In recent years, the use of virtual engineering design processes has become more prevalent within industry. This increase has been facilitated by the availability of cost-effective computational machinery on which to run complex simulations of alternative candidate designs. Nevertheless it is frequently the case that, when working with complex problems, the number of simulation-based design evaluations available is limited. Within both industry and academia, it is usual for the stages of simulation model calibration and model-based optimization to be considered as separate consecutive steps rather than as a combined process. However, there is no guarantee that this approach makes the most efficient use of the available function evaluations. This work presents a new alternating methodology that aims to make more efficient use of the evaluation budget, through switching back and forth between the stages of calibration and optimization. To assess the effectiveness of the method, a new benchmark problem is introduced that contains both model parameters to be estimated and design variables to be selected. The new alternating method is found to possess improved calibration and comparable optimization performance in comparison to the sequential method on a budget of 5000 evaluations.

Generative mechanism-based models of social systems, such as those represented by agent-based simulations, require that intra-agent equations (or rules) be specified. However there are often many different choices available for specifying these equations, which can still be interpreted as falling within a particular class of mechanisms. Whilst it is important for a generative model to reproduce historically observed dynamics, it is also important for the model to be theoretically enlightening. Genetic programs (our own included) often produce concatenations that are highly predictive but are complex and hard to interpret theoretically. Here, we develop a new method - based on multi-objective genetic programming - for automating the exploration of both objectives simultaneously. We demonstrate the method by evolving the equations for an existing agent-based simulation of alcohol use behaviors based on social norms theory, the initial model structure for which was developed by a team of human modelers. We discover a trade-off between empirical fit and theoretical interpretability that offers insight into the social norms processes that influence the change and stasis in alcohol use behaviors over time.

When designing a new product it is often advantageous to use virtual engineering as either a replacement or assistant to more traditional prototyping. Virtual engineering consists of two main stages: (i) development of the simulation model; (ii) use of the model in design optimisation. There is a vast literature on both of these stages in isolation but virtually no studies have considered them in combination. The model calibration and design optimisation processes both however, crucially, draw on the same resource budget for simulation evaluations. When evaluations are expensive, there may be advantages in treating the two stages as combined. This study lays out a joint framework by which such problems can be expressed through a unified mathematical notation. A previously published case study is reviewed within the context of this framework, and directions for further development are discussed.

Multidisciplinary design optimization problems with competing objectives that involve several interacting components can be called complex systems. Nowadays, it is common to partition the optimization problem of a complex system into smaller subsystems, each with a subproblem, in part because it is too difficult to deal with the problem all-at-once. Such an approach is suitable for large organisations where each subsystem can have its own (specialised) design team. However, this requires a design process that facilitates collaboration, and decision making, in an environment where teams may exchange limited information about their own designs, and also where the design teams work at different rates, have different time schedules, and are normally not co-located. A multi-objective optimization methodology to address these features is described. Subsystems exchange information about their own optimal solutions on a peer-to-peer basis, and the methodology enables convergence to a set of optimal solutions that satisfy the overall system. This is demonstrated on an example problem where the methodology is shown to perform as well as the ideal, but "unrealistic" approach, that treats the optimization problem all-at-once.

Decomposition-based algorithms have emerged as one of the most popular classes of solvers for multi-objective optimization. Despite their popularity, a lack of guidance exists for how to configure such algorithms for real-world problems, based on the features or contexts of those problems. One context that is important for many real-world problems is that function evaluations are expensive, and so algorithms need to be able to provide adequate convergence on a limited budget (e.g. 500 evaluations). This study contributes to emerging guidance on algorithm configuration by investigating how the convergence of the popular decomposition-based optimizer MOEA/D, over a limited budget, is affected by choice of component-level configuration. Two main aspects are considered: (1) impact of sharing information; (2) impact of normalisation scheme. The empirical test framework includes detailed trajectory analysis, as well as more conventional performance indicator analysis, to help identify and explain the behaviour of the optimizer. Use of neighbours in generating new solutions is found to be highly disruptive for searching on a small budget, leading to better convergence in some areas but far worse convergence in others. The findings also emphasise the challenge and importance of using an appropriate normalisation scheme.

Real-world optimization problems typically include uncertainties over various aspects of the problem formulation. Some existing algorithms are designed to cope with stochastic multiobjective optimization problems, but in order to benchmark them, a proper framework still needs to be established. This paper presents a novel toolkit that generates scalable, stochastic, multiobjective optimization problems. A stochastic problem is generated by transforming the objective vectors of a given deterministic test problem into random vectors. All random objective vectors are bounded by the feasible objective space, defined by the deterministic problem. Therefore, the global solution for the deterministic problem can also serve as a reference for the stochastic problem. A simple parametric distribution for the random objective vector is defined in a radial coordinate system, allowing for direct control over the dual challenges of convergence towards the true Pareto front and diversity across the front. An example for a stochastic test problem, generated by the toolkit, is provided.

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.

This paper presents a new real-world application of evolutionary computation: identifying parameterisations of a theory-driven model that can reproduce alcohol consumption dynamics observed in a population over time. Population alcohol consumption is a complex system, with multiple interactions between economic and social factors and drinking behaviours, the nature and importance of which are not well-understood. Prediction of time trends in consumption is therefore difficult, but essential for robust estimation of future changes in health-related consequences of drinking and for appraising the impact of interventions aimed at changing alcohol use in society. The paper describes a microsimulation approach in which an attitude-behaviour model, Theory of Planned Behaviour, is used to describe the frequency of drinking by individuals. Consumption dynamics in the simulation are driven by changes in the social roles of individuals over time (parenthood, partnership, and paid labour). An evolutionary optimizer is used to identify parameterisations of the Theory that can describe the observed changes in drinking frequency. Niching is incorporated to enable multiple possible parameterisations to be identified, each of which can accurately recreate history but potentially encode quite different future trends. The approach is demonstrated using evidence from the 1979-1985 birth cohort in England between 2003 and 2010.

