Abstract
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.
Highlights
Introduction and backgroundWe study a class of problems in which solutions to n interrelated optimisation problems are simultaneously required
We report the performance of the proposed approach on the above velocity profile approximation problem when the differential evolution (DE) search algorithm is replaced by simple genetic algorithm (GA), genetic algorithm with elitism (GA-E) [45] and covariance matrix adaptation evolution strategy (CMA-ES) [46]
We have developed an evolutionary approach to solve n optimisation problems simultaneously
Summary
We study a class of problems in which solutions to n interrelated optimisation problems are simultaneously required In this context, each agent solves one optimisation problem and seeks its own optimal strategies while interacting with the others. General agent based approaches have been presented in literature to solve complex interrelated optimisation problems. In transportation, scheduling and planning, agent based approaches are successfully employed for optimisation of train coupling systems [16,17], for routing decision making based on local information in dynamic environment [18], for solving the dynamic scheduling problem of a distributed project with self-interested participants [19], for dealing with energy systems planning and forecasting [20] and for land usage and environmental planning [21].
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