While diffusion models have shown promise for combinatorial optimization (CO), their inference-time scaling cost-efficiency remains relatively underexplored. Existing methods improve solution quality by increasing denoising steps, but the performance often becomes saturated quickly. This paper proposes GenSCO to systematically scale diffusion solvers by an orthogonal dimension of inference-time computation beyond denoising step expansion, i.e., search-driven generation. GenSCO takes generation as a search operator rather than a complete solving process, where each operator cycle combines solution disruption (via local search operators) and diffusion sampling, enabling iterative exploration of the learned solution space. Rather than over-refining current solutions, this paradigm encourages the model to leave local optima and explore a broader area of the solution space, ensuring a more consistent scaling effect.

Recent advances in neural neighborhood search methods have shown potential in tackling Vehicle Routing Problems (VRPs). However, most existing approaches rely on simplistic state representations and fuse heterogeneous information via naive concatenation, limiting their ability to capture rich structural and semantic context. To address these limitations, we propose GAMA, a neural neighborhood search method with Graph-aware Multi-modal Attention model in VRP. GAMA encodes the problem instance and its evolving solution as distinct modalities using graph neural networks, and models their intra- and inter-modal interactions through stacked self- and cross-attention layers. A gated fusion mechanism further integrates the multi-modal representations into a structured state, enabling the policy to make informed and generalizable operator selection decisions. Extensive experiments conducted across various synthetic and benchmark instances demonstrate that the proposed algorithm GAMA significantly outperforms the recent neural baselines. Further ablation studies confirm that both the multi-modal attention mechanism and the gated fusion design play a key role in achieving the observed performance gains.

Fitness landscapes in test-based program synthesis are known to be extremely rugged, with even minimal modifications of programs often leading to fundamental changes in their behavior and, consequently, fitness values. Relying on fitness as the only guidance in iterative search algorithms like genetic programming is thus unnecessarily limiting, especially when combined with purely syntactic search operators that are agnostic about their impact on program behavior. In this study, we propose a semantics-aware search operator that steers the search towards candidate programs that are valuable not only actually (high fitness) but also only potentially, i.e. are likely to be turned into high-quality solutions even if their current fitness is low. The key component of the method is a graph neural network that learns to model the interactions between program instructions and processed data, and produces a saliency map over graph nodes that represents possible search decisions. When applied to a suite of symbolic regression benchmarks, the proposed method outperforms conventional tree-based genetic programming and the ablated variant of the method.

In evolutionary computation, it is commonly assumed that a search algorithm acquires knowledge about a problem instance by sampling solutions from the search space and evaluating them with a fitness function. This is necessarily inefficient because fitness reveals very little about solutions -- yet they contain more information that can be potentially exploited. To address this observation in genetic programming, we propose EvoNUDGE, which uses a graph neural network to elicit additional knowledge from symbolic regression problems. The network is queried on the problem before an evolutionary run to produce a library of subprograms, which is subsequently used to seed the initial population and bias the actions of search operators. In an extensive experiment on a large number of problem instances, EvoNUDGE is shown to significantly outperform multiple baselines, including the conventional tree-based genetic programming and the purely neural variant of the method.

For solving combinatorial optimisation problems with metaheuristics, different search operators are applied for sampling new solutions in the neighbourhood of a given solution. It is important to understand the relationship between operators for various purposes, e.g., adaptively deciding when to use which operator to find optimal solutions efficiently. However, it is difficult to theoretically analyse this relationship, especially in the complex solution space of combinatorial optimisation problems. In this paper, we propose to empirically analyse the relationship between operators in terms of the correlation between their local optima and develop a measure for quantifying their relationship. The comprehensive analyses on a wide range of capacitated vehicle routing problem benchmark instances show that there is a consistent pattern in the correlation between commonly used operators. Based on this newly proposed local optima correlation metric, we propose a novel approach for adaptively selecting among the operators during the search process. The core intention is to improve search efficiency by preventing wasting computational resources on exploring neighbourhoods where the local optima have already been reached. Experiments on randomly generated instances and commonly used benchmark datasets are conducted. Results show that the proposed approach outperforms commonly used adaptive operator selection methods.

