Event-based MILP models for resource-constrained project scheduling problems

International audienceIn this paper we make a comparative study of several mixed integer linear programming (MILP) formulations for resource-constrained project scheduling problems (RCPSPs). First, we present three discrete and continuous time MILP formulations issued from the literature. Second, instead of relying on the traditional discretization of the time horizon, we propose two original MILP formulations for the RCPSP based on the concept of event : the Start/End formulation and the On/Off formulation. These formulations present the advantage of involving fewer variables than the formulations indexed by time. Because the variables of this type of formulations are not function of the time horizon, we have a better capacity to deal with instances of very large scheduling horizon. We also illustrate our contribution with a series of tests on various types of instances with the three MILP formulations issued from the literature together with our two new formulations, and we draw some conclusions on their use

Reformulation and decomposition of integer programs

In this survey we examine ways to reformulate integer and mixed integer programs. Typically, but not exclusively, one reformulates so as to obtain stronger linear programming relaxations, and hence better bounds for use in a branch-and-bound based algorithm. First we cover in detail reformulations based on decomposition, such as Lagrangean relaxation, Dantzig-Wolfe column generation and the resulting branch-and-price algorithms. This is followed by an examination of Benders’ type algorithms based on projection. Finally we discuss in detail extended formulations involving additional variables that are based on problem structure. These can often be used to provide strengthened a priori formulations. Reformulations obtained by adding cutting planes in the original variables are not treated here.Integer program, Lagrangean relaxation, column generation, branch-and-price, extended formulation, Benders' algorithm

Effective Project Scheduling Under Workspace Congestion and Workflow Disturbance Factors

Effective project management implies the use of advanced planning and scheduling methods that allow to determine feasible sequences of activities and to complete a project on time and on budget. Traditional scheduling tools like fundamental Critical Path Method (CPM) and various methods for Resource Constrained Project Scheduling Problem (RCPSP) and Time Constrained Project Scheduling Problem (TCPSP) have many shortcomings for construction projects where spatial factor plays a critically important role. Previous attempts to interpret space as a specific resource were successful for particular problems of line-of-balance scheduling, space scheduling, dynamic layout planning, horizontal and vertical logic scheduling, workspace congestion mitigating, scheduling multiple projects with movable resources, spatial scheduling of repeated and grouped activities and motion planning. However, none of these methods considers the spatio-temporal requirements in a holistic framework of generic RCPSP problem and provides feasible results accounting for workspace and workflow factors. In this paper we start with the classical RCPSP statement and then present mathematically strong formalisation of the extended generalised problem, taking into account workspace congestion and workflow disturbance constraints specified in practically meaningful and computationally constructive ways. For the generalised RCPSP problem an effective scheduling method is proposed. The method tends to minimise the project makespan while satisfying timing constraints and precedence relations, not exceeding resource utilisation limits, avoiding workspace congestions and keeping workflows continuous. The method reuses so-called serial scheduling scheme and provides for additional computational routines and heuristic priority rules to generate feasible schedules satisfying all the imposed requirements. Advantages of the method and prospects for its application to industrial needs are outlined in the paper too

Parallelizing with BDSC, a resource-constrained scheduling algorithm for shared and distributed memory systems

International audienceWe introduce a new parallelization framework for scientific computing based on BDSC, an efficient automatic scheduling algorithm for parallel programs in the presence of resource constraints on the number of processors and their local memory size. BDSC extends Yang and Gerasoulis's Dominant Sequence Clus-tering (DSC) algorithm; it uses sophisticated cost models and addresses both shared and distributed parallel memory architectures. We describe BDSC, its integration within the PIPS compiler infrastructure and its application to the parallelization of four well-known scientific applications: Harris, ABF, equake and IS. Our experiments suggest that BDSC's focus on efficient resource man-agement leads to significant parallelization speedups on both shared and dis-tributed memory systems, improving upon DSC results, as shown by the com-parison of the sequential and parallelized versions of these four applications running on both OpenMP and MPI frameworks

Tools for efficient Deep Learning

In the era of Deep Learning (DL), there is a fast-growing demand for building and deploying Deep Neural Networks (DNNs) on various platforms. This thesis proposes five tools to address the challenges for designing DNNs that are efficient in time, in resources and in power consumption. We first present Aegis and SPGC to address the challenges in improving the memory efficiency of DL training and inference. Aegis makes mixed precision training (MPT) stabler by layer-wise gradient scaling. Empirical experiments show that Aegis can improve MPT accuracy by at most 4\%. SPGC focuses on structured pruning: replacing standard convolution with group convolution (GConv) to avoid irregular sparsity. SPGC formulates GConv pruning as a channel permutation problem and proposes a novel heuristic polynomial-time algorithm. Common DNNs pruned by SPGC have maximally 1\% higher accuracy than prior work. This thesis also addresses the challenges lying in the gap between DNN descriptions and executables by Polygeist for software and POLSCA for hardware. Many novel techniques, e.g. statement splitting and memory partitioning, are explored and used to expand polyhedral optimisation. Polygeist can speed up software execution in sequential and parallel by 2.53 and 9.47 times on Polybench/C. POLSCA achieves 1.5 times speedup over hardware designs directly generated from high-level synthesis on Polybench/C. Moreover, this thesis presents Deacon, a framework that generates FPGA-based DNN accelerators of streaming architectures with advanced pipelining techniques to address the challenges from heterogeneous convolution and residual connections. Deacon provides fine-grained pipelining, graph-level optimisation, and heuristic exploration by graph colouring. Compared with prior designs, Deacon shows resource/power consumption efficiency improvement of 1.2x/3.5x for MobileNets and 1.0x/2.8x for SqueezeNets. All these tools are open source, some of which have already gained public engagement. We believe they can make efficient deep learning applications easier to build and deploy.Open Acces

Hospital-wide therapist scheduling and routing: exact and heuristic methods

In this paper, we address the problem of scheduling and routing physical therapists hospital-wide. At the beginning of a day, therapy jobs are known to a hospital's physical therapy scheduler who decides for each therapy job when, where and by which therapist a job is performed. If a therapist is assigned to a sequence which contains two consecutive jobs that must take place in different treatment rooms, then transfer times must be considered. We propose three approaches to solve the problem. First, an Integer Program (IP) simultaneously schedules therapies and routes therapists. Second, a cutting plane algorithm iteratively solves the therapy scheduling problem without routing constraints and adds cuts to exclude schedules which have no feasible routes. Since hospitals are interested in obtaining quick solutions, we also propose a heuristic algorithm, which schedules therapies sequentially by simultaneously checking routing and resource constraints. Using real-world data from a hospital, we compare the performance of the three approaches. Our computational analysis reveals that our IP formulation fails to solve test, which have more than~30 jobs, to optimality in an acceptable solution time. In contrast, the cutting plane algorithm can solve instances with more than 100 jobs optimally. The heuristic approach obtains good solutions for large real-world instances within fractions of a second