Large Neighborhood Search

The two-dimensional irregular knapsack problem in a fixed circular container is an important combinatorial optimization problem for maximizing material utilization in manufacturing. Conventional geometric packing solvers can produce tightly packed layouts, yet they often partition the residual space into isolated small pockets that cannot fit valuable unplaced polygons. To overcome this late-stage packing bottleneck, we propose a failure-aware large neighborhood search framework named GeoNest, driven by a graph policy trained via reinforcement learning. Specifically, we first construct neighborhoods by pairing failed target polygons with residual pockets. We then use explanatory poses to identify the placed polygons that block candidate insertions. These diagnosed blocking relations define bounded, fixed-item repair subproblems for the underlying geometric solver. Finally, the graph policy selects the most promising subproblem for execution. For evaluation, we introduce CircleNest-Bench, a benchmark comprising 2,391 load-controlled instances from four contour sources, including a held-out industrial CAD source. Experimental results demonstrate that, under the same total time budget, GeoNest improves mean utilization over a state-of-the-art standalone packing solver by about 0.9% on average across the three main test sets and by about 0.6% on the held-out industrial set.

Large neighborhood search normally selects a random subset of decision variables for iterative optimization. For efficiently solving different problems, researchers tend to design variable selection strategies by taking into account structural features from different domains. In this paper, we build an automatic pipeline that is problem-agnostic to all problems in the MiniZinc format. By prompting an LLM with our semantic guidelines, we guide the LLM to produce a graph generator that maps any instance of a problem type to a uniform weighted graph, where nodes represent decision variables and edges represent constraint relationships. These problem-agnostic graphs guide our structure-based local improvement framework (SLIM) in variable selection. Meanwhile, the weighted graph enables all problem instances to share the same generic graph representation, from which the same graph features can be extracted and used for configuration selection. We evaluated our pipeline on instances across 20 MiniZinc competition problems, finding that algorithm selection achieves a 39.5% average problem-weighted win rate against a one-shot Gurobi baseline, more than doubling the best single configuration (19.3%). Configuration and feature ablation boost the performance further to 44.0%, demonstrating that LLM-based semantic generation enables effective automated structure extraction and feature extraction for constraint optimization.

We study continuous planar facility location in which a demand point's captured value decays with distance, with the per-point decay scale varying across points. This heterogeneity is ubiquitous yet underexploited, and one nearest-facility objective unifies decay, clustering, and median goals, containing k-means, the Weber/p-median problem, and maximum covering as special cases. We make four contributions. (i) A tractability classification: the discrete objective is always monotone submodular, so the (1-1/e) greedy guarantee holds regardless of decay shape or heterogeneity, and the continuous cooperative objective is concave if and only if the decay is concave in distance; the clip max(0,d) in common coverage specifications is what destroys concavity, and the classification is tight. (ii) An exact discrete method: the candidate-discretized maximum-cover MIP has an empirically tight LP relaxation (~0% gap) and is solved by branch-and-bound in seconds for n <= 500. (iii) A force-as-gradient / large-neighborhood-search heuristic, within 0.5% of the discrete optimum, that outperforms the (1-1/e) greedy, Cooper-style alternating location-allocation, particle swarm optimization, and weighted k-means (30/30 per-instance wins at K=30, p<10^-9) and is competitive with bespoke solvers on k-means, Weber/p-median, and shape-demand instances. (iv) A real-world study: on 592,667 urban-delivery orders, ignoring the calibrated decay variation loses up to 9.7% of captured demand and relocates facilities by up to 37% of the map; a retail dataset calibrates the decay as exponential with scale R ~ 1.4 km.

This paper introduces the Dynamical Vehicle Orienteering Problem (DVOP), a generalization of the Orienteering Problem (OP). The OP maximizes the reward collected from spatial targets under a limited travel budget; the DVOP extends it by accounting for both external and vehicle-actuated forces. We study the DVOP in the context of multi-rotor Unmanned Aerial Vehicle (UAV) flight planning, using a three-dimensional Point-Mass Model (PMM) constrained by maximum velocity and acceleration magnitudes and subject to gravitational acceleration, with the travel budget expressed as a maximum flight time. Because the DVOP couples reward maximization with time-optimal trajectory planning, it cannot be formulated as a simple graph problem and solved exactly without relaxing or under-actuating the vehicle dynamics. We therefore propose two solution approaches: a Branch-and-Bound (BnB) procedure that combines Non-Linear Programming (NLP) and Mixed-Integer Linear Programming (MILP) to provide high-quality solutions, and a Large Neighborhood Search (LNS) metaheuristic that supplies an initial reward bound and scales to instances intractable for the BnB. The BnB relies on a novel MILP formulation of travel costs based on minimum-time trajectory primitives through target triplets, yielding a tight reward upper bound, while the LNS uses limited thrust decomposition to compute fast, high-quality PMM trajectories. Experiments on benchmark instances show improvements of up to 37 % over state-of-the-art solutions for the Kinematic Orienteering Problem, and a real-world deployment on a multi-rotor UAV verifies the proposed PMM solution trajectories.

