Many real-world decision problems have multiple objectives. For example, when choosing a medical treatment plan, we want to maximize efficacy of the treatment while minimizing side effects. These objectives typically conflict, e.g., we can increase the efficacy of the treatment, but cause more severe side effects. In this book, we outline how to deal with multiple objectives in decision-theoretic planning and reinforcement learning algorithms. ISBN 9781627059602, 129 pages.
Whether it is in the field of production, logistics, in medicine or biology; everywhere the global optimal solution or the set of global optimal solutions is sought. However, most real-world problems are of nonlinear nature and naturally multimodal which poses severe problems to global optimization. Multimodality, the existence of multiple (local) optima, is regarded as one of the biggest challenges for continuous single-objective problems . A lot of algorithms get stuck searching for the global optimum or are requiring many function evaluations to escape local optima. One of the most popular strategies for dealing with multimodal problems are population-based methods like evolutionary algorithms due to their global search abilities . In this paper we will examine another approach of coping with local traps, namely multiobjectivization. By transforming a single-objective into a multi-objective problem, we aim at exploiting the properties of multi-objective landscapes. So far, the characteristics of single-objective optimization problems have often been directly transferred to the multiobjective domain.
Multi-objective optimization aims at finding trade-off solutions to conflicting objectives. These constitute the Pareto optimal set. In the context of expensive-to-evaluate functions, it is impossible and often non-informative to look for the entire set. As an end-user would typically prefer a certain part of the objective space, we modify the Bayesian multi-objective optimization algorithm which uses Gaussian Processes to maximize the Expected Hypervolume Improvement, to focus the search in the preferred region. The cumulated effects of the Gaussian Processes and the targeting strategy lead to a particularly efficient convergence to the desired part of the Pareto set. To take advantage of parallel computing, a multi-point extension of the targeting criterion is proposed and analyzed.
In spite of the recent quick growth of the Evolutionary Multi-objective Optimization (EMO) research field, there has been few trials to adapt the general variation operators to the particular context of the quest for the Pareto-optimal set. The only exceptions are some mating restrictions that take in account the distance between the potential mates - but contradictory conclusions have been reported. This paper introduces a particular mating restriction for Evolutionary Multi-objective Algorithms, based on the Pareto dominance relation: the partner of a non-dominated individual will be preferably chosen among the individuals of the population that it dominates. Coupled with the BLX crossover operator, two different ways of generating offspring are proposed. This recombination scheme is validated within the well-known NSGA-II framework on three bi-objective benchmark problems and one real-world bi-objective constrained optimization problem. An acceleration of the progress of the population toward the Pareto set is observed on all problems.
In multi-task learning, multiple tasks are solved jointly, sharing inductive bias between them. Multi-task learning is inherently a multi-objective problem because different tasks may conflict, necessitating a trade-off. A common compromise is to optimize a proxy objective that minimizes a weighted linear combination of per-task losses. However, this workaround is only valid when the tasks do not compete, which is rarely the case. To this end, we use algorithms developed in the gradient-based multi-objective optimization literature.