Constraint partitioning in penalty formulations for solving temporal planning problems

In this paper, we study the partitioning of constraints in temporal planning problems formulated as mixed-integer nonlinear programming (MINLP) problems. Constraint partitioning is attractive because it leads to much easier subproblems, where each is a significant relaxation of the original problem. Moreover, each subproblem is very similar to the original problem and can be solved by any existing solver with little or no modification. Constraint partitioning, however, introduces global constraints that may be violated when subproblems are evaluated independently. To reduce the overhead in resolving such global constraints, we develop in this paper new conditions and algorithms for limiting the search space to be backtracked in each subproblem. Using a penalty formulation of a MINLP where the constraint functions of the MINLP are transformed into non-negative functions, we present a necessary and sufficient extended saddle-point condition (ESPC) for constrained local minimization. When the penalties are larger than some thresholds, our theory shows a one-to-one correspondence between a constrained local minimum of the MINLP and an extended saddle point of the penalty function. Hence, one way to find a constrained local minimum is to increase gradually the penalties of those violated constraints and to look for a local minimum of the penalty function using any existing algorithm until a solution to the constrained model is found. Next, we extend the ESPC to constraint-partitioned MINLPs and propose a partition-and-resolve strategy for resolving violated global constraints across subproblems. Using the discrete-space ASPEN and the mixed-space MIPS planners to solve subproblems, we show significant improvements on some planning benchmarks, both in terms of the quality of the plans generated and the execution times to find them.     

Sewage flow optimization algorithm for large-scale urban sewer networks based on network community division

By considering the flow control of urban sewer networks to minimize the electricity consumption of pumping stations, a decomposition-coordination strategy for energy savings based on network community division is developed in this paper. A mathematical model characterizing the steady-state flow of urban sewer networks is first constructed, consisting of a set of algebraic equations with the structure transportation capacities captured as constraints. Since the sewer networks have no apparent natural hierarchical structure in general, it is very difficult to identify the clustered groups. A fast network division approach through calculating the betweenness of each edge is successfully applied to identify the groups and a sewer network with arbitrary configuration could be then decomposed into subnetworks. By integrating the coupling constraints of the subnetworks, the original problem is separated into N optimization subproblems in accordance with the network decomposition. Each subproblem is solved locally and the solutions to the subproblems are coordinated to form an appropriate global solution. Finally, an application to a specified large-scale sewer network is also investigated to demonstrate the validity of the proposed algorithm.     

Efficient solution of the 3G network planning problem

The 3G universal mobile telecommunications system (UMTS) planning problem is combinatorially explosive and difficult to solve optimally, though solution methods exist for its three main subproblems (cell, access network, and core network planning). We previously formulated the entire problem as a single integrated mixed-integer linear program (MIP) and showed that only small instances of this global planning problem can be solved to optimality by a commercial MIP solver within a reasonable amount of time (St-Hilaire, Chamberland, & Pierre, 2006). Heuristic methods are needed for larger instances. This paper provides the first complete formulation for the heuristic sequential method (St-Hilaire, Chamberland, & Pierre, 2005) that re-partitions the global formulation into the three conventional subproblems and solves them in sequence using a MIP solver. This greatly improves the solution time, but at the expense of solution quality. We also develop a new hybrid heuristic that uses the results of the sequential method to generate constraints that provide tighter bounds for the global planning problem with the goal of reaching the provable optimum solution much more quickly. We empirically evaluate the speed and solution accuracy of four solution methods: (i) the direct MIP solution of the global planning problem, (ii) a local search heuristic applied to the global planning problem, (iii) the sequential method and (iv) the new hybrid method. The results show that the sequential method provides very good results in a fraction of the time needed for the direct MIP solution of the global problem, and that optimum results can be provided by the hybrid heuristic in greatly reduced time.     

