Improved sampling of the pareto-front in multiobjective genetic optimizations by steady-state evolution: a Pareto converging genetic algorithm

Previous work on multiobjective genetic algorithms has been focused on preventing genetic drift and the issue of convergence has been given little attention. In this paper, we present a simple steady-state strategy, Pareto Converging Genetic Algorithm (PCGA), which naturally samples the solution space and ensures population advancement towards the Pareto-front. PCGA eliminates the need for sharing/niching and thus minimizes heuristically chosen parameters and procedures. A systematic approach based on histograms of rank is introduced for assessing convergence to the Pareto-front, which, by definition, is unknown in most real search problems. We argue that there is always a certain inheritance of genetic material belonging to a population, and there is unlikely to be any significant gain beyond some point; a stopping criterion where terminating the computation is suggested. For further encouraging diversity and competition, a nonmigrating island model may optionally be used; this approach is particularly suited to many difficult (real-world) problems, which have a tendency to get stuck at (unknown) local minima. Results on three benchmark problems are presented and compared with those of earlier approaches. PCGA is found to produce diverse sampling of the Pareto-front without niching and with significantly less computational effort

An evolutionary approach to solve a system of multiple interrelated agent problems

Deterministic approaches to simultaneously solve different interrelated optimisation problems lead to a general class of nonlinear complementarity problem (NCP). Due to differentiability and convexity requirements of the problems, sophisticated algorithms are introduced in literature. This paper develops an evolutionary algorithm to solve the NCPs. The proposed approach is a parallel search in which multiple populations representing different agents evolve simultaneously whilst in contact with each other. In this context, each agent autonomously solves its optimisation programme while sharing its decisions with the neighbouring agents and, hence, it affects their actions. The framework is applied to an environmental and an aerospace application where the obtained results are compared with those found in literature. The convergence and scalability of the approach is tested and its search algorithm performance is analysed. Results encourage the application of such an evolutionary based algorithm for complementarity problems and future work should investigate its development as well as its performance improvements

Learning to Sparsify Travelling Salesman Problem Instances

CPAIOR 2021: 18th International Conference on Integration of Constraint Programming, Artificial Intelligence, and Operations Research, Vienna, Austria, 5 - 8 July 2021In order to deal with the high development time of exact and approximation algorithms for NP-hard combinatorial optimisation problems and the high running time of exact solvers, deep learning techniques have been used in recent years as an end-to-end approach to find solutions. However, there are issues of representation, generalisation, complex architectures, interpretability of models for mathematical analysis etc. using deep learning techniques. As a compromise, machine learning can be used to improve the run time performance of exact algorithms in a matheuristics framework. In this paper, we use a pruning heuristic leveraging machine learning as a pre-processing step followed by an exact Integer Programming approach. We apply this approach to sparsify instances of the classical travelling salesman problem. Our approach learns which edges in the underlying graph are unlikely to belong to an optimal solution and removes them, thus sparsifying the graph and significantly reducing the number of decision variables. We use carefully selected features derived from linear programming relaxation, cutting planes exploration, minimum-weight spanning tree heuristics and various other local and statistical analysis of the graph. Our learning approach requires very little training data and is amenable to mathematical analysis. We demonstrate that our approach can reliably prune a large fraction of the variables in TSP instances from TSPLIB/MATILDA (>85%) while preserving most of the optimal tour edges. Our approach can successfully prune problem instances even if they lie outside the training distribution, resulting in small optimality gaps between the pruned and original problems in most cases. Using our learning technique, we discover novel heuristics for sparsifying TSP instances, that may be of independent interest for variants of the vehicle routing problem.Science Foundation IrelandOpen access funding provided by SF

Hybridization of Biologically Inspired Algorithms for Discrete Optimisation Problems

In the field of Optimization Algorithms, despite the popularity of hybrid designs, not enough consideration has been given to hybridization strategies. This paper aims to raise awareness of the benefits that such a study can bring. It does this by conducting a systematic review of popular algorithms used for optimization, within the context of Combinatorial Optimization Problems. Then, a comparative analysis is performed between Hybrid and Base versions of the algorithms to demonstrate an increase in optimization performance when hybridization is employed