Search Results (40)

The job shop scheduling problem (JSSP) is a paradigmatic and strongly $\mathcal{NP}$-hard combinatorial optimisation problem that underpins production planning in modern manufacturing systems, and constraint programming (CP) has become one of the leading methodologies for tackling it. However, comparative studies of CP solvers for the JSSP have so far been restricted to a single benchmark family, a single instance-size range, or a single hardware setting, which limits the practical guidance they offer to both researchers and practitioners. This paper presents a controlled empirical evaluation of four state-of-the-art CP solvers—IBM ILOG CP Optimizer, Google OR-Tools (CP-SAT), Hexaly, and OptalCP—on the makespan-minimisation JSSP. The four engines are run with default parameters and a uniform 600 s wall-clock time budget on 332 instances drawn from nine canonical benchmark families (Fisher–Thompson, Lawrence, Adams–Balas–Zawack, Applegate–Cook, Yamada–Nakano, Storer–Wu–Vaccari, Taillard, Demirkol–Mehta–Uzsoy, and Da Col–Teppan), spanning sizes from $6\times 6$ to $1000\times 1000$ operations. OptalCP emerges as the most robust engine overall, certifying optimality on 191 of the 332 instances ($57.5\%$) with the smallest average optimality gap ($3.55\%$), followed by CP Optimizer (166 optima), OR-Tools (144), and Hexaly (116), while Hexaly dominates on industrial-scale problems and produces the bulk of the 22 new best-known upper bounds and one new best-known lower bound reported here. A Friedman test followed by Nemenyi post hoc comparisons confirms that OptalCP attains significantly smaller optimality gaps than the three other engines ($p<0.001$). Solver competitiveness depends sharply on instance size and the $n/m$ ratio, with square instances confirmed as the hardest case. In practical terms, these findings support an instance-aware approach to CP solver selection: OptalCP is the default choice for small to large instances of moderate aspect ratio, whereas Hexaly is preferable for industrial-scale problems with tens of thousands of operations or extreme $n/m$ ratios, where it is the only engine that reliably returns high-quality feasible schedules within the time budget. Full article

This article discusses a novel aircraft coordination algorithm for automated vertiport operation. New applications of Innovative Air Mobility (IAM) including inspection, logistics and security UAVs, Urban Air Mobility (UAM) or Regional Air Mobility (RAM) present a coordination challenge, especially near vertiports, as large numbers of vehicles with different characteristics share the airspace, and so avoiding collisions, optimizing resource usage and operating with low human intervention is important.In this paper, this problem is addressed by proposing a new formulation of the aircraft coordination problem that makes use of a discretized airspace to detect potential conflicts and collisions between cooperative and non-cooperative aircraft in the surroundings of a vertiport. The proposed algorithm not only considers the cells traversed by the aircraft, but also the set of adjacent cells, making the algorithm more conservative and robust than other algorithms found in the literature, and achieving a 100% conflict-detection rate. A mathematical model of aircraft dynamics is employed to turn high-level flight plans into detailed aircraft trajectories, using those trajectories to detect potential collisions. The deconfliction problem is formulated as a mixed-integer optimization program that computes orders of pass for every conflict while minimizing the divergence between requested time of arrival (RTA) and estimated time of arrival (ETA). This problem is implemented in OR-Tools to be solved by means of the CP-SAT solver. The validity of the solution is tested by extensive simulation, showing tactical coordination of up to 25 aircraft landing on a vertiport. Full article

Optimization Modulo Theory (OMT) is an important extension of Satisfiability Modulo Theory (SMT), aiming to find models that satisfy constraints while optimizing objective functions. OMT naturally arises in program analysis and formal methods, making OMT solving an important and challenging task. OptiMathSAT is currently the state-of-the-art OMT solver supporting floating-point theories. It incrementally calls an SMT solver to prune the search space step by step until the optimal objective value is found. However, this frequent invocation of the SMT solver is highly inefficient. Therefore, this paper proposes a novel hybrid method consisting of two stages: coarse search and precise search. The coarse search stage quickly finds an approximate optimal model using an optimization search algorithm. The precise search stage then performs an SMT-based binary search starting from the approximate model to find the true optimal model (the OMT solution). Evidently, this hybrid approach reduces computational cost by rapidly shrinking the search space, thereby improving overall solving performance. We evaluated our method on benchmarks derived from SMT-LIB2 and real-world programs. Experimental results show that our method outperforms the current state-of-the-art in both effectiveness and efficiency. Full article