Modern supply chains span diverse operational environments, ranging from e-commerce distribution networks to customized production-to-order manufacturing lines. Across these settings, operational efficiency depends on coordinating two highly interdependent stages: order preparation and downstream delivery. Although these stages are traditionally managed in isolation, real-world fulfillment systems must satisfy stringent delivery expectations under dynamic stochastic order arrivals. To bridge this gap, we introduce the Dynamic Order Fulfillment Problem (DOFP), a new problem class unifying logistical challenges previously studied separately. We model DOFP as a Markov decision process whose state and decision spaces are partitioned into preparation and delivery sub-spaces, linked by synchronization constraints. While recent approaches attempt to optimize both fulfillment stages simultaneously over myopic rolling horizons, our framework isolates and optimizes the downstream delivery policy, treating preparation strictly as a state-level constraint filter. To solve this, we develop the Decomposition-Driven Framework with Value Function Approximation (DDF-VFA), which utilizes a novel policy-level decomposition. This design partitions the search into a delivery-stage master problem and a preparation-stage compatibility subproblem, iteratively refined via feedback loops. DDF-VFA executes this strategy by combining a large-neighborhood search over partial delivery decisions with a neural-network value function approximation for the cost-to-go. Numerical illustrations on two example variants using real-world datasets show that DDF-VFA consistently outperforms benchmarks that optimize the two stages independently or jointly without decomposition. Finally, the framework naturally scales to accommodate additional real-world complexities such as batched or multi-stage preparation.

Operations research practitioners typically tackle NP-hard combinatorial problems using large neighborhood search (LNS), a scalable heuristic that iteratively refines a current solution by locally re-optimizing subsets of its variables. In contrast, most existing approaches for integrating combinatorial optimization layers into neural networks still assume access to an exact global solution, which is computationally intractable. We bridge this gap by introducing regularized LNS (RLNS). By regularizing or perturbing local subproblems, we turn the LNS heuristic into an efficient MCMC sampler over the combinatorial set of feasible solutions, with associated Fenchel-Young losses. Under entropic regularization, we prove that RLNS performs exact block Gibbs sampling. Furthermore, adjusting the number of RLNS iterations allows us to interpolate between pseudolikelihood and exact maximum likelihood estimation, for end-to-end learning without global solvers. We demonstrate our approach on $k$-subset selection, generalized assignment, and stochastic vehicle scheduling problems.

A new variant of the classic capacitated facility location problem, which considers incompatibilities between customers, has recently been introduced in the literature. This problem captures the situation where given pairs of customers cannot be served by the same facility. Such a feature is crucial for many practical cases of location problems, such as the presence of hazardous or polluting materials and contention between competing costumers. In this paper, we propose a Large Neighborhood Search (LNS) method to solve this problem. Within the framework of LNS, we introduce three different destroy operators, which are combined in a hybrid manner, and we use an exact solver in the repair phase. Different algorithmic components are investigated for the design of LNS. The experimental analysis shows that our new method outperforms existing state-of-the-art metaheuristics, providing new best solutions for all available benchmark instances.

Dynamic Programming (DP) and Constraint Programming (CP) are well-established paradigms for solving combinatorial optimization problems. Usually, these two approaches are used separately. This paper aims to show that the two can be combined effectively and elegantly, with DP serving as the primary search framework and CP used as a subroutine to leverage global constraint propagation. This paper presents such an approach for the Partial Shop Scheduling Problem (PSSP), for which a pure DP method has previously been proposed, and efficient CP filtering algorithms are available. The PSSP is a general scheduling problem where each job consists of a set of operations with arbitrary precedence constraints. The approach is flexible enough to accommodate anytime DP strategies, such as anytime column search, whereas the original DP algorithm operated in a strictly layer-wise manner. Moreover, the flexibility of the CP modeling makes it straightforward to incorporate arbitrary precedence constraints. As a result, the model naturally handles any precedence graph and even enables the design of a Large Neighborhood Search (LNS) scheme, in which the DP model is reused, and partial-order schedules are imposed across restarts to improve the incumbent solution. While not competitive with state-of-the-art pure CP solvers for this specific problem, our primary contribution is demonstrating the viability of this hybrid integration.