrangian method that penalizes inequality constraints and solves equality-constrained nonlinear optimization subproblems at every iteration. The subproblems are solved using a matrix-free trust-region sequential quadratic programming (SQP) method that takes advantage of iterative, i.e., inexact linear solvers, and is suitable for large-scale applications. A key feature of ALESQP is a constraint decomposition strategy that allows it to exploit problem-specific variable scalings and inner products. We analyze convergence of ALESQP under different assumptions. We show that strong accumulation points are stationary. Consequently, in finite dimensions ALESQP converges to a stationary point. In infinite dimensions we establish that weak accumulation points are feasible in many practical situations. Under additional assumptions we show that weak accumulation points are stationary. We present several infinite-dimensional examples where ALESQP shows remarkable discretization-independent performance in all of its iterative components, requiring a modest number of iterations to meet constraint tolerances at the level of machine precision. Also, we demonstrate a fully matrix-free solution of an infinite-dimensional problem with nonlinear inequality constraints.

Compact Approximate Linear Programs for Network Revenue Management: Reduction via Constraint Decomposition and Adaptation for Locally Separable Approximation

Compact Approximate Linear Programs for Network Revenue Management: Reduction via Constraint Decomposition and Adaptation for Locally Separable Approximation

Parallel and Distributed Optimization Method With Constraint Decomposition for Energy Management of Microgrids

Energy management in power systems is a thorny optimization problem. With the sizes of systems rising, centralized optimization methods are restricted by their complexities of communications, while distributed optimization methods have emerged as a powerful tool for dealing with increasingly complex systems. However, convergence rates of some widely used distributed optimization methods, such as the standard alternating direction method of multipliers (ADMM), still have room for improvement. In this paper, a parallel and distributed optimization method for energy management of microgrids (MGs) is proposed to boost the convergence rate without sacrificing the accuracy of the optima, in which agents calculate, exchange and update in parallel. At first, a decomposition method is presented, where the objective functions and constraints of an original optimization problem with separable variables are decomposed into local objective functions and constraints for agents, which is the key to our method. Further, agents solve their local optimization problems independently and then exchange determined optima with their neighbors. Finally, the method is evaluated to solve economic dispatch with demand response for microgrids. The simulation results show that compared to the standard ADMM, for a given accuracy, the number of iterations in our method is only one third or even less than that of ADMM. Furthermore, our method can minimize the cost functions of distributed generation on supply side and maximize the profit functions of flexible loads on the demand side.

A Hierarchical Energy-Efficient Service Selection Approach With QoS Constraints for Internet of Things

With the emergence of Service-oriented Architecture (SoA) technologies, service-defined Internet of Things (IoT) applications have been widely developed. However, IoT system is resource-constrained. Devices in IoT usually have limited storage, computation and especially limited energy. Unfortunately, traditional service selection technologies ignore the energy efficiency of services. Although a few studies address energy consumption in service selection or composition, they fail to pay more attention to the dynamic characteristic of IoT, which is not suitable for resource-constrained IoT. In order to resolve this issue, we propose a hierarchical energy efficient service selection approach for resource-constrained IoT. In our approach, a Quality of Service (QoS) guaranteed global constraints decomposition is performed to acquire a group of local QoS constraints. Then, based on the selected local QoS constraints, an energy efficient service selection scheme can be carried out independently according to the dynamic network state. Experimental evaluations demonstrate the capability of our proposed approach.

Wireless-Powered Machine-to-Machine Multicasting in Cellular Networks

In future cellular networks, it is expected that data traffic will increase significantly due to deployments of large numbers of Internet of Things (IoT) objects. The IoT objects operate underlaying a cellular network, and they use Machine-to-Machine (M2M) communication to transmit multicst messages. We propose to use Radio Frequency (RF) Energy Transmitters (ET) to compensate the IoT objects with the energy consumed in forwarding multicast messages. Our goal is to support multicast service for IoT objects and transmit energy to them such that the total transferred energy by the ETs is minimized. We formulated the problem mathematically as a non-convex Mixed Integer Nonlinear Program (MINLP). Due to the difficulty of solving the problem optimally, we decompose the original problem into two sub-problems using Generalized Bender Decomposition with Successive Convex programming (GBD-SCP). Although this method facilitates finding a solution for the problem, the problem is still hard due to binary variables. Hence, we propose the Constraints Decomposition with SCP and Binary Variable Relaxation (CDR) algorithm to solve the problem more efficiently. Simulation results show that the proposed algorithm achieves a performance close to the GBD-SCP algorithm while the computation time is reduced significantly when the network size is larger.

