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One of the main components of multi-objective, and therefore, many-objective evolutionary algorithms, is the selection mechanism. It is responsible for performing two main tasks simultaneously. First, it has to promote convergence by selecting solutions which are as close as possible to the Pareto optimal set. And second, it has to promote diversity in the solution set provided. In the current work, an exhaustive study that involves the comparison of several selection mechanisms with different features is performed. Particularly, Pareto-based and indicator-based selection schemes, which belong to well-known multi-objective optimisers, are considered. The paper aims to discuss these issues.

Each of those mechanisms is incorporated into a common multi-objective evolutionary algorithm framework. The main goal of the study is to measure the diversity preserved by each of those selection methods when addressing many-objective optimisation problems. The Walking Fish Group test suite, a set of optimisation problems with a scalable number of objective functions, is taken into account to perform the experimental evaluation.

The computational results highlight that the the reference-point-based selection scheme of the Non-dominated Sorting Genetic Algorithm III and a modified version of the Non-dominated Sorting Genetic Algorithm II, where the crowding distance is replaced by the Euclidean distance, are able to provide the best performance, not only in terms of diversity preservation, but also in terms of convergence.

The performance provided by the use of the Euclidean distance as part of the selection scheme indicates this is a promising line of research and, to the best of the knowledge, it has not been investigated yet.

Taking into account the importance of e‐commerce and the current applications of AI techniques in this area, this research aims to adequate the design of a multi‐agent system for the provisioning of e‐services in u‐commerce environments. This proposal is centred on the methods of evaluation in a u‐e‐commerce environment.

The multi‐agent systems (MAS) approach is based on an MAS model developed for AmI that has been redesigned to support u‐commerce. The use of a recommendation system, previously developed by the research group, is suggested for this MAS. The methodological proposal centres on the evaluation of this type of system.

The evaluation of this type of system is the principal problem of current research. Therefore, this is the main contribution of the paper.

The different evaluation methods that are proposed, whether qualitative or quantitative, offer the possibility of measuring the added value that the context can give to the use of e‐services in different domains of application. Qualitative evaluation should consider the customer as a central piece in the system. In addition, quantitative methods should objectively evaluate the contribution of context to the application.

At present, there is no single method for evaluating the benefits of different u‐commerce systems, so a new method needs to be found based on these techniques.

The research proposes an MAS designed for u‐commerce domains, analyzes the capacity of trust management techniques in this environment, and proposes several evaluation methods to show the benefits of context information in the use of e‐services. Several real developments are described to show the different applications of MAS in u‐commerce and how evaluation is carried out.