We applied the Google OR-Tools Constraint Programming with Satisfiability (CP-SAT) solver to the nurse scheduling problem (NSP) to efficiently generate feasible and high-quality schedules under complex real-world constraints. The proposed model integrates hard and soft constraints, including workload balance, fairness, and staffing sufficiency, within a unified optimization framework. A genetic algorithm (GA) is implemented as a baseline for comparison. Experimental results show that GA does not consistently produce feasible solutions, whereas CP-SAT achieves feasible schedules satisfying all constraints and is approximately 224.6 times faster than GA on the tested instance. This demonstrates CP-SAT’s superior efficiency, robustness, and applicability for solving NSP. Full article

The Nash equilibrium is a central concept in game theory, widely used across economics, social sciences, computer science, and artificial intelligence. However, computing Nash equilibria, especially in multi-player games, is a complex and computationally challenging task. Among the various types of Nash equilibria, the unique pure-strategy Nash equilibrium payoffs possess particularly desirable properties that make them suitable for deeper analysis and application. In this paper, we propose a first-order logical framework for three-player finite games, inspired by the notion of Pareto optimality, to identify a class of games with unique pure-strategy Nash equilibrium payoffs. By utilizing a SAT solver and the finite verifiability of ternary clauses, we automatically discover several families of three-player games that exhibit unique pure-strategy Nash equilibrium payoffs. This approach provides new insights into the computational aspects of game theory and offers an automated method for discovering novel game-theoretic structures. Full article

This paper is a theoretical contribution that introduces a new reasoning framework for SAT solving based on resolvable networks (RNs). RNs provide a graph-based representation of propositional satisfiability in which clauses are interpreted as directed reaches between disjoint subsets of Boolean variables (nodes). Building on this framework, we introduce a novel RN-based SAT solver, called RN-Solver, which replaces local assignment-driven branching by global reasoning over token distributions. Token distributions, interpreted as truth assignments, are generated by monotone CNF–DNF dualization applied to white (all-positive) clauses. New white clauses are derived via resolution along private-pivot chains, and the solver’s progression is governed by a taxonomy of token distributions (black-blocked, terminal, active, resolved, and non-resolved). The main results establish the soundness and completeness of the RN-Solver. Experimentally, the solver performs very well on pigeonhole formulas, where the separation between white and black clauses enables effective global reasoning. In contrast, its current implementation performs poorly on random 3-SAT instances, highlighting both practical limitations and significant opportunities for optimization and theoretical refinement. The presented RN-Solver implementation is a proof-of-concept which validates the underlying theory rather than a state-of-the-art competitive solver. One promising direction is the generalization of strongly connected components from directed graphs to resolvable networks. Finally, the token-based perspective naturally suggests a connection to token-superposition Petri net models. Full article

The Satisfiability Problem (SAT), a fundamental NP-complete problem, is widely applied in integrated circuit verification, artificial intelligence planning, and other fields, where the growing scale and complexity of practical problems demand higher solving efficiency. Due to redundant search paths, serialized reasoning steps, and inefficient pure literal detection, traditional serial SAT solvers require efficient parallelization of the pure literal rule. This paper adopts a parallel solving algorithm for the pure literal rule based on matrix representation. The algorithm can solve the shortcomings of poor universality, insufficient parallel collaborative mechanisms, and clause reduction. We first introduce a Clause-Numerical Incidence Matrix (CNIM) representation to provide a unified mathematical model for parallel operations. Second, we design a Column Vectors Pure Literal Parallel Topological Detection (CVPLPTD) algorithm that achieves pure literal detection with $O(mn/p)$ time complexity (p being the number of parallel threads) within the coefficient range $[1.0\times mn/p, 1.2\times mn/p]$. Finally, we adopt a dynamic matrix reduction strategy that compresses the matrix scale through row and column deletion after each pure literal assignment to reduce computational load. These innovations integrate matrix algebra and parallel computing, effectively breaking through the efficiency limitations of solving large-scale SAT problems while ensuring good universality across different computing platforms. Full article

With the rapid adoption of electric vehicles (EVs), optimizing charging infrastructure and route planning has become increasingly crucial. Traditional methods such as Linear Programming (LP) have been widely used to address these challenges. However, these approaches often struggle with scalability, computational efficiency, and the ability to handle complex logical constraints involving multiple decision factors like distance, time, cost, battery levels, and charging station compatibility. To overcome these limitations, this study proposes a novel Boolean Satisfiability (SAT)-based optimization framework for intelligent EV charging station recommendation. Unlike conventional approaches, the proposed model encodes real-world constraints into Conjunctive Normal Form (CNF) using De Morgan’s Theorem, allowing efficient processing through the CP-SAT solver. This logical transformation enables the systematic representation of intricate relationships between variables, ensuring better compatibility and computational efficiency. The SAT-based framework was applied to intercity EV routing scenarios, where it demonstrated substantial improvements over traditional methods in terms of route optimization, cost reduction, and charging station relevance. Notably, the SAT model was effective in avoiding redundant charging recommendations, selecting only those stations necessary to complete the route while satisfying all energy and infrastructure constraints. Moreover, the solver showed rapid convergence and greater adaptability under varied operational scenarios. In conclusion, this study highlights the effectiveness of SAT-based modeling—particularly its CNF formulation and logical expressiveness—in delivering a scalable, intelligent, and efficient solution for real-time EV route planning and charging station optimization. Full article

