We consider the problem of multi-objective (MO) blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto-set of solutions by minimizing the number of function evaluations. For example, in hardware design optimization, we need to find the designs that trade-off performance, energy, and area overhead using expensive simulations. We propose a novel approach referred to as Max-value Entropy Search for Multi-objective Optimization (MESMO) to solve this problem. MESMO employs an output-space entropy based acquisition function to efficiently select the sequence of inputs for evaluation for quickly uncovering high-quality solutions. We also provide theoretical analysis to characterize the efficacy of MESMO.
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.
This paper deals with these problems by using a new decomposition-based algorithm called: "Fractal geometric decomposition base algorithm" (FDA). It is a deterministic metaheuristic developed to solve large-scale continuous optimization problems . It can be noticed, that we call large scale problems those having the dimension greater than 1000. In this research, we are interested in using FDA to deal with MOPs because in the literature decomposition based algorithms have been with more less success applied to solve these problems, their main problem is related to their complexity. In this work, the goal is to deal with this complexity problem by keeping the same level of efficiency. FDA is based on "divide-and-conquer" paradigm where the sub-regions are hyperspheres rather than hypercubes on classical approaches. In order to identify the Pareto optimal solutions, we propose to extend FDA using the scalarization approach. We called the proposed algorithm Mo-FDA.