Interest in this research area is also driven by the importance of ensuring an efficient and satisfying client service policy after a product delivery, which substantially contributes to the maintain of the market share [15]. The workforce scheduling problem focuses on the elaboration of models and solution methods for planning in-field personnel activities, including their mobilization between different locations. Moreover, the problem consists in the elaboration of workload allocation and routing of technician crews, as well as the scheduling of their operations at the level of task locations, which include industrial facilities, patient homes, telecommunication infrastructure, etc. In addition, many objectives and challenges may be considered, such as increasing productivity, reducing transportation costs, increasing the number of fulfilled tasks, reducing outsourcing costs, reducing overtime, balancing technician workloads, etc. Furthermore, to have a reliable and satisfactory organization of the workforce in the field, several requirements and constraints have to be met: in addition to the vehicle routing problem classical constraints (capacity and time windows) and work regulations (breaks and workload). Other aspects could be taken into consideration such as skill types and competency levels required by each task, precedence constraints between several tasks for the same customer, priorities, limited crews of technicians, and sometimes the use of specific tools and spare parts. In this paper, we address a variant of the technician routing and scheduling problem (TRSP) presented by Pillac et al.[24]. Given a crew of technicians and a set of tasks to fulfill at their respective locations, the goal is to assign subsets of tasks to individual technicians and construct the routes for each technician in such a way that the total duration of the routes is minimized. Several types of constraints must be respected by each route.

A lot of real-world applications could be modeled as the Mixed-Integer Non-Linear Programming (MINLP) problems, and some prominent examples include portfolio optimization, resource allocation, image classification, as well as path planning. Actually, most of the models for these applications are non-convex and always involve some conflicting objectives. Hence, the Multi-Objective Evolutionary Algorithm (MOEA), which does not require the gradient information and is efficient at dealing with the multi-objective optimization problems, is adopted frequently for these problems. In this work, we discuss the coding scheme for MOEA in MINLP, and the major discussion focuses on the constrained portfolio optimization problem, which is a classic financial problem and could be naturally modeled as MINLP. As a result, the challenge, faced by a direct coding scheme for MOEA in MINLP, is pointed out that the searching in multiple search spaces is very complicated. Thus, a Compressed Coding Scheme (CCS), which converts an MINLP problem into a continuous problem, is proposed to address this challenge. The analyses and experiments on 20 portfolio benchmark instances, of which the number of available assets ranging from 31 to 2235, consistently indicate that CCS is not only efficient but also robust for dealing with the constrained multi-objective portfolio optimization.

In this article, we work towards the goal of developing agents that can learn to act in complex worlds. We develop a probabilistic, relational planning rule representation that compactly models noisy, nondeterministic action effects, and show how such rules can be effectively learned. Through experiments in simple planning domains and a 3D simulated blocks world with realistic physics, we demonstrate that this learning algorithm allows agents to effectively model world dynamics.

Automating the design of heuristic search methods is an active research field within computer science, artificial intelligence and operational research. In order to make these methods more generally applicable, it is important to eliminate or reduce the role of the human expert in the process of designing an effective methodology to solve a given computational search problem. Researchers developing such methodologies are often constrained on the number of problem domains on which to test their adaptive, self-configuring algorithms; which can be explained by the inherent difficulty of implementing their corresponding domain specific software components. This paper presents HyFlex, a software framework for the development of cross-domain search methodologies. The framework features a common software interface for dealing with different combinatorial optimisation problems, and provides the algorithm components that are problem specific. In this way, the algorithm designer does not require a detailed knowledge the problem domains, and thus can concentrate his/her efforts in designing adaptive general-purpose heuristic search algorithms. Four hard combinatorial problems are fully implemented (maximum satisfiability, one dimensional bin packing, permutation flow shop and personnel scheduling), each containing a varied set of instance data (including real-world industrial applications) and an extensive set of problem specific heuristics and search operators. The framework forms the basis for the first International Cross-domain Heuristic Search Challenge (CHeSC), and it is currently in use by the international research community. In summary, HyFlex represents a valuable new benchmark of heuristic search generality, with which adaptive cross-domain algorithms are being easily developed, and reliably compared.

In this article, we discuss the problem of transferring search heuristics from one planner to another. More specifically, we demonstrate how to transfer the domain-dependent heuristics acquired by one planner into a second planner. Our motivation is to improve the efficiency and the efficacy of the second planner by allowing it to use the transferred heuristics to capture domain regularities that it would not otherwise recognize. Our experimental results show that the transferred knowledge does improve the second planner's performance on novel tasks over a set of seven benchmark planning domains.