Learning about Farkas' lemma and how it can inform Benders decomposition to learn from infeasibility, applied to the capacitated facility location problem. The post How Benders Decomposition Works, Part II: Feasibility Cuts appeared first on Towards Data Science .
A friendly introduction to one of the most powerfull optimization techniques using the uncapacitated facility location problem The post How Benders Decomposition Works Part I: Optimality Cuts appeared first on Towards Data Science .
arXiv:2606. 07403v1 Announce Type: cross Abstract: Benders decomposition is a fundamental framework for solving large-scale mixed-integer optimization problems with complicating variables that, when fixed, yield significantly easier subproblems.
arXiv:2601. 06542v2 Announce Type: replace-cross Abstract: In this paper, we investigate the Resource-Constrained Project Scheduling Problem (RCPSP) with Time-of-Use (TOU) energy tariffs and machine states, a variant of RCPSP for production scheduling, where energy price is part of the criteria and one highly energy-demanding machine can be in one of the following three states: proc, idle, or off.
arXiv:2608. 11230v1 Announce Type: new Abstract: This paper introduces the edge-based contiguous p-median (ECpM) problem to partition the roads in a network into a given number of compact and contiguous territories.
arXiv:2609.39559v1 Announce Type: new Abstract: In this work we study the problem of MAPFC, a post-optimization step for Multi-Agent Path Finding (MAPF) plans where we are given a feasible plan produ...
arXiv:2609. 17464v1 Announce Type: cross Abstract: Multi-agent systems split a task across a tree of agents and justify the split with folklore: smaller contexts, cleaner separation, parallelism.
arXiv:2607. 22550v1 Announce Type: cross Abstract: We propose a learning-augmented Benders decomposition framework to solve large-scale two-stage stochastic mixed-integer programs.
The paper introduces Pivot-and-Station Multi-Agent Path Finding (PS‑MAPF), a variant of MAPF where a subset of agents must visit interchangeable pivots before all agents occupy anonymous stations. It provides a full solvability characterization: every instance on a 2‑edge‑connected graph is solvable, and for arbitrary connected graphs a structural effective‑distance measure relative to unoccupied vertices gives a necessary and sufficient condition. The authors prove that minimizing station‑makespan or station‑flowtime is NP‑hard even with a single pivot, and present three algorithms—a complete baseline, a SAT‑based optimal solver, and Pivot‑Prioritized Planning (PPP), which solves 74‑89% of benchmark instances with significantly lower makespan and flowtime than the baseline.
Building an ALNS heuristic in Python for vehicle routing, time windows, capacity constraints, and mandatory driver breaks. The post Los Movimientos, Part II: Solving Large Pickup-and-Delivery Problems with Adaptive Large Neighborhood Search appeared first on Towards Data Science .
Multi-agent systems split a task across a tree of agents and justify the split with folklore: smaller contexts, cleaner separation, parallelism. We ask what the split does to how much of what the leav...
How local optimization in last‑mile delivery can quietly break the system The post The System Always Knows: Why Local Efficiency and System Performance Are Not the Same Problem appeared first on Towards Data Science .
arXiv:2608. 16861v1 Announce Type: cross Abstract: We initiate a polyhedral study of the graph multi-separator problem proposed by Irmai et al.