Robin C. Purshouse

Evolutionary algorithms in control systems engineering: a survey

Abstract Challenging optimisation problems, which elude acceptable solution via conventional methods, arise regularly in control systems engineering. Evolutionary algorithms (EAs) permit flexible representation of decision variables and performance evaluation and are robust to difficult search environments, leading to their widespread uptake in the control community. Significant applications are discussed in parameter and structure optimisation for controller design and model identification, in addition to fault diagnosis, reliable systems, robustness analysis, and robot control. Hybrid neural and fuzzy control schemes are also described. The important role of EAs in multiobjective optimisation is highlighted. Evolutionary advances in adaptive control and multidisciplinary design are predicted.

On the Evolutionary Optimization of Many Conflicting Objectives

This study explores the utility of multiobjective evolutionary algorithms (using standard Pareto ranking and diversity-promoting selection mechanisms) for solving optimization tasks with many conflicting objectives. Optimizer behavior is assessed for a grid of mutation and recombination operator configurations. Performance maps are obtained for the dual aims of proximity to, and distribution across, the optimal tradeoff surface. Performance sweet-spots for both variation operators are observed to contract as the number of objectives is increased. Classical settings for recombination are shown to be suitable for small numbers of objectives but correspond to very poor performance for higher numbers of objectives, even when large population sizes are used. Explanations for this behavior are offered via the concepts of dominance resistance and active diversity promotion.

Many-Objective optimization: an engineering design perspective

Evolutionary multicriteria optimization has traditionally concentrated on problems comprising 2 or 3 objectives. While engineering design problems can often be conveniently formulated as multiobjective optimization problems, these often comprise a relatively large number of objectives. Such problems pose new challenges for algorithm design, visualisation and implementation. Each of these three topics is addressed. Progressive articulation of design preferences is demonstrated to assist in reducing the region of interest for the search and, thereby, simplified the problem. Parallel coordinates have proved a useful tool for visualising many objectives in a two-dimensional graph and the computational grid and wireless Personal Digital Assistants offer technological solutions to implementation difficulties arising in complex system design.

Estimated effect of alcohol pricing policies on health and health economic outcomes in England: an epidemiological model

BACKGROUND Although pricing policies for alcohol are known to be effective, little is known about how specific interventions affect health-care costs and health-related quality-of-life outcomes for different types of drinkers. We assessed effects of alcohol pricing and promotion policy options in various population subgroups. METHODS We built an epidemiological mathematical model to appraise 18 pricing policies, with English data from the Expenditure and Food Survey and the General Household Survey for average and peak alcohol consumption. We used results from econometric analyses (256 own-price and cross-price elasticity estimates) to estimate effects of policies on alcohol consumption. We applied risk functions from systemic reviews and meta-analyses, or derived from attributable fractions, to model the effect of consumption changes on mortality and disease prevalence for 47 illnesses. FINDINGS General price increases were effective for reduction of consumption, health-care costs, and health-related quality of life losses in all population subgroups. Minimum pricing policies can maintain this level of effectiveness for harmful drinkers while reducing effects on consumer spending for moderate drinkers. Total bans of supermarket and off-license discounting are effective but banning only large discounts has little effect. Young adult drinkers aged 18-24 years are especially affected by policies that raise prices in pubs and bars. INTERPRETATION Minimum pricing policies and discounting restrictions might warrant further consideration because both strategies are estimated to reduce alcohol consumption, and related health harms and costs, with drinker spending increases targeting those who incur most harm. FUNDING Policy Research Programme, UK Department of Health.

Evolutionary many-objective optimisation: an exploratory analysis

This inquiry explores the effectiveness of a class of modern evolutionary algorithms, represented by NSGA-II, for solving optimisation tasks with many conflicting objectives. Optimiser behaviour is assessed for a grid of recombination operator configurations. Performance maps are obtained for the dual aims of proximity to, and distribution across, the optimal trade-off surface. Classical settings for recombination are shown to be suitable for small numbers of objectives but correspond to very poor performance as the number of objectives is increased, even when large population sizes are used. Explanations for this behaviour are offered via the concepts of dominance resistance and active diversity promotion.

Preference-Inspired Coevolutionary Algorithms for Many-Objective Optimization

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 ε-dominance relation-based algorithm [ ε-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, ε-MOEA, and MOEA/D. All the algorithms outperformed random search.

Policy options for alcohol price regulation: the importance of modelling population heterogeneity.

Context and aims Internationally, the repertoire of alcohol pricing policies has expanded to include targeted taxation, inflation-linked taxation, taxation based on alcohol-by-volume (ABV), minimum pricing policies (general or targeted), bans of below-cost selling and restricting price-based promotions. Policy makers clearly need to consider how options compare in reducing harms at the population level, but are also required to demonstrate proportionality of their actions, which necessitates a detailed understanding of policy effects on different population subgroups. This paper presents selected findings from a policy appraisal for the UK government and discusses the importance of accounting for population heterogeneity in such analyses. Method We have built a causal, deterministic, epidemiological model which takes account of differential preferences by population subgroups defined by age, gender and level of drinking (moderate, hazardous, harmful). We consider purchasing preferences in terms of the types and volumes of alcoholic beverages, prices paid and the balance between bars, clubs and restaurants as opposed to supermarkets and off-licenses. Results Age, sex and level of drinking fundamentally affect beverage preferences, drinking location, prices paid, price sensitivity and tendency to substitute for other beverage types. Pricing policies vary in their impact on different product types, price points and venues, thus having distinctly different effects on subgroups. Because population subgroups also have substantially different risk profiles for harms, policies are differentially effective in reducing health, crime, work-place absence and unemployment harms. Conclusion Policy appraisals must account for population heterogeneity and complexity if resulting interventions are to be well considered, proportionate, effective and cost-effective.

