Efficiency of the solution representations for the hybrid flow shop scheduling problem with makespan objective

In this paper we address the classical hybrid flow shop scheduling problem with makespan objective. As this problem is known to be NP-hard and a very common layout in real-life manufacturing scenarios, many studies have been proposed in the literature to solve it. These contributions use different solution representations of the feasible schedules, each one with its own advantages and disadvantages. Some of them do not guarantee that all feasible semiactive schedules are represented in the space of solutions –thus limiting in principle their effectiveness– but, on the other hand, these simpler solution representations possess clear advantages in terms of having consistent neighbourhoods with well-defined neighbourhood moves. Therefore, there is a trade-off between the solution space reduction and the ability to conduct an efficient search in this reduced solution space. This trade-off is determined by two aspects, i.e. the extent of the solution space reduction, and the quality of the schedules left aside by this solution space reduction. In this paper, we analyse the efficiency of the different solution representations employed in the literature for the problem. More specifically, we first establish the size of the space of semiactive schedules achieved by the different solution representations and, secondly, we address the issue of the quality of the schedules that can be achieved by these representations using the optimal solutions given by several MILP models and complete enumeration. The results obtained may contribute to design more efficient algorithms for the hybrid flow shop scheduling problem.Ministerio de Ciencia e Innovación DPI2016-80750-

Survey on Combinatorial Register Allocation and Instruction Scheduling

Register allocation (mapping variables to processor registers or memory) and instruction scheduling (reordering instructions to increase instruction-level parallelism) are essential tasks for generating efficient assembly code in a compiler. In the last three decades, combinatorial optimization has emerged as an alternative to traditional, heuristic algorithms for these two tasks. Combinatorial optimization approaches can deliver optimal solutions according to a model, can precisely capture trade-offs between conflicting decisions, and are more flexible at the expense of increased compilation time. This paper provides an exhaustive literature review and a classification of combinatorial optimization approaches to register allocation and instruction scheduling, with a focus on the techniques that are most applied in this context: integer programming, constraint programming, partitioned Boolean quadratic programming, and enumeration. Researchers in compilers and combinatorial optimization can benefit from identifying developments, trends, and challenges in the area; compiler practitioners may discern opportunities and grasp the potential benefit of applying combinatorial optimization

Taming Numbers and Durations in the Model Checking Integrated Planning System

The Model Checking Integrated Planning System (MIPS) is a temporal least commitment heuristic search planner based on a flexible object-oriented workbench architecture. Its design clearly separates explicit and symbolic directed exploration algorithms from the set of on-line and off-line computed estimates and associated data structures. MIPS has shown distinguished performance in the last two international planning competitions. In the last event the description language was extended from pure propositional planning to include numerical state variables, action durations, and plan quality objective functions. Plans were no longer sequences of actions but time-stamped schedules. As a participant of the fully automated track of the competition, MIPS has proven to be a general system; in each track and every benchmark domain it efficiently computed plans of remarkable quality. This article introduces and analyzes the most important algorithmic novelties that were necessary to tackle the new layers of expressiveness in the benchmark problems and to achieve a high level of performance. The extensions include critical path analysis of sequentially generated plans to generate corresponding optimal parallel plans. The linear time algorithm to compute the parallel plan bypasses known NP hardness results for partial ordering by scheduling plans with respect to the set of actions and the imposed precedence relations. The efficiency of this algorithm also allows us to improve the exploration guidance: for each encountered planning state the corresponding approximate sequential plan is scheduled. One major strength of MIPS is its static analysis phase that grounds and simplifies parameterized predicates, functions and operators, that infers knowledge to minimize the state description length, and that detects domain object symmetries. The latter aspect is analyzed in detail. MIPS has been developed to serve as a complete and optimal state space planner, with admissible estimates, exploration engines and branching cuts. In the competition version, however, certain performance compromises had to be made, including floating point arithmetic, weighted heuristic search exploration according to an inadmissible estimate and parameterized optimization

User-Base Station Association in HetSNets: Complexity and Efficient Algorithms

This work considers the problem of user association to small-cell base stations (SBSs) in a heterogeneous and small-cell network (HetSNet). Two optimization problems are investigated, which are maximizing the set of associated users to the SBSs (the unweighted problem) and maximizing the set of weighted associated users to the SBSs (the weighted problem), under signal-to-interference-plus-noise ratio (SINR) constraints. Both problems are formulated as linear integer programs. The weighted problem is known to be NP-hard and, in this paper, the unweighted problem is proved to be NP-hard as well. Therefore, this paper develops two heuristic polynomial-time algorithms to solve both problems. The computational complexity of the proposed algorithms is evaluated and is shown to be far more efficient than the complexity of the optimal brute-force (BF) algorithm. Moreover, the paper benchmarks the performance of the proposed algorithms against the BF algorithm, the branch-and-bound (B\&B) algorithm and standard algorithms, through numerical simulations. The results demonstrate the close-to-optimal performance of the proposed algorithms. They also show that the weighted problem can be solved to provide solutions that are fair between users or to balance the load among SBSs

Efficient heuristics for the hybrid flow shop scheduling problem with missing operations

In this paper, we address the hybrid flowshop scheduling problem for makespan minimisation. More specifically, we are interested in the special case where there are missing operations, i.e. some stages are skipped, a condition inspired in a realistic problem found in a plastic manufacturer. The main contribution of our paper is twofold. On the one hand we carry out a computational analysis to study the hardness of the hybrid flowshop scheduling problem with missing operations as compared to the classical hybrid flowshop problem. On the other hand, we propose a set of heuristics that captures some special features of the missing operations and compare these algorithms with already existing heuristics for the classical hybrid flowshop, and for the hybrid flowshop problem with missing operations. The extensive computational experience carried out shows that our proposal outperforms existing methods for the problem, indicating that it is possible to improve the makespan by interacting with the jobs with missing operations.Ministerio de Ciencia e Innovación DPI2016-80750-