Multi-objective robust energy management for all-electric shipboard microgrid under uncertain wind and wave

An all-electric ship (AES) uses diesel generators and energy storage system (ESS) to meet both propulsion and service loads. Thus, it can be viewed as a mobile microgrid. During the operation of an AES, significant uncertainties such as water wave and wind introduce considerable speed loss, which may lead to severe voyage delays. To fully address this issue, a new robust energy management model is proposed to coordinately schedule an AES’s power generation and voyage considering the uncertain wave and wind. Two objectives are minimized simultaneously: the fuel consumption (FC) and energy efficiency operational indicator (EEOI). The problem is formulated as a bi-level robust optimization model after certain constraint decomposition. Normal boundary intersection method is utilized to solve this multi-objective programming. Compared with existing joint scheduling methods, the proposed method can fully guarantee the on-time rates of AES in various uncertain scenarios and providing high-quality Pareto solutions.

Two-Step Multi-Objective Management of Hybrid Energy Storage System in All-Electric Ship Microgrids

The all-electric ship (AES) usually employs battery energy storage systems (ESSs) in the shipboard microgrid. However, the battery-only storage usually experiences frequent deep discharging or charging to meet the sudden load variations in a voyage, which may lead to significant degradation of battery lifetime. This paper, hybridizes two types of ESSs and proposes a two-step multi-objective optimization method for hybrid ESS (HESS) management. The first step regulates the HESS with the onboard diesel generators to simultaneously optimize both the economic and environmental objectives, and the second step is to split the active power of HESS into two individual ESSs for minimizing the battery cycle degradation. The first step is formulated as a bi-level optimization model through constraint decomposition. Then, a normal boundary intersection method combining with the column-and-constraint generation algorithm is developed to solve the proposed model. Extensive simulations demonstrate that the HESS can effectively resolve the power-density shortage of the battery-only system, and its integration into AES is able to extend the battery lifetime and improve both the economic and environmental indices.

Dynamic Service Selection Based on Adaptive Global QoS Constraints Decomposition

As there are more and more available Web services with the same or similar functionalities but different Quality of Service (QoS), the challenge of QoS-aware service composition is to efficiently select appropriate component services to achieve maximum utility and meet the global QoS constraints with low time cost. In this paper, we propose a dynamic service selection approach based on adaptive global QoS constraints decomposition. Fuzzy logic technology and Cultural Genetic Algorithm are used to adaptively decompose global QoS constraints into near-optimal local constraints. According to the near-optimal local constraints, the optimal service is selected for each service class during the running time efficiently. Experimental results show that the proposed approach not only achieves the near-optimal solution, but also significantly reduces the computation time, and has good adaptability and scalability.

An Automatic Configuration Algorithm for Reliable and Efficient Composite Services

Reusability is a central concept of Web services as it allows for the construction of composite services. Thus, an existing composite service can be combined with other composite services to form more complex nested or hierarchical services. Reliability and efficiency are the main requirements of composite services construction. The reliability requirements are rigorously defined by designers using the accepted termination states concept. The efficiency requirements are tightly related to a set of quality-of-service (QoS) constraints that are required by customers. In this paper, we first developed a hierarchical model for composite services. Based on this model, we developed a recursive procedure for the automatic computation of the transactional reliability and QoS of composite services. Second, we proposed a new concept, called required efficiency level, to offer more flexibility to the customers to specify their needs in terms of QoS. Third, we developed a new composite service configuration (CSC) algorithm for the construction and adaptation of composite services while considering the reliability and efficiency requirements. The originality of the CSC algorithm consists in a new recursive global QoS constraint decomposition procedure. Finally, we conducted a set of experiments to evaluate the benefits of the proposed CSC algorithm in comparison with the related work. These experiments confirm that our CSC algorithm is able to generate, in a timely fashion, reliable, and efficient composite services.

