A genetic algorithm for student academic resource allocation

Existing neural combinatorial optimization solvers frame solution search as imitation of optimal decisions, inherently limiting their utility to single-objective minimization and static constraints. We propose GOAL, a conditioned diffusion solver over relational graph representations that enables controllable decision generations by conditioning on human-specified objectives. We introduce a heterogeneous graph encoding in which distinct edge types, corresponding to different classes of constraints, define the message passing structure of the graph neural network, which allows information to propagate selectively according to the ontology of each constraint. GOAL is instantiated and evaluated on three canonical scheduling benchmarks of various constraint complexity: the Flow Shop Problem (FSP), the Job Shop Scheduling Problem (JSP), and the Flexible Job Shop Scheduling Problem (FJSP). Generalization is demonstrated across structurally distinct constraint regimes and problem types without architectural modification. On all three benchmarks, GOAL achieves 100% solution feasibility and near-zero MAPE (below 0.20%) on multiple objectives for problem sizes up to 20 jobs and 60 operations, outperforming NSGA-II and MOEA/D in both solution quality and inference speed by up to 25x.

Low autocorrelation binary sequences problem (LABS) is a hard combinatorial optimization challenge with important applications in communications, signal processing, and satellite navigation. This paper proposes a hybrid search framework that combines Thompson sampling with parallel self-avoiding walks to adaptively allocate computational effort across restriction classes of the LABS search space. By modeling partitions as arms in a multi-armed bandit setting, the proposed method dynamically shifts search resources toward partitions that empirically produce higher merit factors while maintaining exploration of less-sampled regions. The approach is further accelerated through GPU-parallel execution, shared posterior updates, efficient neighborhood evaluation, and a Bloom filter for cycle prevention. In addition, we use a two-stage optimization strategy that first searches constrained partitioned skew-symmetric spaces and then refines the best candidates in the unrestricted space. Experiments on long binary sequences show that the proposed method improves the previously best-known results for 35 sequence lengths in the range $450 \le L \le 527$ and for $L=573$. In particular, we report a new longest sequence with merit factor exceeding $8.0$, obtained for $L=451$. The results also show that Thompson sampling effectively prioritizes partitions with better observed performance, confirming the value of online, data-driven resource allocation in LABS optimization. Overall, the proposed framework provides a scalable and effective strategy for high-performance merit factor maximization.

Problems defined on binary decision spaces have been intensively studied in the theory of multi-objective evolutionary algorithms (MOEAs). In contrast, no mathematical runtime analyses exist so far for MOEAs dealing with decision variables that take a finite number $r > 2$ of values, despite the prevalence of such problems in practice. In this work, we begin to fill this research gap. We analyze how the classic SEMO algorithm with unit-strength local mutation computes the Pareto front of an $r$-valued counterpart of the classic \oneminmax benchmark. For the expected number of function evaluations until the Pareto front is covered by the population of this MOEA, we prove an upper bound of $O(n^2 r^2 \log n)$ and a near-tight lower bound of $Ω(n^2 r (r + \log n))$. We can close the small remaining gap between these two bounds by considering a variant of the algorithm that accepts only strictly better solutions; for this variant, we show an upper bound of $O(n^2 r (r + \log n))$, matching our lower bound (which also holds for this variant). Our results suggest that classic MOEAs encounter no significant additional difficulties when dealing with multi-valued decision variables. However, significantly more advanced tools may be required to obtain tight bounds for algorithms with more complex population dynamics.