arXiv subjects

Khanh Van To

Publications and source records attributed to Khanh Van To.

8 recordsLinked to original sources

arXiv2026

Continuity-First Lexicographic Optimization for Home-Care Resource Allocation

Home-care allocation must balance continuity of care, caregiver overtime, and caregiver-service compatibility. The published formulation of the Home-Care Optimal Resource Allocation Problem (HCORAP) uses a weighted policy (Weighted) to combine these outcomes, allowing compatibility gains to offset poorer continuity or additional overtime. We introduce LEX-COS, a lexicographic objective for HCORAP that first minimizes continuity violations, then overtime, and finally maximizes compatibility. We give an exact MaxSAT implementation and construct HCORAP-LC, a reproducible 48-instance synthetic evaluation suite with limited caregiver capacity. Compared with Weighted, LEX-COS reduces both continuity violations and overtime in 42 of 48 instances, without increasing either measure in any instance, while yielding lower compatibility. In 36 instances, LEX-COS achieves better continuity and lower overtime than every Weighted-optimal allocation. On the separate 48-instance Original benchmark, Gurobi and CPLEX, two leading commercial MIP solvers, resolve every instance under both policies and are substantially faster than EvalMaxSAT. EvalMaxSAT also resolves the full benchmark under LEX-COS. Within EvalMaxSAT, replacing sorting networks with Totalizer improves runtime under Weighted, with no clear gain under LEX-COS. These results characterize the effects of giving continuity and overtime explicit priority in home-care allocation.

cs.LO↗

arXiv2026

Cycle time minimization for the simple assembly line balancing problem under peak power constraints

Peak power limits restrict concurrent tasks and may increase assembly-line cycle time. To the best of our knowledge, this study is the first to minimize cycle time for the simple assembly line balancing problem type 2 (SALBP-2) with a fixed number of workstations and a fixed limit on total instantaneous power. An exact satisfiability (SAT) method finds feasible schedules, searches systematically for shorter cycles, and proves optimality when possible. Two reproducible formulas define looser and tighter power limits for 72 cases based on the standard SALBP library, with Gurobi and CPLEX providing commercial MIP and CP comparisons. Relative to standard SALBP-2 optima, the two limits increase the best-known cycle time by 16.49% and 61.02% on average. The best-performing SAT configurations find a feasible solution for every case, solve more cases to optimality than each commercial solver, and when both prove optimality, are almost always faster under the reported settings.

cs.LO↗

arXiv2026

Compact SAT and MaxSAT Encodings for Business-to-Business Meeting Scheduling with Idle-Time Balancing

Business-to-business meeting scheduling assigns requested pairwise meetings to time slots and locations under availability, capacity, conflict, and precedence constraints. The published Boolean formulation retains meeting-slot assignments that propagation can eliminate and encodes precedence relations with pairwise clauses. We present compact SAT and MaxSAT encodings based on solution-preserving domain filtering, variables shared at selected precedence boundaries, and an objective that minimizes the range of participants' internal idle-slot totals. Experiments on 126 official and 100 higher-density derived instances examine domain filtering, precedence representation, transitive relations, and optimization method. Compared with an adapted published MaxSAT formulation using the same objective, the proposed encoding reduces the median clause count by 40.3% and median peak memory usage by 55.9%. Domain filtering alone reduces assignment variables by 24.1% and clauses by 16.2%. Sharing variables at selected precedence boundaries reduces clauses by 0.5%-1.0% on official precedence instances and by up to 5.5% at the highest derived density. The idle-time measure distinguishes one-slot interruptions from longer waits, while aggregate idle time provides a complementary measure. Compared with Gurobi, a leading commercial solver, all three SAT and MaxSAT methods solve every official instance with lower median total times.

cs.LO↗

arXiv2026

Proving Optimality for the Bandwidth Multicoloring Problem via SAT

The Bandwidth Multicoloring Problem (BMCP) is an NP-hard extension of the Bandwidth Coloring Problem (BCP) with important applications in telecommunications, resource allocation, and scheduling. While state-of-the-art metaheuristics can efficiently produce high-quality solutions, they cannot certify global optimality. Existing exact approaches based on Constraint Programming (CP) and Integer Programming (IP) provide such guarantees but typically require extensive computation and still lag behind metaheuristics in solution quality, leaving many benchmark instances without optimality certificates. In this paper, we present the first SAT-based exact framework for the BMCP. Our main contribution is an efficient SAT encoding that compactly models both intra-vertex and inter-vertex color distance constraints. Combined with tight color domain reduction and an incremental SAT-solving strategy, the proposed formulation significantly prunes the search space and enables efficient exact optimization. Experimental results on the GEOM and MS-CAP benchmark suites demonstrate substantial improvements over previous exact approaches. On the challenging GEOM benchmark, the proposed framework proves optimality for more instances within only one hour of computation than the previous CP/IP approach, which required a 48-hour time limit, while also verifying the optimality of several previously reported best-known solutions. These results demonstrate that SAT-based reasoning provides an effective exact optimization framework for the BMCP and substantially expands the range of benchmark instances whose optimality can be certified.