Bayesian method for system reliability assessment of overlapping pass/fail data

For high reliability and long life systems, system pass/fail data are often rare. Integrating lower-level data, such as data drawn from the subsystem or component pass/fail testing, the Bayesian analysis can improve the precision of the system reliability assessment. If the multi-level pass/fail data are overlapping, one challenging problem for the Bayesian analysis is to develop a likelihood function. Since the computation burden of the existing methods makes them infeasible for multi-component systems, this paper proposes an improved Bayesian approach for the system reliability assessment in light of overlapping data. This approach includes three steps: fristly searching for feasible paths based on the binary decision diagram, then screening feasible points based on space partition and constraint decomposition, and finally simplifying the likelihood function. An example of a satellite rolling control system demonstrates the feasibility and the efficiency of the proposed approach.

Reliable Web service composition based on QoS dynamic prediction

Web service dynamic composition is a key technology for creating value-added services by composing available services and applications. With the rapid development of web service, cloud computing, big data and internet of things, more and more services with identical functionality and different Quality of Service (QoS) are available; moreover, QoS of Web services are highly dynamic, so, how to create composite Web services reliably and efficiently is still an open issue. For this problem, this paper proposes a reliable Web service composition method based on global QoS constraints decomposition and QoS dynamic prediction. The approach includes two critical phases: firstly, before service composition, global QoS constraints are decomposed into local constraints, and the problem of Web service dynamic composition is transformed to a local optimization problem; secondly, during the running time, optimal Web service is selected for the current abstract service based on predicted QoS values. Experiment results show that our approach can greatly enhance the reliability of composite Web service.

Optimal Decoupling in Linear Constraint Systems

Decomposition is a technique to obtain complete solutions by assembling independently obtained partial solutions. In particular, constraint decomposition plays an important role in distributed databases, distributed scheduling and violation detection: It enables conflict-free local decision making, while avoiding communication overloading. One of the main issues in decomposition is the loss of flexibility due to decomposition. Here, flexibility roughly refers to the freedom in choosing suitable values for the variables in order to satisfy the constraints. In this paper, we concentrate on linear constraint systems and efficient decomposition techniques for them. Using a generalization of a flexibility metric developed for Simple Temporal Networks, we show how an efficient decomposition technique for linear constraint systems can be derived that minimizes the loss of flexibility. As a by-product of this decomposition technique, we propose an intuitively attractive flexibility metric for linear constraint systems where decomposition does not incur any loss of flexibility.

An approach for selecting best available services through a new method of decomposing QoS constraints

Quality of Service (QoS) plays as a discriminating factor for selecting appropriate services that meet the given user's non-functional requirements during service composition. There is a compelling need to select suitable services quickly so that the composition can meet dynamic needs. Recently, local selection approaches for QoS-based selection have been put forward toward reduced time complexity. A methodology for selecting the best available service combination for a given user requirement (workflow) with a new method of decomposing QoS constraints is proposed in this paper. The methodology consists of two phases, namely `Constraint Decomposition Phase' and `Service Selection Phase'. In the Constraint Decomposition Phase, a unique method is proposed to decompose the given non-functional (global or workflow level) constraints into local constraints for individual tasks in the workflow. Each individual task with its local constraints forms a subproblem. In the Service Selection phase, each subproblem is resolved by finding the best available service from its respective service class using an iterative searching procedure. A prototype has been implemented, and the low computation time of the proposed method makes it well suited to dynamic composition. The proposed method of decomposing constraints is independent of number of services in a service class, and the method is applicable to any combinational workflow with AND, OR and Loop patterns. Further, a new method for computing response time of OR execution pattern which guarantees successful execution of each path in an OR pattern is a remarkable contribution of this work.

Web service dynamic composition based on decomposition of global QoS constraints

Virtual enterprise is a temporary network of independent companies or enterprises that can quickly bring together to fulfill a value-added task. With the development of Web service technologies, the enterprise business systems can be encapsulated as Web services. Establishing a virtual enterprise is actually a process of Web service composition. As more and more Web services with the same functionalities and different Quality of Service (QoS) are available, QoS-aware Web service dynamic composition becomes an active research issue. Although several solutions have been provided for this issue, most of these methods based on global optimization, their poor performance render them inappropriate for applications with dynamic and real-time requirements. Moreover, these methods do not consider the commercial agreements and historical contact information between Web services with combination relationship. In this paper, we propose an approach for Web service dynamic composition based on global QoS constraints decomposition. The proposed method consists of three steps: Firstly, global QoS constraints are decomposed into local constraints optimally by a new algorithm named Culture Genetic Algorithm. Secondly, QoS values determination rules are designed to determine QoS values of candidate services. Thirdly, best Web services that can satisfy the local constraints are selected for each task during the running time. Experimental results show that our approach has better performance in solving the problem of QoS-aware Web service dynamic composition.