Many real world optimization problems involve uncertainties. A solution for such a problem is expected to be robust to these uncertainties. Commonly, robustness is attained by choosing the solution's parameters such that the solution's performance is less influenced by negative effects of the uncertain parameters' variations. This robustness may be viewed as a passive robustness, because once the solution's parameters are chosen, the robustness is inherent in the solution and no further action, to suppress the effect of uncertainties, is expected. However, it is acknowledged that enhanced robustness comes at the expense of peak performances. In this paper, active robust optimization is presented as a new robust optimization approach. It considers products that are able to adapt to environmental changes. The enhanced robustness of these solutions is attained by adaptation, which reduces the loss in performance due to environmental changes. A new optimization problem named active robust optimization problem is formulated. The problem amalgamates robust optimization with dynamic optimization to evaluate the performance of a candidate solution, while considering possible environmental conditions. The adaptation's influence on the solution's performance and cost is considered as well. Hence, the problem is formulated as a multiobjective problem that simultaneously aims at low costs and high performance. Since these goals are commonly in conflict, the solution is a set of optimal adaptive solutions. An evolutionary algorithm is proposed in order to evolve this set. An example of optimizing an adaptive optical table is provided. It is shown that an adaptive product, which is an outcome of the suggested approach, may be superior to an equivalent product that is not adaptive.

Preference-inspired co-evolutionary algorithms (PICEAs) are a novel class of population-based approaches for multi-objective optimization. PICEA-g is one realization of PICEAs in which goal vectors are taken as preferences and are co-evolved with the candidate solutions during the search. The performance of PICEA-g is affected by the distribution of the co-evolved goal vectors. In PICEA-g, new goal vectors are generated within pre-defined bounds determined by the ideal and anti-ideal points in each generation. Such bounds are often unknown or at least problem knowledge requires. In this paper, firstly, we analyse the influence of different initial bounds to the performance of PICEA-g. Then, we propose a method, called cutting plane, which adaptively sets proper bounds for the generation of goal vectors, adjusting the search effort toward different objective appropriately, and therefore guide the candidate solutions toward the Pareto optimal front efficiently. Experimental results show that this adaptive approach is effective.

Preference-inspired co-evolutionary algorithm (PICEA) is a novel class of multi-objective evolutionary algorithm. In PICEA, the usual candidate solutions are guided toward the Pareto optimal front by co-evolving a set of decision maker preferences during the search process. PICEA-g is one realization of PICEAs in which goal vectors are taken as preferences. This study points out one limitation of this method -the obtained solutions are distributed unevenly along the Pareto optimal front. To handle this limitation, an improved fitness assignment method is proposed in which the density information of the solutions is considered. Experimental results, in terms of the selected performance metrics, show this improved fitness assignment method is effective.

Decomposition-based methods are an increasingly popular choice for a posteriori multi-objective optimization. However the ability of such methods to describe a trade-off surface depends on the choice of weighting vectors defining the set of subproblems to be solved. Recent adaptive approaches have sought to progressively modify the weighting vectors to obtain a desirable distribution of solutions. This paper argues that adaptation imposes a non-negligible cost -- in terms of convergence -- on decomposition-based algorithms. To test this hypothesis, the process of adaptation is abstracted and then subjected to experimentation on established problems involving between three and 11 conflicting objectives. The results show that adaptive approaches require longer traversals through objectivespace than fixed-weight approaches. Since fixed weights cannot, in general, be specified in advance, it is concluded that the new wave of decomposition-based methods offer no immediate panacea to the well-known conflict between convergence and distribution afflicting Pareto-based a posteriori methods.

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

This paper presents a specialized multiobjective evolutionary algorithm SPEA2 (Strength Pareto Evolutionary Algorithm 2) coupled, separetely, with four placement heuristics for solving the 2D Guillotine Strip Packing Problem. In this study, the problem requires minimization of both the amount of wasted material and the number of independent cuts required by a packing. With the goal of solving this multiobjective version of the problem, the construction phase of the GRASP algorithm (Greedy Randomized Adaptive Search Procedure) is used to generate a portion of the initial population of SPEA2. Four different placement heuristics, Next-Fit, a variation of Next-Fit, Best-Fit and First-Fit, were coupled with SPEA2 and were tested on a set of test data. The results show that the presented methodology is able to generate a good set of candidate solutions for each test problem. A statistical comparison methodology, based on multiobjective principles, was used to compare the four algorithm variants.

Preference-inspired co-evolutionary algorithms (PICEAs) are a new class of approaches which have been demonstrated to perform well on multi-objective problems (MOPs). The good performance of PICEAs is largely due to its clever fitness calculation method which is in a competitive co-evolutionary way. However, this fitness calculation method has a potential limitation. In this work, we analyze this limitation and propose to implement PICEAs within a local structure (LPICEAs). By using the local structure, the benefits of local operations are incorporated into PICEAs. Meanwhile, the limitation of the original fitness calculation method is solved. In details, the candidate solutions are firstly partitioned into several clusters according to a clustering technique. Then the evolutionary operations, i.e. selection-for-survival and genetic-variation are executed on each cluster, separately. To validate the performance of LPICEAs, LPICEAs are compared to PICEAs on some benchmarks functions. Experimental results indicate LPICEAs significantly outperform PICEAs on most of the benchmarks. Moreover, the influence of LPICEAs to the tuning of the parameter k, i.e. the number of clusters used in LPICEAs is studied. The results indicate that the performance of LPICEAs is sensitive to the parameter k.

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.

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.