Abstract. Real-world problems often involve the optimisation of multiple conflicting objectives. These problems, referred to as multi-objective optimisation problems, are especially challenging when more than three objectives are considered simultaneously. This paper proposes an algorithm to address this class of problems. The proposed algorithm is an evolutionary algorithm based on an evolution strategy framework, and more specifically, on the Covariance Matrix Adaptation Pareto Archived Evolution Strategy (CMA-PAES). A novel selection mechanism is introduced and integrated within the framework. This selection mechanism makes use of an adaptive grid to perform a local approximation of the hypervolume indicator which is then used as a selection criterion. The proposed implementation, named Covariance Matrix Adaptation Pareto Archived Evolution Strategy with Hypervolume-sorted Adaptive Grid Algorithm (CMA-PAES-HAGA), overcomes the limitation of CMA-PAES in handling more than two objectives and displays a remarkably good performance on a scalable test suite in five, seven, and ten-objective problems. The performance of CMA-PAES-HAGA has been compared with that of a competition winning meta-heuristic, representing the state-of-the-art in this sub-field of multi-objective optimisation.The proposed algorithm has been tested in a seven-objective real-world application, i.e. the design of an aircraft lateral control system. In this optimisation problem, CMA-PAES-HAGA greatly outperformed its competitors.

Pattern Search is a family of optimisation algorithms that improve upon an initial solution by performing moves along the directions of a basis of vectors. In its original definition Pattern Search moves along the directions of each variable. Amongst its advantages, the algorithm does not require any knowledge of derivatives or analytical expression of the function to optimise. However, the performance of Pattern Search is heavily problem dependent since the search directions can be very effective on some problems and lead to poor performance on others. The present article proposes a novel enhancement of Pattern Search that explores the space by using problem-dependent search directions. Some points are sampled within the basin of attraction and the diagonalisation of the covariance matrix associated with the distribution of these points is performed. The proposed Covariance Pattern Search improves upon an initial point by varying it along the directions identified by the eigenvectors of the covariance matrix.

Solutions to real-world problems often require the simultaneous optimisation of multiple conflicting objectives. In the presence of four or more objectives, the problem is referred to as a "many-objective optimisation problem". A problem of this category introduces many challenges, one of which is the e↵ective and e cient selection of optimal solutions.The hypervolume indicator (or s-metric), i.e. the size of dominated objective space, is an e↵ective selection criterion for many-objective optimisation. The indicator is used to measure the quality of a nondominated set, and can be used to sort solutions for selection as part of the contributing hypervolume indicator. However, hypervolume based selection methods can have a very high, if not infeasible, computational cost.The present study proposes a novel hypervolume driven selection mechanism for many-objective problems, whilst maintaining a feasible computational cost. This approach, named the Hypervolume Adaptive Grid Algorithm (HAGA), uses two-phases (narrow and broad) to prevent population-wide calculation of the contributing hypervolume indicator. Instead, HAGA only calculates the contributing hypervolume indicator for grid populations, i.e. for a few solutions, which are close in proximity (in the objective space) to a candidate solution when in competition for survival. The result is a trade-o↵ between complete accuracy in selecting the fittest individuals in regards to hypervolume quality, and a feasible computational time in many-objective space. The real-world e ciency of the proposed selection mechanism is demonstrated within the optimisation of a classifier for concealed weapon detection.

Abstract.This paper proposes a novel algorithm for addressing multi-objective optimisation problems, by employing a progressive preference articulation approach to decision making. This enables the interactive incorporation of problem knowledge and decision maker preferences during the optimisation process. A novel progressive preference articulation mechanism, derived from a statistical technique, is herein proposed and implemented within a multi-objective framework based on evolution strategy search and hypervolume indicator selection. The proposed algorithm is named the Weighted Z-score Covariance Matrix Adaptation Pareto Archived Evolution Strategy with Hypervolume-sorted Adaptive Grid Algorithm (WZ-HAGA).WZ-HAGA is based on a framework that makes use of evolution strategy logic with covariance matrix adaptation to perturb the solutions, and a hypervolume indicator driven algorithm to select successful solutions for the subsequent generation. In order to guide the search towards interesting regions, a preference articulation procedure composed of four phases and based on the weighted z-score approach is employed. The latter procedure cascades into the hypervolume driven algorithm to perform the selection of the solutions at each generation.Numerical results against five modern algorithms representing the state-of-the-art in multi-objective optimisation demonstrate that the proposed WZ-HAGA outperforms its competitors in terms of both the hypervolume indicator and pertinence to the regions of interest.

The energy transition is the pathway to transform the global economy away from its current dependence on fossil fuels towards net zero carbon emissions. This requires the rapid and large-scale deployment of renewable energy. However, most renewables, such as wind and solar, are intermittent and hence generation and demand do not necessarily match. One way to overcome this problem is to use excess renewable power to generate hydrogen by electrolysis, which is used as an energy store, and then consumed in fuel cells, or burnt in generators and boilers on demand, much as is presently done with natural gas, but with zero emissions. Using hydrogen in this way necessitates large-scale storage: the most practical manner to do this is deep underground in salt caverns, or porous rock, as currently implemented for natural gas and carbon dioxide. This paper reviews the concepts, and challenges of underground hydrogen storage. As well as summarizing the state-of-theart, with reference to current and proposed storage projects, suggestions are made for future work and gaps in our current understanding are highlighted. The role of hydrogen in the energy transition and storage methods are described in detail. Hydrogen flow and its fate in the subsurface are reviewed, emphasizing the unique challenges compared to other types of gas storage. In addition, site selection criteria are considered in the light of current field experience.