• Energy Research

The simultaneous optimization of many objectives (in excess of 3), in order to obtain a full and satisfactory set of tradeoff solutions to support a posteriori decision making, remains a challenging problem. The concept of coevolving a family of decision-maker preferences together with a population of candidate solutions is studied here and demonstrated to have promising performance characteristics for such problems. After introducing the concept of the preference-inspired coevolutionary algorithm (PICEA), a realization of this concept, PICEA-g, is systematically compared with four of the best-in-class evolutionary algorithms (EAs); random search is also studied as a baseline approach. The four EAs used in the comparison are a Pareto-dominance relation-based algorithm (NSGA-II), an e-dominance relation-based algorithm [ e-multiobjective evolutionary algorithm (MOEA)], a scalarizing function-based algorithm (MOEA/D), and an indicator-based algorithm [hypervolume-based algorithm (HypE)]. It is demonstrated that, for bi-objective problems, all of the multi-objective evolutionary algorithms perform competitively. As the number of objectives increases, PICEA-g and HypE, which have comparable performance, tend to outperform NSGA-II, e-MOEA, and MOEA/D. All the algorithms outperformed random search.

Engineering design optimization problems increasingly require computationally expensive high-fidelity simulation models to evaluate candidate designs. The evaluation budget may be small, limiting the effectiveness of conventional multi-objective evolutionary algorithms. Bayesian optimization algorithms (BOAs) are an alternative approach for expensive problems but are underdeveloped in terms of support for constraints and non-continuous design variables—both of which are prevalent features of real-world design problems. This study investigates two constraint handling strategies for BOAs and introduces the first BOA for mixed-integer problems, intended for use on a real-world engine design problem. The new BOAs are empirically compared to their closest competitor for this problem—the multi-objective evolutionary algorithm NSGA-II, itself equipped with constraint handling and mixed-integer components. Performance is also analysed on two benchmark problems which have similar features to the engine design problem, but are computationally cheaper to evaluate. The BOAs offer statistically significant convergence improvements of between 5.9% and 31.9% over NSGA-II across the problems on a budget of 500 design evaluations. Of the two constraint handling methods, constrained expected improvement offers better convergence than the penalty function approach. For the engine problem, the BOAs identify improved feasible designs offering 36.4% reductions in nitrogen oxide emissions and 2.0% reductions in fuel consumption when compared to a notional baseline design. The use of constrained mixed-integer BOAs is recommended for expensive engineering design optimization problems.

AbstractAimsTo estimate the probability of transitioning between different categories of alcohol use (drinking states) among a nationally representative cohort of United States (US) adults and to identify the effects of socio‐demographic characteristics on those transitions.Design, setting and participantsSecondary analysis of data from the National Epidemiologic Survey of Alcohol and Related Conditions (NESARC), a prospective cohort study conducted in 2001–02 and 2004–05; a US nation‐wide, population‐based study. Participants included 34 165 adults (mean age = 45.1 years, standard deviation = 17.3; 52% women).MeasurementsAlcohol use was self‐reported and categorized based on the grams consumed per day: (1) non‐drinker (no drinks in past 12 months), (2) category I (women = ≤ 20; men = ≤ 40), (3) category II (women = 21–40; men = 41–60) and (4) category III (women = ≥ 41; men = ≥ 61). Multi‐state Markov models estimated the probability of transitioning between drinking states, conditioned on age, sex, race/ethnicity and educational attainment. Analyses were repeated with alcohol use categorized based on the frequency of heavy episodic drinking.FindingsThe highest transition probabilities were observed for staying in the same state; after 1 year, the probability of remaining in the same state was 90.1% [95% confidence interval (CI) = 89.7%, 90.5%] for non‐drinkers, 90.2% (95% CI = 89.9%, 90.5%) for category I, 31.8% (95% CI = 29.7, 33.9%) category II and 52.2% (95% CI = 46.0, 58.5%) for category III. Women, older adults, and non‐Hispanic Other adults were less likely to transition between drinking states, including transitions to lower use. Adults with lower educational attainment were more likely to transition between drinking states; however, they were also less likely to transition out of the ‘weekly HED’ category. Black adults were more likely to transition into or stay in higher use categories, whereas Hispanic/Latinx adults were largely similar to White adults.ConclusionsIn this study of alcohol transition probabilities, some demographic subgroups appeared more likely to transition into or persist in higher alcohol consumption states.

Many real-world problems have multiple competing objectives and can often be formulated as multi-objective optimisation problems. Multi-objective evolutionary algorithms (MOEAs) have proven very effective in obtaining a set of trade-off solutions for such problems. This research seeks to improve both the accuracy and the diversity of these solutions through the local application of evolutionary operators to selected sub-populations. A local operation-based implementation framework is presented in which a population is partitioned, using hierarchical clustering, into a pre-defined number of sub-populations. Environment-selection and genetic-variation are then applied to each sub-population. The effectiveness of this approach is demonstrated on 2- and 4-objective benchmark problems. The performance of each of four best-in-class MOEAs is compared with their modified local operation-based versions derived from this framework. In each case the introduction of the local operation-based approach improves performance. Further, it is shown that the combined use of local environment-selection and local genetic-variation is better than the application of either local environment-selection or local genetic-variation alone. Preliminary results indicate that the selection of a suitable number of sub-populations is related to problem dimension as well as to population size.

For real-world problems, the task of decision-makers is to identify a solution that can satisfy a set of performance criteria, which are often in conflict with each other. Multi-objective evolutionary algorithms tend to focus on obtaining a family of solutions that represent the trade-offs between the criteria; however ultimately a single solution must be selected. This need has driven a requirement to incorporate decision-maker preference models into such algorithms - a technique that is very common in the wider field of multiple criteria decision making. This paper reviews techniques which have combined evolutionary multi-objective optimization and multiple criteria decision making. Three classes of hybrid techniques are presented: a posteriori, a priori, and interactive, including methods used to model the decision-makers preferences and example algorithms for each category. To encourage future research directions, a commentary on the remaining issues within this research area is also provided.

Many-objective optimisation problems remain challenging for many state-of-the-art multi-objective evolutionary algorithms. Preference-inspired co-evolutionary algorithms PICEAs which co-evolve the usual population of candidate solutions with a family of decision-maker preferences during the search have been demonstrated to be effective on such problems. However, it is unknown whether PICEAs are robust with respect to the parameter settings. This study aims to address this question. First, a global sensitivity analysis method – the Sobol’ variance decomposition method – is employed to determine the relative importance of the parameters controlling the performance of PICEAs. Experimental results show that the performance of PICEAs is controlled for the most part by the number of function evaluations. Next, we investigate the effect of key parameters identified from the Sobol’ test and the genetic operators employed in PICEAs. Experimental results show improved performance of the PICEAs as more preferences are co-evolved. Additionally, some suggestions for genetic operator settings are provided for non-expert users.