Effects of minimum unit pricing for alcohol on different income and socioeconomic groups: a modelling study

Summary Background Several countries are considering a minimum price policy for alcohol, but concerns exist about the potential effects on drinkers with low incomes. We aimed to assess the effect of a £0·45 minimum unit price (1 unit is 8 g/10 mL ethanol) in England across the income and socioeconomic distributions. Methods We used the Sheffield Alcohol Policy Model (SAPM) version 2.6, a causal, deterministic, epidemiological model, to assess effects of a minimum unit price policy. SAPM accounts for alcohol purchasing and consumption preferences for population subgroups including income and socioeconomic groups. Purchasing preferences are regarded as the types and volumes of alcohol beverages, prices paid, and the balance between on-trade (eg, bars) and off-trade (eg, shops). We estimated price elasticities from 9 years of survey data and did sensitivity analyses with alternative elasticities. We assessed effects of the policy on moderate, hazardous, and harmful drinkers, split into three socioeconomic groups (living in routine or manual households, intermediate households, and managerial or professional households). We examined policy effects on alcohol consumption, spending, rates of alcohol-related health harm, and opportunity costs associated with that harm. Rates of harm and costs were estimated for a 10 year period after policy implementation. We adjusted baseline rates of mortality and morbidity to account for differential risk between socioeconomic groups. Findings Overall, a minimum unit price of £0·45 led to an immediate reduction in consumption of 1·6% (−11·7 units per drinker per year) in our model. Moderate drinkers were least affected in terms of consumption (−3·8 units per drinker per year for the lowest income quintile vs 0·8 units increase for the highest income quintile) and spending (increase in spending of £0·04 vs £1·86 per year). The greatest behavioural changes occurred in harmful drinkers (change in consumption of −3·7% or −138·2 units per drinker per year, with a decrease in spending of £4·01), especially in the lowest income quintile (−7·6% or −299·8 units per drinker per year, with a decrease in spending of £34·63) compared with the highest income quintile (−1·0% or −34·3 units, with an increase in spending of £16·35). Estimated health benefits from the policy were also unequally distributed. Individuals in the lowest socioeconomic group (living in routine or manual worker households and comprising 41·7% of the sample population) would accrue 81·8% of reductions in premature deaths and 87·1% of gains in terms of quality-adjusted life-years. Interpretation Irrespective of income, moderate drinkers were little affected by a minimum unit price of £0·45 in our model, with the greatest effects noted for harmful drinkers. Because harmful drinkers on low incomes purchase more alcohol at less than the minimum unit price threshold compared with other groups, they would be affected most by this policy. Large reductions in consumption in this group would however coincide with substantial health gains in terms of morbidity and mortality related to reduced alcohol consumption. Funding UK Medical Research Council and Economic and Social Research Council (grant G1000043).

Conflict, harmony, and independence: relationships in evolutionary multi-criterion optimisation

This paper contributes a platform for the treatment of large numbers of criteria in evolutionary multi-criterion optimisation theory through consideration of the relationships between pairs of criteria. In a conflicting relationship, as performance in one criterion is improved, performance in the other is seen to deteriorate. If the relationship is harmonious, improvement in one criterion is rewarded with simultaneous improvement in the other. The criteria may be independent of each other, where adjustment to one never affects adjustment to the other. Increasing numbers of conflicting criteria pose a great challenge to obtaining a good representation of the global trade-off hypersurface, which can be countered using decision-maker preferences. Increasing numbers of harmonious criteria have no effect on convergence to the surface but difficulties may arise in achieving a good distribution. The identification of independence presents the opportunity for a divide-and-conquer strategy that can improve the quality of trade-off surface representations.

Generalized decomposition and cross entropy methods for many-objective optimization

Decomposition-based algorithms for multi-objective optimization problems have increased in popularity in the past decade. Although convergence to the Pareto optimal front (PF) for such algorithms can often be superior to that of Pareto-based alternatives, the problem of effectively distributing Pareto optimal solutions in a high-dimensional space has not been solved. In this work, we introduce a novel concept which we call generalized decomposition. Generalized decomposition provides a framework with which the decision maker (DM) can guide the underlying search algorithm toward specific regions of interest, or the entire Pareto front, with the desired distribution of Pareto optimal solutions. The method simplifies many-objective problems by unifying the three performance objectives of an a posteriori multi-objective optimizer - convergence to the PF, evenly distributed Pareto optimal solutions and coverage of the entire front - to only one, that of convergence. A framework, established on generalized decomposition, and an estimation of distribution algorithm (EDA) based on low-order statistics, namely the cross-entropy method, is created to illustrate the benefits of the proposed concept for many-objective problems. The algorithm - MACE-gD - is shown to be highly competitive with the existing best-in-class decomposition-based algorithm (MOEA/D) and a more elaborate EDA method (RM-MEDA).