Efficient solution of the 3G network planning problem

The 3G universal mobile telecommunications system (UMTS) planning problem is combinatorially explosive and difficult to solve optimally, though solution methods exist for its three main subproblems (cell, access network, and core network planning). We previously formulated the entire problem as a single integrated mixed-integer linear program (MIP) and showed that only small instances of this global planning problem can be solved to optimality by a commercial MIP solver within a reasonable amount of time ( St-Hilaire, Chamberland, & Pierre, 2006). Heuristic methods are needed for larger instances. This paper provides the first complete formulation for the heuristic sequential method ( St-Hilaire, Chamberland, & Pierre, 2005) that re-partitions the global formulation into the three conventional subproblems and solves them in sequence using a MIP solver. This greatly improves the solution time, but at the expense of solution quality. We also develop a new hybrid heuristic that uses the results of the sequential method to generate constraints that provide tighter bounds for the global planning problem with the goal of reaching the provable optimum solution much more quickly. We empirically evaluate the speed and solution accuracy of four solution methods: (i) the direct MIP solution of the global planning problem, (ii) a local search heuristic applied to the global planning problem, (iii) the sequential method and (iv) the new hybrid method. The results show that the sequential method provides very good results in a fraction of the time needed for the direct MIP solution of the global problem, and that optimum results can be provided by the hybrid heuristic in greatly reduced time.     

A tabu search algorithm for the global planning problem of third generation mobile networks

In this paper, we propose a tabu search (TS) algorithm for the global planning problem of third generation (3G) universal mobile telecommunications system (UMTS) networks. This problem is composed of three NP-hard subproblems: the cell, the access network and the core network planning subproblems. Therefore, the global planning problem consists in selecting the number, the location and the type of network nodes (including the base stations, the radio network controllers, the mobile switching centers and the serving GPRS (General Packet Radio Service) support nodes) as well as the interconnections between them. After describing our metaheuristic, a systematic set of experiments is designed to assess its performance. The results show that quasi-optimal solutions can be obtained with the proposed approach.     

Methods based on discrete optimization for finding road network rehabilitation strategies

We study a dynamic optimization problem arising in the (long-term) planning of road rehabilitation activities. In this area one seeks a pavement resurfacing plan for a road network under budget constraints. Our main approach is to model this as an integer programming problem with underlying dynamic programming structure. We investigate properties of this model and propose a solution method based on Lagrangian relaxation where one gets subproblems that are shortest path problems. Some computational experiences based on realistic data are reported.     

A globally and quadratically convergent algorithm for general nonlinear programming problems

This paper presents an algorithm for the minimization of a nonlinear objective function subject to nonlinear inequality and equality constraints. The proposed method has the two distinguishing properties that, under weak assumptions, it converges to a Kuhn-Tucker point for the problem and under somewhat stronger assumptions, the rate of convergence is quadratic. The method is similar to a recent method proposed by Rosen in that it begins by using a penalty function approach to generate a point in a neighborhood of the optimum and then switches to Robinson's method. The new method has two new features not shared by Rosen's method. First, a correct choice of penalty function parameters is constructed automatically, thus guaranteeing global convergence to a stationary point. Second, the linearly constrained subproblems solved by the Robinson method normally contain linear inequality constraints while for the method presented here, only linear equality constraints are required. That is, in a certain sense, the new method “knows” which of the linear inequality constraints will be active in the subproblems. The subproblems may thus be solved in an especially efficient manner. Preliminary computational results are presented.     

