Pareto optimization with small data by learning across common objective spaces.

In multi-objective optimization, it becomes prohibitively difficult to cover the Pareto front (PF) as the number of points scales exponentially with the dimensionality of the objective space. The challenge is exacerbated in expensive optimization domains where evaluation data is at a premium. To overcome insufficient representations of PFs, Pareto estimation (PE) invokes inverse machine learning to map preferred but unexplored regions along the front to the Pareto set in decision space. However, the accuracy of the inverse model depends on the training data, which is inherently scarce/small given high-dimensional/expensive objectives. To alleviate this small data challenge, this paper marks a first study on multi-source inverse transfer learning for PE. A method to maximally utilize experiential source tasks to augment PE in the target optimization task is proposed. Information transfers between heterogeneous source-target pairs is uniquely enabled in the inverse setting through the unification provided by common objective spaces. Our approach is tested experimentally on benchmark functions as well as on high-fidelity, multidisciplinary simulation data of composite materials manufacturing processes, revealing significant gains to the predictive accuracy and PF approximation capacity of Pareto set learning. With such accurate inverse models made feasible, a future of on-demand human-machine interaction facilitating multi-objective decisions is envisioned.

Cognizant Multitasking in Multiobjective Multifactorial Evolution: MO-MFEA-II.

Humans have the ability to identify recurring patterns in diverse situations encountered over a lifetime, constantly understanding relationships between tasks and efficiently solving them through knowledge reuse. The capacity of artificial intelligence systems to mimic such cognitive behaviors for effective problem solving is deemed invaluable, particularly when tackling real-world problems where speed and accuracy are critical. Recently, the notion of evolutionary multitasking has been explored as a means of solving multiple optimization tasks simultaneously using a single population of evolving individuals. In the presence of similarities (or even partial overlaps) between high-quality solutions of related optimization problems, the resulting scope for intertask genetic transfer often leads to significant performance speedup-as the cost of re-exploring overlapping regions of the search space is reduced. While multitasking solvers have led to recent success stories, a known shortcoming of existing methods is their inability to adapt the extent of transfer in a principled manner. Thus, in the absence of any prior knowledge about the relationships between optimization functions, a threat of predominantly negative (harmful) transfer prevails. With this in mind, this article presents a realization of a cognizant evolutionary multitasking engine within the domain of multiobjective optimization. Our proposed algorithm learns intertask relationships based on overlaps in the probabilistic search distributions derived from data generated during the course of multitasking-and accordingly adapts the extent of genetic transfers online. The efficacy of the method is substantiated on multiobjective benchmark problems as well as a practical case study of knowledge transfers from low-fidelity optimization tasks to substantially reduce the cost of high-fidelity optimization.

A Simple and Fast Hypervolume Indicator-Based Multiobjective Evolutionary Algorithm.

To find diversified solutions converging to true Pareto fronts (PFs), hypervolume (HV) indicator-based algorithms have been established as effective approaches in multiobjective evolutionary algorithms (MOEAs). However, the bottleneck of HV indicator-based MOEAs is the high time complexity for measuring the exact HV contributions of different solutions. To cope with this problem, in this paper, a simple and fast hypervolume indicator-based MOEA (FV-MOEA) is proposed to quickly update the exact HV contributions of different solutions. The core idea of FV-MOEA is that the HV contribution of a solution is only associated with partial solutions rather than the whole solution set. Thus, the time cost of FV-MOEA can be greatly reduced by deleting irrelevant solutions. Experimental studies on 44 benchmark multiobjective optimization problems with 2-5 objectives in platform jMetal demonstrate that FV-MOEA not only reports higher hypervolumes than the five classical MOEAs (nondominated sorting genetic algorithm II (NSGAII), strength Pareto evolutionary algorithm 2 (SPEA2), multiobjective evolutionary algorithm based on decomposition (MOEA/D), indicator-based evolutionary algorithm, and S-metric selection based evolutionary multiobjective optimization algorithm (SMS-EMOA)), but also obtains significant speedup compared to other HV indicator-based MOEAs.