This paper introduces a lightweight cryptographic hash algorithm, LWH-128, developed using a sponge-based construction and specifically adapted for operation under constrained computational and energy conditions typical of embedded systems and Internet of Things devices. The algorithm employs a two-layer processing structure based on simple logical operations (XOR, cyclic shifts, and S-boxes) and incorporates a preliminary diffusion transformation function G, along with the Davis–Meyer compression scheme, to enhance irreversibility and improve cryptographic robustness. A comparative analysis of hardware implementation demonstrates that LWH-128 exhibits balanced characteristics in terms of circuit complexity, memory usage, and processing speed, making it competitive with existing lightweight hash algorithms. As part of the cryptanalytic evaluation, a Boolean SATisfiability (SAT) Problem-based model of the compression function is constructed in the form of a conjunctive normal form of Boolean variables. Experimental results using the Parkissat SAT solver show an exponential increase in computational time as the number of unknown input bits increased. These findings support the conclusion that the LWH-128 algorithm exhibits strong resistance to preimage attacks based on SAT-solving techniques. Full article

Differential cryptanalysis is one of the fundamental cryptanalysis techniques to evaluate the security of the block cipher. In many cases, resistance to differential cryptanalysis is proven through the upper bound of the differential characteristic probability, not the differential probability. Since the attacker uses a differential rather than a differential characteristic, resistance based on a differential characteristic tends to overestimate the security level of the block cipher. Such an overestimation is notably observed in lightweight block ciphers SKINNY, Midori, and CRAFT. In this paper, we examine the gap between the differential characteristics and the differential probability of lightweight block ciphers. We present practical methods for computing differential probability using a multistage graph. Using these methods, we count the exact number of maximum differential characteristics with fixed plaintext/ciphertext difference and activity pattern. By the exact number of maximum differential characteristics, we can calculate the probability that is closer to the real differential probability. In addition, by modifying the method, we compute a more accurate differential probability by considering the characteristics of the lower probability. We find differential distinguishers of 9-round Midori64 with probability $2^{-61.58}$, 9-round SKINNY64 with $2^{-58.67}$ and 14-round CRAFT with $2^{-60.32}$. Furthermore, we find a related-tweakey differential distinguisher of 11-round SKINNY64-64 with $2^{-55.93}$ and a related-tweak differential distinguisher of 17-round CRAFT with probability $2^{-63.37}$. Finally, we explain why these gaps are notable in Midori64, SKINNY64 and CRAFT by relating the S-box differential distribution table. Full article

This study introduces a novel two-stage model for assessing and enhancing business excellence based on the EFQM framework. The Fuzzy Analytic Hierarchy Process (FAHP) is used in the first stage to calculate the weight vectors of criteria and sub-criteria, incorporating uncertainty through triangular fuzzy numbers (TFNs). In the second stage, the OR-Tools CP-SAT solver is used to solve the selection and improvement of sub-criteria as a multidimensional knapsack problem with mixed min/max constraints. In this way, a new and enhanced model for evaluating business excellence is presented—one that takes into account the company’s current capabilities and circumstances while also providing management with a starting point for enhancing business performance. The model is validated using data from a manufacturing company in central Serbia. The findings suggest that improvement efforts should not be symmetrically distributed across all EFQM criteria and sub-criteria. Instead, an asymmetric approach provides efficient resource allocation while maximizing business excellence improvements. This study emphasizes the balance or symmetry between subjective decision-makers’ assessments and mathematically based optimization, demonstrating the practical applicability of the proposed method in strategic decision-making under resource constraints. Full article

We propose SAT-GATv2, a graph neural network (GNN)-based model designed to solve the Boolean satisfiability problem (SAT) through graph-based deep learning techniques. SAT-GATv2 transforms SAT formulas into graph structures, leveraging message-passing neural networks (MPNNs) to propagate local information and dynamic attention mechanisms (GATv2) to accurately capture inter-node dependencies and enhance node feature representations. Unlike traditional heuristic-driven SAT solvers, SAT-GATv2 adopts a data-driven approach, learning structural patterns directly from graph representations and providing a complementary framework to existing methods. Experimental results demonstrate that SAT-GATv2 achieves an accuracy improvement of 1.75–5.51% over NeuroSAT on challenging random 3-SAT(n) instances, highlighting its effectiveness in handling difficult problem distributions, and outperforms other GNN-based models on SR(n) datasets, showcasing its scalability and adaptability. Ablation studies validate the critical roles of MPNNs and GATv2 in improving prediction accuracy and scalability. While SAT-GATv2 does not yet surpass CDCL-based solvers in overall performance, it addresses their limitations in scalability and adaptability to complex instances, offering an efficient graph-based alternative for tackling larger and more complex SAT problems. This study establishes a foundation for integrating deep learning with combinatorial optimization, emphasizing its potential for applications in artificial intelligence and operations research. Full article

