André A. Ciré

A hybrid model for a multiproduct pipeline planning and scheduling problem

Brazilian petrobras is one of the world largest oil companies. Recurrently, it faces a very difficult planning and scheduling problem: how to operate a large pipeline network in order to adequately transport oil derivatives and biofuels from refineries to local markets. In spite of being more economical and environmentally safer, the use of a complex pipeline network poses serious operational difficulties related to resource allocation and temporal constraints. The current approaches known from the literature only consider a few types of constraints and restricted topologies, hence they are far from being applicable to real instances from petrobras. We propose a hybrid framework based on a two-phase problem decomposition strategy. A novel Constraint Programming (CP) model plays a key role in modelling operational constraints that are usually overlooked in literature, but that are essential in order to guarantee viable solutions. The full strategy was implemented and produced very adequate results when tested over large real instances.

Planning and Scheduling the Operation of a Very Large Oil Pipeline Network

Brazilian petrobras is one of the world largest oil companies. Recurrently, it faces a very difficult over-constrained planning challenge: how to operate a large pipeline network in order to adequately transport oil derivatives and biofuels from refineries to local markets. In spite of being more economical and environmentally safer, the use of a complex pipeline network poses serious operational difficulties. The network has a complex topology, with around 30 interconnecting pipelines, over 30 different products in circulation, and about 14 distribution depots which harbor more than 200 tanks, with a combined capacity for storing up to 65 million barrels. The problem is how to schedule individual pumping operations, given the daily production and demand of each product, at each location in the network, over a given time horizon. We describe a solution based on a two-phase problem decomposition strategy. A novel Constraint Programming (CP) model plays a key role in modeling operational constraints that are usually overlooked in literature, but that are essential in order to guarantee viable solutions. The use of CP was crucial, since it allowed the modeling of complex constraints, including nonlinearities. The full strategy was implemented and produced very adequate results when tested over large real instances. In contrast, other approaches known from the literature failed, even when applied to much less complex networks.

Variable ordering for the application of BDDs to the maximum independent set problem

The ordering of variables can have a significant effect on the size of the reduced binary decision diagram (BDD) that represents the set of solutions to a combinatorial optimization problem. It also influences the quality of the objective function bound provided by a limited-width relaxation of the BDD. We investigate these effects for the maximum independent set problem. By identifying variable orderings for the BDD, we show that the width of an exact BDD can be given a theoretical upper bound for certain classes of graphs. In addition, we draw an interesting connection between the Fibonacci numbers and the width of exact BDDs for general graphs. We propose variable ordering heuristics inspired by these results, as well as a k-layer look-ahead heuristic applicable to any problem domain. We find experimentally that orderings that result in smaller exact BDDs have a strong tendency to produce tighter bounds in relaxation BDDs.

Discrete Optimization with Decision Diagrams

We propose a general branch-and-bound algorithm for discrete optimization in which binary decision diagrams (BDDs) play the role of the traditional linear programming relaxation. In particular, relaxed BDD representations of the problem provide bounds and guidance for branching, and restricted BDDs supply a primal heuristic. Each problem is given a dynamic programming model that allows one to exploit recursive structure, even though the problem is not solved by dynamic programming. A novel search scheme branches within relaxed BDDs rather than on values of variables. Preliminary testing shows that a rudimentary BDD-based solver is competitive with or superior to a leading commercial integer programming solver for the maximum stable set problem, the maximum cut problem on a graph, and the maximum 2-satisfiability problem. Specific to the maximum cut problem, we tested the BDD-based solver on a classical benchmark set and identified tighter relaxation bounds than have ever been found by any technique, nearly closing the entire optimality gap on four large-scale instances.

BDD-based heuristics for binary optimization

In this paper we introduce a new method for generating heuristic solutions to binary optimization problems. We develop a technique based on binary decision diagrams. We use these structures to provide an under-approximation to the set of feasible solutions. We show that the proposed algorithm delivers comparable solutions to a state-of-the-art general-purpose optimization solver on randomly generated set covering and set packing problems.

MDD propagation for sequence constraints

We study propagation for the Sequence constraint in the context of constraint programming based on limited-width MDDs. Our first contribution is proving that establishing MDD-consistency for Sequence is NP-hard. Yet, we also show that this task is fixed parameter tractable with respect to the length of the sub-sequences. In addition, we propose a partial filtering algorithm that relies on a specific decomposition of the constraint and a novel extension of MDD filtering to node domains. We experimentally evaluate the performance of our proposed filtering algorithm, and demonstrate that the strength of the MDD propagation increases as the maximum width is increased. In particular, MDD propagation can outperform conventional domain propagation for Sequence by reducing the search tree size and solving time by several orders of magnitude. Similar improvements are observed with respect to the current best MDD approach that applies the decomposition of Sequence into Among constraints.

Mixed integer programming vs logic-based Benders decomposition for planning and scheduling

A recent paper by Heinz and Beck (CPAIOR 2012) found that mixed integer software has become competitive with or superior to logic-based Benders decomposition for the solution of facility assignment and scheduling problems. Their implementation of Benders differs, however, from that described in the literature they cite and therefore results in much slower performance than previously reported. We find that when correctly implemented, the Benders method remains 2 to 3 orders of magnitude faster than the latest commercial mixed integer software on larger instances, thus reversing the conclusion of the earlier paper.

Parallel Combinatorial Optimization with Decision Diagrams

We propose a new approach for parallelizing search for combinatorial optimization that is based on a recursive application of approximate Decision Diagrams. This generic scheme can, in principle, be applied to any combinatorial optimization problem for which a decision diagram representation is available. We consider the maximum independent set problem as a specific case study, and show how a recently proposed sequential branch-and-bound scheme based on approximate decision diagrams can be parallelized efficiently using the X10 parallel programming and execution framework. Experimental results using our parallel solver, DDX10, running on up to 256 compute cores spread across a cluster of machines indicate that parallel decision diagrams scale effectively and consistently. Moreover, on graphs of relatively high density, parallel decision diagrams often outperform state-of-the-art parallel integer programming when both use a single 32-core machine.

Heuristics and Constraint Programming Hybridizations for a Real Pipeline Planning and Scheduling Problem

Pipeline network systems are considered the major option for transporting petroleum derivatives from refineries to local markets, in view of their many economic and environmental advantages. This article deals with a large real-world pipeline system planning and scheduling problem, in which different products should be transported in a pipeline network in order to supply market demands, while also satisfying hard operational constraints related to product sequencing, flow rates and tank capacities. We propose a novel hybrid approach based on two iterative phases comprised by a heuristic strategy and a Constraint Programming model. The resulting algorithm was tested with real-world instances yielding feasible solutions for all of them.

Lagrangian bounds from decision diagrams

Relaxed decision diagrams have recently been used in constraint programming to improve constraint propagation and optimization reasoning. In most applications, however, a decision diagram is compiled with respect to a single combinatorial structure. We propose to expand this representation by incorporating additional constraints in the decision diagram via a Lagrangian relaxation. With this generic approach we can obtain stronger bounds from the same decision diagram, while the associated cost-based filtering allows for further refining the relaxation. Experimental results on the traveling salesman problem with time windows show that the improved Lagrangian bounds can drastically reduce solution times.