Linear equalities in blackbox optimization

2014 ◽  
Vol 61 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Charles Audet ◽  
Sébastien Le Digabel ◽  
Mathilde Peyrega
2020 ◽  
Vol 34 (06) ◽  
pp. 10044-10052 ◽  
Author(s):  
Syrine Belakaria ◽  
Aryan Deshwal ◽  
Nitthilan Kannappan Jayakodi ◽  
Janardhan Rao Doppa

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 while 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 uncertainty-aware search framework referred to as USeMO to efficiently select the sequence of inputs for evaluation to solve this problem. The selection method of USeMO consists of solving a cheap MO optimization problem via surrogate models of the true functions to identify the most promising candidates and picking the best candidate based on a measure of uncertainty. We also provide theoretical analysis to characterize the efficacy of our approach. Our experiments on several synthetic and six diverse real-world benchmark problems show that USeMO consistently outperforms the state-of-the-art algorithms.


2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Ibrahim M. Chamseddine ◽  
Michael Kokkolaras

Previous work in air transportation system-of-systems (ATSoSs) design optimization considered integrated aircraft sizing, fleet allocation, and route network configuration. The associated nested multidisciplinary formulation posed a numerically challenging blackbox optimization problem; therefore, direct search methods with convergence properties were used to solve it. However, the complexity of the blackbox impedes greatly the solution of larger-scale problems, where the number of considered nodes in the route network is high. The research presented here adopts a rule-based route network design inspired by biological transfer principles. This bio-inspired approach decouples the network configuration problem from the optimization loop, leading to significant numerical simplifications. The usefulness of the bio-inspired approach is demonstrated by comparing its results to those obtained using the nested formulation for a 15 city network. We then consider introduction of new aircraft as well as a larger problem with 20 cities.


2012 ◽  
Vol 27 (4-5) ◽  
pp. 613-624 ◽  
Author(s):  
Charles Audet ◽  
J. E. Dennis ◽  
Sébastien Le Digabel

2021 ◽  
Vol 79 (1) ◽  
pp. 1-34
Author(s):  
Charles Audet ◽  
Kwassi Joseph Dzahini ◽  
Michael Kokkolaras ◽  
Sébastien Le Digabel

Author(s):  
Yi Ren ◽  
Clayton Scott ◽  
Panos Y. Papalambros

We examine the problem of eliciting the most preferred designs of a user from a finite set of designs through iterative pairwise comparisons presented to the user. The key challenge is to select proper queries (i.e., presentations of design pairs to the user) in order to minimize the number of queries. Previous work formulated elicitation as a blackbox optimization problem with comparison (binary) outputs, and a heuristic search algorithm similar to Efficient Global Optimization (EGO) was used to solve it. In this paper, we propose a query algorithm that minimizes the expected number of queries directly, assuming that designs are embedded in a known space and user preference is a linear function of design variables. Besides its theoretical foundation, the proposed algorithm shows empirical performance better than the EGO search algorithm in both simulated and real-user experiments. A novel approximation scheme is also introduced to alleviate the scalability issue of the proposed algorithm, making it tractable for a large number of design variables or of candidate designs.


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