Decision Diagrams for Discrete Optimization: A Survey of Recent Advances

Castro, Margarita P.; Ciré, André A.; Beck, J. Christopher

doi:10.1287/ijoc.2022.1170

Cited by 10 publications

(3 citation statements)

References 57 publications

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“…In the last decade, BDDs found their application also in combinatorial optimisation, where they are successfully applied to well-studied standard optimisation problems (Andersen et al 2007;Cire and van Hoeve 2013;Bergman et al 2014;Kinable, Cire, and van Hoeve 2017). For a detailed introduction we refer to the textbook by Bergman et al (2016) and to the survey of recent advances by Castro, Cire, and Beck (2022).…”

Section: Bdds For the 2dssp Constraintmentioning

confidence: 99%

Parallel Batch Processing for the Coating Problem

Horn

Demirović

Yorke-Smith

2023

ICAPS

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We solve a challenging scheduling problem with parallel batch processing and two-dimensional shelf strip packing constraints that arises in the tool coating field. Tools are assembled on so-called planetaries (batches) before they are loaded into coating machines to get coated. The assembling is not trivial and must fulfil specific constraints, which we refer to as shelf strip packing constraints. Further, each tool is associated with a starting time window s.t. tools can only be put on the same planetary if their time window overlap. The objective is to minimise the makespan and the number of required planetaries. Since the problem naturally decomposes into scheduling and packing parts, we tackle the problem with a two-phase logic-based Benders decomposition approach. The master problem assigns items to batches. The first phase solves as subproblem the packing problem by checking if the assignment is feasible, whereas the second phase solves the scheduling subproblem. The approach is compared with a monolithic mixed integer linear programming approach as well as a monolithic constraint programming approach. Experimental evaluation shows that our proposed approach outperforms the state-of-the-art benchmarks by solving more instances to optimality in a shorter time.

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Section: Bdds For the 2dssp Constraintmentioning

confidence: 99%

Parallel Batch Processing for the Coating Problem

Horn

Demirović

Yorke-Smith

2023

ICAPS

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“…In addition to their computational efficiency for certain problem types, one of the key benefits of DD-based approaches is that they are highly generic in the sense that in order to apply them, one basically only needs a Dynamic Programming (DP) formulation of the problem to be considered along with the specification of a so-called merge operator. For an excellent survey of the recent advancements in DD-based approaches for solving discrete optimization problems, we refer to (Castro, Cire, and Beck 2022).…”

Section: Introductionmentioning

confidence: 99%

Using Clustering to Strengthen Decision Diagram Bounds for Discrete Optimization

Nafar,

Römer

2024

AAAI

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Offering a generic approach to obtaining both upper and lower bounds, decision diagrams (DDs) are becoming an increasingly important tool for solving discrete optimization problems. In particular, they provide a powerful and often complementary alternative to other well-known generic bounding mechanisms such as the LP relaxation. A standard approach to employ DDs for discrete optimization is to formulate the problem as a Dynamic Program and use that formulation to compile a DD top-down in a layer-by-layer fashion. To limit the size of the resulting DD and to obtain bounds, one typically imposes a maximum width for each layer which is then enforced by either merging nodes (resulting in a so-called relaxed DD that provides a dual bound) or by dropping nodes (resulting in a so-called restricted DD that provides a primal bound). The quality of the DD bounds obtained from this top-down compilation process heavily depends on the heuristics used for the selection of the nodes to merge or drop. While it is sometimes possible to engineer problem-specific heuristics for this selection problem, the most generic approach relies on sorting the layer’s nodes based on objective function information. In this paper, we propose a generic and problem-agnostic approach that relies on clustering nodes based on the state information associated with each node. In a set of computational experiments with different knapsack and scheduling problems, we show that our approach generally outperforms the classical generic approach, and often achieves drastically better bounds both with respect to the size of the DD and the time used for compiling the DD.

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“…Multivalued decision diagrams (MDDs) are a useful graphical tool for compactly storing the solution space of discrete optimization problems. In the last few years, a staggering number of new applications for MDDs have been proposed (Castro et al, 2022), such as representing global constraints (Uña et al, 2019;Verhaeghe et al, 2018;Vion & Piechowiak, 2018), handling stochastic variables (Lozano & Smith, 2018;Latour et al, 2019), and performing post-optimality analysis (Serra & Hooker, 2019). MDDs are particularly useful for generating strong dual bounds (Cappart et al, 2019;Castro et al, 2020;Hoeve, 2021;Maschler & Raidl, 2021;Cappart et al, 2022;Gentzel et al, 2020), especially on optimization problems where linear relaxations perform poorly.…”

Section: Introductionmentioning

confidence: 99%

Improved Peel-and-Bound: Methods for Generating Dual Bounds with Multivalued Decision Diagrams

Rudich

Cappart

Rousseau

2023

jair

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Decision diagrams are an increasingly important tool in cutting-edge solvers for discrete optimization. However, the field of decision diagrams is relatively new, and is still incorporating the library of techniques that conventional solvers have had decades to build. We drew inspiration from the warm-start technique used in conventional solvers to address one of the major challenges faced by decision diagram based methods. Decision diagrams become more useful the wider they are allowed to be, but also become more costly to generate, especially with large numbers of variables. In the original version of this paper, we presented a method of peeling off a sub-graph of previously constructed diagrams and using it as the initial diagram for subsequent iterations that we call peel-and-bound. We tested the method on the sequence ordering problem, and our results indicate that our peel-and-bound scheme generates stronger bounds than a branch-and-bound scheme using the same propagators, and at significantly less computational cost. In this extended version of the paper, we also propose new methods for using relaxed decision diagrams to improve the solutions found using restricted decision diagrams, discuss the heuristic decisions involved with the parallelization of peel-and-bound, and discuss how peel-and-bound can be hyper-optimized for sequencing problems. Furthermore, we test the new methods on the sequence ordering problem and the traveling salesman problem with time-windows (TSPTW), and include an updated and generalized implementation of the algorithm capable of handling any discrete optimization problem. The new results show that peel-and-bound outperforms ddo (a decision diagram based branch-and-bound solver) on the TSPTW. We also close 15 open benchmark instances of the TSPTW.

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Decision Diagrams for Discrete Optimization: A Survey of Recent Advances

Cited by 10 publications

References 57 publications

Parallel Batch Processing for the Coating Problem

Parallel Batch Processing for the Coating Problem

Using Clustering to Strengthen Decision Diagram Bounds for Discrete Optimization

Improved Peel-and-Bound: Methods for Generating Dual Bounds with Multivalued Decision Diagrams

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