The minimisation of cost functions is crucial in various optimisation fields. However, identifying their global minimum remains challenging owing to the huge computational cost incurred. This work analytically expresses the computational cost to identify an approximate global minimum for a class of cost functions defined under a high-dimensional discrete state space. Then, we derive an optimal global search scheme that minimises the computational cost. Mathematical analyses demonstrate that a combination of the gradient descent algorithm and the selection and crossover algorithm--with a biased crossover weight--maximises the search efficiency. Remarkably, its computational cost is of the square root order in contrast to that of the conventional gradient descent algorithms, indicating a quadratic speedup of global search. We corroborate this proposition using numerical analyses of the travelling salesman problem. The simple computational architecture and minimal computational cost of the proposed scheme are highly desirable for biological organisms and neuromorphic hardware.

We consider a class of visual analogical reasoning problems that involve discovering the sequence of transformations by which pairs of input/output images are related, so as to analogously transform future inputs. This program synthesis task can be easily solved via symbolic search. Using a variation of the `neural analogical reasoning' approach of (Velickovic and Blundell 2021), we instead search for a sequence of elementary neural network transformations that manipulate distributed representations derived from a symbolic space, to which input images are directly encoded. We evaluate the extent to which our `neural reasoning' approach generalizes for images with unseen shapes and positions.

Optimization problems with set submodular objective functions have many real-world applications. In discrete scenarios, where the same item can be selected more than once, the domain is generalized from a 2-element set to a bounded integer lattice. In this work, we consider the problem of maximizing a monotone submodular function on the bounded integer lattice subject to a cardinality constraint. In particular, we focus on maximizing DR-submodular functions, i.e., functions defined on the integer lattice that exhibit the diminishing returns property. Given any epsilon > 0, we present a randomized algorithm with probabilistic guarantees of O(1 - 1/e - epsilon) approximation, using a framework inspired by a Stochastic Greedy algorithm developed for set submodular functions by Mirzasoleiman et al. We then show that, on synthetic DR-submodular functions, applying our proposed algorithm on the integer lattice is faster than the alternatives, including reducing a target problem to the set domain and then applying the fastest known set submodular maximization algorithm.

Class expression learning is a branch of explainable supervised machine learning of increasing importance. Most existing approaches for class expression learning in description logics are search algorithms or hard-rule-based. In particular, approaches based on refinement operators suffer from scalability issues as they rely on heuristic functions to explore a large search space for each learning problem. We propose a new family of approaches, which we dub synthesis approaches. Instances of this family compute class expressions directly from the examples provided. Consequently, they are not subject to the runtime limitations of search-based approaches nor the lack of flexibility of hard-rule-based approaches. We study three instances of this novel family of approaches that use lightweight neural network architectures to synthesize class expressions from sets of positive examples. The results of their evaluation on four benchmark datasets suggest that they can effectively synthesize high-quality class expressions with respect to the input examples in under a second on average. Moreover, a comparison with the state-of-the-art approaches CELOE and ELTL suggests that we achieve significantly better F-measures on large ontologies. For reproducibility purposes, we provide our implementation as well as pre-trained models in the public GitHub repository at https://github.com/ConceptLengthLearner/NCES

Branch-and-cut is the most widely used algorithm for solving integer programs, employed by commercial solvers like CPLEX and Gurobi. Branch-and-cut has a wide variety of tunable parameters that have a huge impact on the size of the search tree that it builds, but are challenging to tune by hand. An increasingly popular approach is to use machine learning to tune these parameters: using a training set of integer programs from the application domain at hand, the goal is to find a configuration with strong predicted performance on future, unseen integer programs from the same domain. If the training set is too small, a configuration may have good performance over the training set but poor performance on future integer programs. In this paper, we prove sample complexity guarantees for this procedure, which bound how large the training set should be to ensure that for any configuration, its average performance over the training set is close to its expected future performance. Our guarantees apply to parameters that control the most important aspects of branch-and-cut: node selection, branching constraint selection, and cutting plane selection, and are sharper and more general than those found in prior research.

My research area is heuristic search in Artificial Intelligence. I am interested in all aspects of heuristic search, including theoretical foundations, new search algorithms, the study and development of heuristics and applying all these to different domains and settings.

To solve difficult problems heuristically, requires detailed attention to computational efficiency. This paper describes how a heuristic problem solving system, HPA, attempts to find a near optimal solution to the traveling salesman problem. A critical innovation over previous search algorithms is an explicit dynamic weighting of the heuristic information. The heuristic information is weighted inversely proportional to its depth in the search tree -- in consequence it produces a narrower depth first search than traditional weightings. At the same time, dynamic weighting retains the catastrophe protection of ordinary branch and bound algorithms.

Flow Shop Scheduling (FSS) has been widely researched due to its application in many types of fields, while the human participant brings great challenges to this problem. Manpower scheduling captures attention for assigning workers with diverse proficiency to the appropriate stages, which is of great significance to production efficiency. In this paper, we present a novel algorithm called Self-encoding Barnacle Mating Optimizer (SBMO), which solves the FSS problem considering worker proficiency, defined as a new problem, Flow Shop Manpower Scheduling Problem (FSMSP). The highlight of the SBMO algorithm is the combination with the encoding method, crossover and mutation operators. Moreover, in order to solve the local optimum problem, we design a neighborhood search scheme. Finally, the extensive comparison simulations are conducted to demonstrate the superiority of the proposed SBMO. The results indicate the effectiveness of SBMO in approximate ratio, powerful stability, and execution time, compared with the classic and popular counterparts.

Gene expression datasets are usually of high dimensionality and therefore require efficient and effective methods for identifying the relative importance of their attributes. Due to the huge size of the search space of the possible solutions, the attribute subset evaluation feature selection methods tend to be not applicable, so in these scenarios feature ranking methods are used. Most of the feature ranking methods described in the literature are univariate methods, so they do not detect interactions between factors. In this paper we propose two new multivariate feature ranking methods based on pairwise correlation and pairwise consistency, which we have applied in three gene expression classification problems. We statistically prove that the proposed methods outperform the state of the art feature ranking methods Clustering Variation, Chi Squared, Correlation, Information Gain, ReliefF and Significance, as well as feature selection methods of attribute subset evaluation based on correlation and consistency with multi-objective evolutionary search strategy.

Allocating physical layer resources to users based on channel quality, buffer size, requirements and constraints represents one of the central optimization problems in the management of radio resources. The solution space grows combinatorially with the cardinality of each dimension making it hard to find optimal solutions using an exhaustive search or even classical optimization algorithms given the stringent time requirements. This problem is even more pronounced in MU-MIMO scheduling where the scheduler can assign multiple users to the same time-frequency physical resources. Traditional approaches thus resort to designing heuristics that trade optimality in favor of feasibility of execution. In this work we treat the MU-MIMO scheduling problem as a tree-structured combinatorial problem and, borrowing from the recent successes of AlphaGo Zero, we investigate the feasibility of searching for the best performing solutions using a combination of Monte Carlo Tree Search and Reinforcement Learning. To cater to the nature of the problem at hand, like the lack of an intrinsic ordering of the users as well as the importance of dependencies between combinations of users, we make fundamental modifications to the neural network architecture by introducing the self-attention mechanism. We then demonstrate that the resulting approach is not only feasible but vastly outperforms state-of-the-art heuristic-based scheduling approaches in the presence of measurement uncertainties and finite buffers.