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A multi-stratum design is a useful tool for industrial experimentation, where factors that have levels which are harder to set than others, due to time or cost constraints, are frequently included. The number of different levels of hardness to set defines the number of strata that should be used. The simplest case is the split-plot design, which includes two strata and two sets of factors defined by their level of hardness-to-set. In this paper, we propose a novel computational algorithm which can be used to construct optimal multi-stratum designs for any number of strata and up to six optimality criteria simultaneously. Our algorithm allows the study of the entire Pareto front of the optimization problem and the selection of the designs representing the desired trade-off between the competing objectives. We apply our algorithm to several real case scenarios and we show that the efficiencies of the designs obtained present experimenters with several good options according to their objectives.

Many industrial experiments involve one or more restrictions on the randomization. In such cases, the split-plot design structure, in which the experimental runs are performed in groups, is a commonly used cost-efficient approach that reduces the number of independent settings of the hard-to-change factors. Several criteria can be adopted for optimizing split-plot experimental designs: the most frequently used are D-optimality and I-optimality. A multi-objective approach to the optimal design of split-plot experiments, the coordinate-exchange two-phase local search (CE-TPLS), is proposed. The CE-TPLS algorithm is able to approximate the set of experimental designs which concurrently minimize the D-criterion and the I-criterion. It allows for a flexible choice of the number of hard-to-change factors, the number of easy-to-change factors, the number of whole plots and the total sample size. When tested on four case studies from the literature, the proposed algorithm returns meaningful sets of experimental designs, covering the whole spectrum between the two objectives. On most of the analyzed cases, the CE-TPLS algorithm returns better results than those reported in the original papers and outperforms the state-of-the-art algorithm in terms of computational time, while retaining a comparable performance in terms of the quality of the optima for each single objective. © 2013 Elsevier Inc. All rights reserved.

Cooperation is fundamental to the evolution of human society. We regularly observe cooperative behaviour in everyday life and in controlled experiments with anonymous people, even though standard economic models predict that they should deviate from the collective interest and act so as to maximise their own individual payoff. However, there is typically heterogeneity across subjects: some may cooperate, while others may not. Since individual factors promoting cooperation could be used by institutions to indirectly prime cooperation, this heterogeneity raises the important question of who these cooperators are. We have conducted a series of experiments to study whether benevolence, defined as a unilateral act of paying a cost to increase the welfare of someone else beyond one's own, is related to cooperation in a subsequent one-shot anonymous Prisoner's dilemma. Contrary to the predictions of the widely used inequity aversion models, we find that benevolence does exist and a large majority of people behave this way. We also find benevolence to be correlated with cooperative behaviour. Finally, we show a causal link between benevolence and cooperation: priming people to think positively about benevolent behaviour makes them significantly more cooperative than priming them to think malevolently. Thus benevolent people exist and cooperate more.