Prices stabilization for inexact unit-commitment problems

A widespread and successful approach to tackle unit-commitment problems is constraint decomposition: by dualizing the linking constraints, the large-scale nonconvex problem decomposes into smaller independent subproblems. The dual problem consists then in finding the best Lagrangian multiplier (the optimal “price”); it is solved by a convex nonsmooth optimization method. Realistic modeling of technical production constraints makes the subproblems themselves difficult to solve exactly. Nonsmooth optimization algorithms can cope with inexact solutions of the subproblems. In this case however, we observe that the computed dual solutions show a noisy and unstable behaviour, that could prevent their use as price indicators. In this paper, we present a simple and easy-to-implement way to stabilize dual optimal solutions, by penalizing the noisy behaviour of the prices in the dual objective. After studying the impact of a general stabilization term on the model and the resolution scheme, we focus on the penalization by discrete total variation, showing the consistency of the approach. We illustrate our stabilization on a synthetic example, and real-life problems from EDF (the French Electricity Board).

QoS decomposition for service composition using genetic algorithm

Recently, a lot of research has been dedicated to optimizing the QoS-aware service composition. This aims at selecting the optimal composed service from all possible service combinations regarding user's end-to-end quality requirements. Existing solutions often employ the global optimization approach, which does not show promising performance. Also, the complexity of such methods extensively depends on the number of available web-services, which continuously increase along with the growth of the Internet. Besides, the local optimization approaches have been rarely utilized, since they may violate the global constraints. In this paper, we propose a top-down structure, named quality constraints decomposition (QCD) here, to decompose the global constraints into the local constraints, using the genetic algorithm (GA). Then the best web service for each task is selected through a simple linear search. In contrast to existing methods, the QCD approach mainly depends on a limited set of tasks, which is considerably less complex, especially in the case of dynamically distributed service composition. Experimental results, based on a well-known data set of web services (QWSs), show the advantages of the QCD method in terms of computation time, considering the number of web services.

View-based propagator derivation

When implementing a propagator for a constraint, one must decide about variants: When implementing min, should one also implement max? Should one implement linear constraints both with unit and non-unit coefficients? Constraint variants are ubiquitous: implementing them requires considerable (if not prohibitive) effort and decreases maintainability, but will deliver better performance than resorting to constraint decomposition. This paper shows how to use views to derive propagator variants, combining the efficiency of dedicated propagator implementations with the simplicity and effortlessness of decomposition. A model for views and derived propagators is introduced. Derived propagators are proved to be perfect in that they inherit essential properties such as correctness and domain and bounds consistency. Techniques for systematically deriving propagators such as transformation, generalization, specialization, and type conversion are developed. The paper introduces an implementation architecture for views that is independent of the underlying constraint programming system. A detailed evaluation of views implemented in Gecode shows that derived propagators are efficient and that views often incur no overhead. Views have proven essential for implementing Gecode, substantially reducing the amount of code that needs to be written and maintained.

An algorithm for training a large scale support vector machine for regression based on linear programming and decomposition methods

This paper presents a method to train a Support Vector Regression (SVR) model for the large-scale case where the number of training samples supersedes the computational resources. The proposed scheme consists of posing the SVR problem entirely as a Linear Programming (LP) problem and on the development of a sequential optimization method based on variables decomposition, constraints decomposition, and the use of primal–dual interior point methods. Experimental results demonstrate that the proposed approach has comparable performance with other SV-based classifiers. Particularly, experiments demonstrate that as the problem size increases, the sparser the solution becomes, and more computational efficiency can be gained in comparison with other methods. This demonstrates that the proposed learning scheme and the LP-SVR model are robust and efficient when compared with other methodologies for large-scale problems.