cs.LO↗

arXiv2026

An Efficient MaxSAT-DDD Approach for Train Rescheduling via Precedence Propagation and Hybrid AMO Encodings

Train rescheduling repairs disturbed timetables while enforcing train-path precedence, resource capacity, and delay objectives. Dynamic Discretization Discovery (DDD) avoids full time discretization by refining only time points needed to certify feasibility and optimality. We strengthen a recent MaxSAT-DDD model through two encoding changes. First, resource conflicts are encoded as time-dependent at-most-one cliques, using pairwise clauses for small cliques and a sequential counter for large cliques. Second, earliest feasible times are propagated along train paths before the first DDD iteration. We evaluate four MaxSAT variants, two SAT optimization backends, Gurobi/CPLEX MILP models, and CPLEX CP on 72 instances and three delay objectives. MaxSAT-DDD solves all stepwise instances in about 23 ms on average. MaxSAT-Default reduces rounded-cost runtime from 794 to 479 ms, and the ablation study reports up to 79.6\% runtime reduction on the common-solved subset of hard continuous track instances.

cs.LO↗

arXiv2026

Solving the Two-dimensional single stock size Cutting Stock Problem with SAT and MaxSAT

Cutting rectangular items from stock sheets to satisfy demands while minimizing waste is a central manufacturing task. The Two-Dimensional Single Stock Size Cutting Stock Problem (2D-CSSP) generalizes bin packing by requiring multiple copies of each item type, which causes a strong combinatorial blow-up. We present a SAT-based framework where item types are expanded by demand, each copy has a sheet-assignment variable and non-overlap constraints are activated only for copies assigned to the same sheet. We also introduce an infeasible-orientation elimination rule that fixes rotation variables when only one orientation can fit the sheet. For minimizing the number of sheets, we compare three approaches: non-incremental SAT with binary search, incremental SAT with clause reuse across iterations and weighted partial MaxSAT. On the Cui--Zhao benchmark suite, our best SAT configurations certify two to three times more instances as provably optimal and achieve lower optimality gaps than OR-Tools, CPLEX and Gurobi. The relative ranking among SAT approaches depends on rotation: incremental SAT is strongest without rotation, while non-incremental SAT is more effective when rotation increases formula size.

cs.AI↗

arXiv2026

SAT Encodings for Bandwidth Coloring: A Systematic Design Study

The Bandwidth Coloring Problem (BCP) generalizes graph coloring by enforcing minimum separation constraints between adjacent vertices and arises in frequency assignment applications. While SAT-based approaches have shown promise for exact BCP solving, the encoding design space remains largely unexplored. This paper presents a systematic study of SAT encodings for the BCP, proposing a unified framework with six encoding methods across three categories: one-variable, two-variable, and block encodings. We evaluate the impact of key features including incremental solving and symmetry breaking. While symmetry breaking has been studied for graph coloring, it has not been systematically evaluated for SAT-based BCP solvers. Our analysis reveals significant interaction effects between encoding choices and solver configurations. The proposed framework achieves state-of-the-art performance on GEOM and MS-CAP benchmarks. Block encodings solve GEOM120b, the hardest instance, to proven optimality in approximately 1000 seconds, whereas previous methods could not solve it within a one-hour time limit.

cs.LO↗

arXiv2025

Compact SAT Encoding for Power Peak Minimization

The Simple Assembly Line Balancing Problem with Power Peak Minimization (SALBP-3PM) minimizes maximum instantaneous power usage while assigning $n$ tasks to $m$ workstations and determining execution schedules within given cycle time constraints. This NP-hard problem couples workstation assignment, temporal sequencing, and power aggregation, presenting significant computational challenges for exact optimization methods. Existing Boolean Satisfiability (SAT) and Maximum Satisfiability (MaxSAT) approaches suffer from baseline encodings generating $O(m^2)$ clauses per precedence edge. We introduce a Compact SAT Encoding (CSE) achieving $O(m)$ clauses per transitive precedence edge using sequential counter techniques. We instantiate four optimization variants: Clause-Based iterative SAT, Pseudo-Boolean (PB) Constraint iterative SAT, MaxSAT, and Incremental SAT. Comprehensive experimental evaluation on benchmark instances demonstrates consistent performance improvements over state-of-the-art approaches, enabling exact optimization on previously intractable industrial-scale instances. The encoding principles generalize to other assembly line balancing variants and broader scheduling problems with precedence constraints.

cs.LO↗