Multi-objective optimization shapes ecological variation

Ecological systems contain a huge amount of quantitative variation between and within species and locations, which makes it difficult to obtain unambiguous verification of theoretical predictions. Ordinary experiments consider just a few explanatory factors and are prone to providing oversimplified answers because they ignore the complexity of the factors that underlie variation. We used multi-objective optimization (MO) for a mechanistic analysis of the potential ecological and evolutionary causes and consequences of variation in the life-history traits of a species of moth. Optimal life-history solutions were sought for environmental conditions where different life stages of the moth were subject to predation and other known fitness-reducing factors in a manner that was dependent on the duration of these life stages and on variable mortality rates. We found that multi-objective optimal solutions to these conditions that the moths regularly experience explained most of the life-history variation within this species. Our results demonstrate that variation can have a causal interpretation even for organisms under steady conditions. The results suggest that weather and species interactions can act as underlying causes of variation, and MO acts as a corresponding adaptive mechanism that maintains variation in the traits of organisms

A constrained multi-objective surrogate-based optimization algorithm

Surrogate models or metamodels are widely used in the realm of engineering for design optimization to minimize the number of computationally expensive simulations. Most practical problems often have conflicting objectives, which lead to a number of competing solutions which form a Pareto front. Multi-objective surrogate-based constrained optimization algorithms have been proposed in literature, but handling constraints directly is a relatively new research area. Most algorithms proposed to directly deal with multi-objective optimization have been evolutionary algorithms (Multi-Objective Evolutionary Algorithms -MOEAs). MOEAs can handle large design spaces but require a large number of simulations, which might be infeasible in practice, especially if the constraints are expensive. A multi-objective constrained optimization algorithm is presented in this paper which makes use of Kriging models, in conjunction with multi-objective probability of improvement (PoI) and probability of feasibility (PoF) criteria to drive the sample selection process economically. The efficacy of the proposed algorithm is demonstrated on an analytical benchmark function, and the algorithm is then used to solve a microwave filter design optimization problem

A Bayesian approach to constrained single- and multi-objective optimization

This article addresses the problem of derivative-free (single- or multi-objective) optimization subject to multiple inequality constraints. Both the objective and constraint functions are assumed to be smooth, non-linear and expensive to evaluate. As a consequence, the number of evaluations that can be used to carry out the optimization is very limited, as in complex industrial design optimization problems. The method we propose to overcome this difficulty has its roots in both the Bayesian and the multi-objective optimization literatures. More specifically, an extended domination rule is used to handle objectives and constraints in a unified way, and a corresponding expected hyper-volume improvement sampling criterion is proposed. This new criterion is naturally adapted to the search of a feasible point when none is available, and reduces to existing Bayesian sampling criteria---the classical Expected Improvement (EI) criterion and some of its constrained/multi-objective extensions---as soon as at least one feasible point is available. The calculation and optimization of the criterion are performed using Sequential Monte Carlo techniques. In particular, an algorithm similar to the subset simulation method, which is well known in the field of structural reliability, is used to estimate the criterion. The method, which we call BMOO (for Bayesian Multi-Objective Optimization), is compared to state-of-the-art algorithms for single- and multi-objective constrained optimization