Group planning with time constraints

Embedding planning systems in real-world domains has led to the necessity of Distributed Continual Planning (DCP) systems where planning activities are distributed across multiple agents and plan generation may occur concurrently with plan execution. A key challenge in DCP systems is how to coordinate activities for a group of planning agents. This problem is compounded when these agents are situated in a real-world dynamic domain where the agents often encounter differing, incomplete, and possibly inconsistent views of their environment. To date, DCP systems have only focused on cases where agents’ behavior is designed to optimize a global plan. In contrast, this paper presents a temporal reasoning mechanism for self-interested planning agents. To do so, we model agents’ behavior based on the Belief-Desire-Intention (BDI) theoretical model of cooperation, while modeling dynamic joint plans with group time constraints through creating hierarchical abstraction plans integrated with temporal constraints network. The contribution of this paper is threefold: (i) the BDI model specifies a behavior for self interested agents working in a group, permitting an individual agent to schedule its activities in an autonomous fashion, while taking into consideration temporal constraints of its group members; (ii) abstract plans allow the group to plan a joint action without explicitly describing all possible states in advance, making it possible to reduce the number of states which need to be considered in a BDI-based approach; and (iii) a temporal constraints network enables each agent to reason by itself about the best time for scheduling activities, making it possible to reduce coordination messages among a group. The mechanism ensures temporal consistency of a cooperative plan, enables the interleaving of planning and execution at both individual and group levels. We report on how the mechanism was implemented within a commercial training and simulation application, and present empirical evidence of its effectiveness in real-life scenarios and in reducing communication to coordinate group members’ activities.     

A hybrid method for hydroelectric generation scheduling using an artificial neural network

This paper presents a decomposition method for finding an optimal operating policy of interconnected hydroelectric power plants using an artificial neural network. The coupling constraints on reservoir storage at the end of the planning horizon are relaxed using coordinating multipliers that result in interval wise decomposition of the overall problem. Resulting subproblems are solved sequentially, which reduces the complexity of the problem. Each subproblem is solved using a two-phase neural network approach. An efficient heuristic algorithm is developed to find the feasible solution. A case study considering scheduling of the Bhakra-Beas reservoir system is also presented in this paper. The new method demonstrates the potential of achieving an improved performance.     

Optimum motion planning in joint space for robots using genetic algorithms

The optimum motion planning in joint space (OMPJS) for robots, which generally consists of two subproblems, optimum path planning and optimum trajectory planning, was considered as a whole in the paper. A new method for optimum motion planning problem based on an improved genetic algorithm is proposed, which is more general, flexible and effective. This approach incorporates kinematics constraints, dynamics constraints, and control constraints of robotic manipulator. The simulation results for a two and a three degrees of freedom robots are presented and discussed. The simulations are based on genetic algorithm class library WGAClass 1.0 developed by us with Borland C++ 3.1.     

一种集成最后一公里的四方物流网络设计问题启发式算法

最后一公里分销网络可以帮助企业达成高响应性的供应链管理目标,集成最后一公里四方物流网络设计问题成为网络设计的一个重要研究方向.解决该问题需要对分销中心的位置,三方物流的选择、分配以及其车辆路径规划进行决策.在满足车辆路径规划、流守恒等约束条件下,以最小化网络构建费用为目标建立混合整数规划模型.由于该问题的NP-难特性,...     

An integrated system for knowledge sharing among heterogeneous knowledge derivation systems

Solving problems in a complex application domain often requires a seamles integration of some existing knowledge derivation systems which have been independently developed for solving subproblems using different inferencing schemes. This paper presents the design and implementation of an Integrated Knowledge Derivation System (IKDS) which allows the user to query against a global database containing data derivable by the rules and constraints of a number of cooperative heterogeneous systems. The global knowledge representation scheme, the global knowledge manipulation language and the global knowledge processing mechanism of IKDS are described in detail. For global knowledge representation, the dynamic aspects of knowledge such as derivational relationships and restrictive dependencies among data items are modeled by a Function Graph to uniformly represent the capabilities (or knowledge) of the rule-based systems, while the usual static aspects such as data items and their structural interrelationships are modeled by an object-oriented model. For knowledge manipulation, three types of high-level, exploratory queries are introduced to allow the user to query the global knowledge base. For deriving the best global answers for queries, the global knowledge processing mechanism allows the rules and constraints in different component systems to be indiscriminately exploited despite the incompatibilities in their inferencing mechanisms and interpretation schemes. Several key algorithms required for the knowledge processing mechanism are described in this paper. The main advantage of this integration approach is that rules and constraints can in effect be shared among heterogeneous rule-based systems so that they can freely exchange their data and operate as parts of a single system. IKDS achieves the integration at the rule level instead of at the system level. It has been implemented in C running in a network of heterogenous component systems which contain three independently developed expert systems with different rule formats and inferencing mechanisms.Database Systems Research and Development Center, Department of Computer Information Sciences, Department of Electrical Engineering, University of Florida     

