Evolutionary many-objective optimisation: pushing the boundaries

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonMany-objective optimisation poses great challenges to evolutionary algorithms. To start with, the ineffectiveness of the Pareto dominance relation, which is the most important criterion in multi-objective optimisation, results in the underperformance of traditional Pareto-based algorithms. Also, the aggravation of the conflict between proximity and diversity, along with increasing time or space requirement as well as parameter sensitivity, has become key barriers to the design of effective many-objective optimisation algorithms. Furthermore, the infeasibility of solutions' direct observation can lead to serious difficulties in algorithms' performance investigation and comparison. In this thesis, we address these challenges, aiming to make evolutionary algorithms as effective in many-objective optimisation as in two- or three-objective optimisation. First, we significantly enhance Pareto-based algorithms to make them suitable for many-objective optimisation by placing individuals with poor proximity into crowded regions so that these individuals can have a better chance to be eliminated. Second, we propose a grid-based evolutionary algorithm which explores the potential of the grid to deal with many-objective optimisation problems. Third, we present a bi-goal evolution framework that converts many objectives of a given problem into two objectives regarding proximity and diversity, thus creating an optimisation problem in which the objectives are the goals of the search process itself. Fourth, we propose a comprehensive performance indicator to compare evolutionary algorithms in optimisation problems with various Pareto front shapes and any objective dimensionality. Finally, we construct a test problem to aid the visual investigation of evolutionary search, with its Pareto optimal solutions in a two-dimensional decision space having similar distribution to their images in a higher-dimensional objective space. The work reported in this thesis is the outcome of innovative attempts at addressing some of the most challenging problems in evolutionary many-objective optimisation. This research has not only made some of the existing approaches, such as Pareto-based or grid-based algorithms that were traditionally regarded as unsuitable, now effective for many-objective optimisation, but also pushed other important boundaries with novel ideas including bi-goal evolution, a comprehensive performance indicator and a test problem for visual investigation. All the proposed algorithms have been systematically evaluated against existing state of the arts, and some of these algorithms have already been taken up by researchers and practitioners in the field.Department of Computer Science, Brunel University Londo

Analysis of the fitness landscape for the class of combinatorial optimisation problems

Anatomy of the fitness landscape for a group of well known combinatorial optimisation problems is studied in this research and the similarities and the differences between their landscapes are pointed out. In this research we target the analysis of the fitness landscape for MAX-SAT, Graph-Colouring, Travelling Salesman and Quadratic Assignment problems. Belonging to the class of NP-Hard problems, all these problems become exponentially harder as the problem size grows. We study a group of properties of the fitness landscape for these problems and show what properties are shared by different problems and what properties are different. The properties we investigate here include the time it takes for a local search algorithm to find a local optimum, the number of local and global optima, distance between local and global optima, expected cost of found optima, probability of reaching a global optimum and the cost of the best configuration in the search space. The relationship between these properties and the system size and other parameters of the problems are studied, and it is shown how these properties are shared or differ in different problems. We also study the long-range correlation within the search space, including the expected cost in the Hamming sphere around the local and global optima, the basin of attraction of the local and global optima and the probability of finding a local optimum as a function of its cost. We believe these information provide good insight for algorithm designers

Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Opt

In this paper, we present Neural k-Opt (NeuOpt), a novel learning-to-search (L2S) solver for routing problems. It learns to perform flexible k-opt exchanges based on a tailored action factorization method and a customized recurrent dual-stream decoder. As a pioneering work to circumvent the pure feasibility masking scheme and enable the autonomous exploration of both feasible and infeasible regions, we then propose the Guided Infeasible Region Exploration (GIRE) scheme, which supplements the NeuOpt policy network with feasibility-related features and leverages reward shaping to steer reinforcement learning more effectively. Additionally, we equip NeuOpt with Dynamic Data Augmentation (D2A) for more diverse searches during inference. Extensive experiments on the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) demonstrate that our NeuOpt not only significantly outstrips existing (masking-based) L2S solvers, but also showcases superiority over the learning-to-construct (L2C) and learning-to-predict (L2P) solvers. Notably, we offer fresh perspectives on how neural solvers can handle VRP constraints. Our code is available: https://github.com/yining043/NeuOpt.Comment: Accepted at NeurIPS 202

Reactive approach for automating exploration and exploitation in ant colony optimization

Ant colony optimization (ACO) algorithms can be used to solve nondeterministic polynomial hard problems. Exploration and exploitation are the main mechanisms in controlling search within the ACO. Reactive search is an alternative technique to maintain the dynamism of the mechanics. However, ACO-based reactive search technique has three (3) problems. First, the memory model to record previous search regions did not completely transfer the neighborhood structures to the next iteration which leads to arbitrary restart and premature local search. Secondly, the exploration indicator is not robust due to the difference of magnitudes in distance matrices for the current population. Thirdly, the parameter control techniques that utilize exploration indicators in their feedback process do not consider the problem of indicator robustness. A reactive ant colony optimization (RACO) algorithm has been proposed to overcome the limitations of the reactive search. RACO consists of three main components. The first component is a reactive max-min ant system algorithm for recording the neighborhood structures. The second component is a statistical machine learning mechanism named ACOustic to produce a robust exploration indicator. The third component is the ACO-based adaptive parameter selection algorithm to solve the parameterization problem which relies on quality, exploration and unified criteria in assigning rewards to promising parameters. The performance of RACO is evaluated on traveling salesman and quadratic assignment problems and compared with eight metaheuristics techniques in terms of success rate, Wilcoxon signed-rank, Chi-square and relative percentage deviation. Experimental results showed that the performance of RACO is superior than the eight (8) metaheuristics techniques which confirmed that RACO can be used as a new direction for solving optimization problems. RACO can be used in providing a dynamic exploration and exploitation mechanism, setting a parameter value which allows an efficient search, describing the amount of exploration an ACO algorithm performs and detecting stagnation situations

Multi-robot path planning for budgeted active perception with self-organising maps

© 2016 IEEE. We propose a self-organising map (SOM) algorithm as a solution to a new multi-goal path planning problem for active perception and data collection tasks. We optimise paths for a multi-robot team that aims to maximally observe a set of nodes in the environment. The selected nodes are observed by visiting associated viewpoint regions defined by a sensor model. The key problem characteristics are that the viewpoint regions are overlapping polygonal continuous regions, each node has an observation reward, and the robots are constrained by travel budgets. The SOM algorithm jointly selects and allocates nodes to the robots and finds favourable sequences of sensing locations. The algorithm has polynomial-bounded runtime independent of the number of robots. We demonstrate feasibility for the active perception task of observing a set of 3D objects. The viewpoint regions consider sensing ranges and self-occlusions, and the rewards are measured as discriminability in the ensemble of shape functions feature space. Simulations were performed using a 3D point cloud dataset from a real robot in a large outdoor environment. Our results show the proposed methods enable multi-robot planning for budgeted active perception tasks with continuous sets of candidate viewpoints and long planning horizons