Solving the university timetabling problem is crucial as it ensures efficient use of resources, minimises scheduling conflicts, and enhances overall productivity. This paper presents a comprehensive review of university timetabling problems using integer programming algorithms. This study explores various integer programming techniques and their effectiveness in optimising complex scheduling requirements in higher education institutions. We analysed 95 integer programming-based models developed for solving university timetabling problems, covering relevant research from 1990 to 2023. The goal is to provide insights into the evolution of these algorithms and their impact on improving university scheduling. We identify that the implementation rate of models using integer programming is 98%, which is much higher than 34% implementation rates using meta-heuristics algorithms from the existing review. The integer programming models are analysed by the problem types, solutions, tools, and datasets. For three types of timetabling problems including course timetabling, class timetabling, and exam timetabling, we dive deeper into the commercial solvers CPLEX (47), Gurobi (11), Lingo (5), Open Solver (4), C++ GLPK (4), AIMMS (2), GAMS (2), XPRESS (2), CELCAT (1), AMPL (1), and Google OR-Tools CP-SAT (1) and identify that CPLEX is the most frequently used integer programming solver. We explored the uses of machine learning algorithms and the hybrid solutions of combining the integer programming and machine learning algorithms in higher education timetabling solutions. We also identify areas for future work, which includes an emphasis on using integer programming algorithms in other industrial areas, and using machine learning models for university timetabling to allow data-driven solutions. Full article

Millimeter-wave (mm-Wave) phased array systems need to meet the transmitter (Tx) equivalent isotropic radiated power (EIRP) requirement, and that depends mainly on the design of two key sub-components: (1) the antenna array and (2) the Tx power amplifier (PA) in the front-end-modules (FEMs). Simulations using an electromagnetic (EM) solver carried out in Cadence AWR with AXIEM suggest that for two uniform square patch antenna arrays at 24 GHz, the 4 element array has ~6 dB lower antenna gain and twice the half power beam width (HPBW) compared to the 16 element array. We also present measurements and post-layout parasitic-extracted (PEX) EM simulation data taken on two broadband mm-Wave PAs designed in our lab that cover the key portions of the fifth-generation (5G) FR2-band (i.e., 24.25–52.6 GHz) that lies between the super-high-frequency (SHF, i.e., 3–30 GHz) band and the extremely-high-frequency (EHF, i.e., 30–300 GHz) band: one designed in a 22 nm fully depleted silicon on insulator (FD-SOI) CMOS process, and the other in an advanced 40 nm Gallium Nitride (GaN) high-electron-mobility transistor (HEMT) process. The FD-SOI PA achieves saturated output power (P_OUT,SAT) of ~14 dBm and peak power-added efficiency (PAE) of ~20% with ~14 dB of gain and 3 dB bandwidth (BW) from ~19.1 to 46.5 GHz in measurement, while the GaN PA achieves measured P_OUT,SAT of ~24 dBm and peak PAE of ~20% with ~20 dB gain and 3 dB BW from ~19.9 to 35.2 GHz. The PAs’ measured data are in good agreement with the PEX EM simulated data, and 3rd Watt-level GaN PA design data are also presented, but with simulated PEX EM data only. Assuming each antenna element will be driven by one FEM and each phased array targets the same 65 dBm EIRP, millimeter wave (mm-Wave) antenna arrays using the Watt-level GaN PAs and FEMs are expected to achieve roughly 2× wider HPBW with 4× reduction in the array size compared with the arrays using Si FEMs, which shall alleviate the thorny mm-Wave line-of-sight (LOS)-blocking problems significantly. Full article

The possible existence of a Moore graph of diameter 2 and degree 57 has been an open question for more than six decades. In this paper, certain subgraphs of this graph, referred to as t-subgraphs, are considered. Exploiting symmetry by assuming a cyclic group of permutations representing edges joining leaf nodes of branches of a tree, a tractable constraint model for t-subgraphs is created. This can be solved using the Google OR Tools CP-SAT solver. Larger potential t-subgraphs than those currently known are constructed. This further extends a construction of certain sets of mutually orthogonal Latin rectangles. The implications for non-existence proofs of the Moore graph are considered. Full article