A Hybrid Particle Swarm Branch-and-Bound (HPB) Optimizer for Mixed Discrete Nonlinear Programming

This paper proposes a new algorithm for solving mixed discrete nonlinear programming (MDNLP) problems, designed to efficiently combine particle swarm optimization (PSO), which is a well-known global optimization technique, and branch-and-bound (BB), which is a widely used systematic deterministic algorithm for solving discrete problems. The proposed algorithm combines the global but slow search of PSO with the rapid but local search capabilities of BB, to simultaneously achieve an improved optimization accuracy and a reduced requirement for computational resources. It is capable of handling arbitrary continuous and discrete constraints without the use of a penalty function, which is frequently cumbersome to parameterize. At the same time, it maintains a simple, generic, and easy-to-implement architecture, and it is based on the sequential quadratic programming for solving the NLP subproblems in the BB tree. The performance of the new hybrid PSO–BB architecture algorithm is evaluated against real-world MDNLP benchmark problems, and it is found to be highly competitive compared with existing algorithms.      

Distributed Model Predictive Control: Synchronous and Asynchronous Computation

Model predictive control (MPC) has become one of the leading technologies to control complex processes, to a great extent, as a result of its flexibility and explicit handling of constraints. Given a dynamic problem (DP), MPC converts DP into a series of static optimization problems, thereby allowing the use of standard optimization techniques to compute the control signals. The reliance of MPC on centralized computations, however, stands as a barrier to its use in the real-time operation of large dynamic networks. To this end, this paper proposes an extension to MPC by decomposing DP into a network of small but coupled subproblems and solving them with a network of asynchronous agents. The net result, after each agent applies MPC to its dynamic subproblem, is a series of sets of static subproblems. Our focus is on the simultaneous solution of these sets of static subproblems. The paper delivers a framework to carry out the decomposition and develops conditions under which the iterative synchronous processes of the agents converge to solutions. Furthermore, it proposes heuristics for asynchronous convergence and reports experimental results from prototypical dynamic networks, demonstrating the effectiveness of the proposed extension.     

Tractable supply chain production planning,modeling nonlinear lead time and quality of service constraints

This paper addresses the task of coordinated planning of a supply chain (SC). Work in process (WIP) in each facility participating in the SC, finished goods inventory, and backlogged demand costs are minimized over the planning horizon. In addition to the usual modeling of linear material flow balance equations, variable lead time (LT) requirements, resulting from the increasing incremental WIP as a facility’s utilization increases, are also modeled. In recognition of the emerging significance of quality of service (QoS), that is, control of stockout probability to meet demand on time, maximum stockout probability constraints are also modeled explicitly. Lead time and QoS modeling require incorporation of nonlinear constraints in the production planning optimization process. The quantification of these nonlinear constraints must capture statistics of the stochastic behavior of production facilities revealed during a time scale far shorter than the customary weekly time scale of the planning process. The apparent computational complexity of planning production against variable LT and QoS constraints has long resulted in MRP-based scheduling practices that ignore the LT and QoS impact to the plan’s detriment. The computational complexity challenge was overcome by proposing and adopting a time-scale decomposition approach to production planning, where short-time-scale stochastic dynamics are modeled in multiple facility-specific subproblems that receive tentative targets from a deterministic master problem and return statistics to it. A converging and scalable iterative methodology is implemented, providing evidence that significantly lower cost production plans are achievable in a computationally tractable manner.     

一种配电网络差分禁忌线路规划方法

针对配电网络规划问题,基于差分进化算法(DE)和禁忌搜索算法(TS)协同优化框架,提出了一种差分禁忌混合算法(DETS)。首先,将配电约束条件划分为硬约束和软约束,硬约束用于保证配电网络拓扑结构的合理性;软约束用于提高种群多样性。然后,设计DE及TS两层优化结构,外层利用DE快速收敛特性为内层提供较好的初始个体;内层利用TS贡献全局搜索能力,避免陷入局部最优。其次,设计修复算子来避免DE算法易产生不可行解的问题。最后,采用10个标准测试函数验证了DETS算法的性能,同时利用DETS算法实现了某市的中低压配电网络线路规划。     

A Train Dispatching Model Under a Stochastic Environment: Stable Train Routing Constraints and Reformulation

After major capacity breakdown(s) on a railway network, train dispatchers need to generate appropriate dispatching plans to recover the impacted train schedule from perturbations and minimize the expected total train delay time under stochastic scenarios. In this paper, we propose a cumulative flow variables-based integer programming model for dispatching trains under a stochastic environment on a general railway network. Stable Train Routing (STR) constraints are introduced to ensure that trains traverse on the same route across different capacity breakdown scenarios, which are further reformulated to equivalent linear inequality constraints. Track occupancy and safety headways are modelled as side constraints which are dualized through a proposed Lagrangian relaxation solution framework. The original complex train dispatching problem is then decomposed to a set of single-train and single-scenario optimization subproblems. For each subproblem, a standard label correcting algorithm is embedded for finding the time dependent least cost path on a space-time network. The resulting dual solutions can be transformed to feasible solutions through priority rules. Numerical experiments are conducted to demonstrate the efficiency and effectiveness of the proposed solution approach.     

An integrated traffic model for multimedia wireless networks

Multimedia wireless networks are seen today as one of the key factors for the success of the global communication infrastructure in the near future. Such networks will have to handle a range of heterogeneous traffic classes with different QoS requirements. Their design, planning and control must be supported by suitable traffic models capable of dealing with a new set of constraints where QoS management and mobility play an important role.This paper proposes a traffic model for a cellular multimedia wireless network characterized by the integration of mobility and traffic management aspects. User mobility is modeled through a Markov renewal process, which allows for non-exponential cell residence times and may restrict the user mobility to existent paths in the system. A Markov-modulated fluid process is used to describe the changes in the bandwidth requirements of each mobile over the duration of its calls, including the periods where the mobile is inactive (without call).Based on the proposed model, the number of mobiles per class of traffic in a cell and the handoff processes are characterized. System performance results, such as new and handoff call blocking probabilities, for network planning are derived. Also, the distribution of the required capacity in a short time interval for network control is obtained. Simulations were carried out to validate the analytical results. The comparisons have shown that the integrated model may be regarded as a good basis to build useful teletraffic engineering tools for multimedia wireless networks.     

A performance optimization algorithm for controller reconfiguration in fault tolerant distributed model predictive control

This paper presents a performance optimization algorithm for controller reconfiguration in fault tolerant distributed model predictive control for large-scale systems. After the fault has been detected and diagnosed, several controller reconfigurations are proposed as candidate corrective actions for fault compensation. The solution of a set of constrained optimization problems with different actuator and setpoint reconfigurations is derived by means of an original approach, exploiting the information on the active constraints in the non-faulty subsystems. Thus, the global optimization problem is split into two optimization subproblems, which enable the online computational burden to be greatly reduced. Subsequently, the performances of different candidate controller reconfigurations are compared, and the better performing one is selected and then implemented to compensate the fault effects. Efficacy of the proposed approach has been shown by applying it to the benzene alkylation process, which is a benchmark process in distributed model predictive control.