Bayesian Global Optimization (BGO) is a very efficient technique to optimize expensive evaluation problems. However, the application domain is limited to continuous search spaces when using a BGO... Show moreBayesian Global Optimization (BGO) is a very efficient technique to optimize expensive evaluation problems. However, the application domain is limited to continuous search spaces when using a BGO algorithm. To solve mixed integer problems with a BGO algorithm, this paper adapts the heterogeneous distance function to construct the Kriging models and applies these new Kriging models in Multi-objective Bayesian Global Optimization (MOBGO). The proposed mixed integer MOBGO algorithm and the traditional MOBGO algorithm are compared on three mixed integer multi-objective optimization problems (MOP), w.r.t. the mean value of the hypervolume (HV) and the related standard deviation. Show less
Blom, K. van der; Yang, K.; Bäck, T.; Emmerich, M.T.M. 2019
Many problems are of a mixed integer nature, rather than being restricted to a single variable type. Although mixed integer algorithms exist for the single-objective case, work on the multi... Show moreMany problems are of a mixed integer nature, rather than being restricted to a single variable type. Although mixed integer algorithms exist for the single-objective case, work on the multi-objective case remains limited. Evolution strategies are stochastic optimisation algorithms that feature step size adaptation mechanisms and are typically used in continuous domains. More recently they were generalised to mixed integer problems. In this work, first steps are taken towards extending the single-objective mixed integer evolution strategy for the multi-objective case. First results are promising, but step size adaptation for the multi-objective case can likely be improved. Show less
Terrestrial plants may experience nutrient and oxygen stress when they are submerged, and increases in flooding are anticipated with climate change. It has been well reported that plants usually... Show moreTerrestrial plants may experience nutrient and oxygen stress when they are submerged, and increases in flooding are anticipated with climate change. It has been well reported that plants usually shift biomass allocation and produce more roots in response to nutrient deficiency. However, it is unclear whether plants experiencing oxygen deficiency stimulate biomass allocation to roots to enhance nutrient absorption, similar to how plants experiencing nutrient deficiency behave. We investigated the responses of the terrestrial species Alternanthera philoxeroides, upon root flooding, to nutrient versus dissolved oxygen deficiency in terms of plant growth, biomass allocation, root production, root efficiency (plant growth sustained per unit root surface area), and root aerenchyma formation. Both nutrient and dissolved oxygen deficiency hampered the growth of root-flooded plants. As expected, plants experiencing nutrient deficiency increased biomass allocation to roots and exhibited lower root efficiency; in contrast, plants experiencing dissolved oxygen deficiency decreased biomass allocation to roots but achieved higher root efficiency. The diameter of aerenchyma channels in roots were enlarged in plants experiencing dissolved oxygen deficiency but did not change in plants experiencing nutrient deficiency. The widening of aerenchyma channels in roots could have improved the oxygen status and thereby the nutrient absorption capability of roots in low oxygen environments, which might benefit the plants to tolerate flooding. Show less
Prognostics and Health Management (PHM) attracts increasing interest of many researchers due to its potentially important applications in diverse disciplines and industries. In general, PHM systems... Show morePrognostics and Health Management (PHM) attracts increasing interest of many researchers due to its potentially important applications in diverse disciplines and industries. In general, PHM systems use real-time and historical state information of subsystems and components of the operating systems to provide actionable information, enabling intelligent decision-making for improved performance, safety, reliability, and maintainability. Every year, a substantial number of papers in this area including theory and practical applications, appear in academic journals, conference proceedings and technical reports. This paper aims to summarize and review researches, developments and recent contributions in PHM for automotive- and aerospace industries. It can also be considered as the starting point for researchers and practitioners in general to assist them through PHM implementation and help them to accomplish their work more easily. Show less
The Expected Hypervolume Improvement (EHVI) is a frequently used infill criterion in Multi-Objective Bayesian Global Optimization (MOBGO), due to its good ability to lead the exploration. Recently,... Show moreThe Expected Hypervolume Improvement (EHVI) is a frequently used infill criterion in Multi-Objective Bayesian Global Optimization (MOBGO), due to its good ability to lead the exploration. Recently, the computational complexity of EHVI calculation is reduced to O(n log n) for both 2-D and 3-D cases. However, the optimizer in MOBGO still requires a significant amount of time, because the calculation of EHVI is carried out in each iteration and usually tens of thousands of the EHVI calculations are required. This paper derives a formula for the Expected Hypervolume Improvement Gradient (EHVIG) and proposes an efficient algorithm to calculate EHVIG. The new criterion (EHVIG) is utilized by two different strategies to improve the efficiency of the optimizer discussed in this paper. Firstly, it enables gradient ascent methods to be used in MOBGO. Moreover, since the EHVIG of an optimal solution should be a zero vector, it can be regarded as a stopping criterion in global optimization, e.g., in Evolution Strategies. Empirical experiments are performed on seven benchmark problems. The experimental results show that the second proposed strategy, using EHVIG as a stopping criterion for local search, can outperform the normal MOBGO on problems where the optimal solutions are located in the interior of the search space. For the ZDT series test problems, EHVIG still can perform better when gradient projection is applied. Show less
A common method to solve expensive function evaluation problem is using Bayesian Global Optimization, instead of Evolutionary Algorithms. However, the execution time of multi-objective... Show moreA common method to solve expensive function evaluation problem is using Bayesian Global Optimization, instead of Evolutionary Algorithms. However, the execution time of multi-objective Bayesian Global Optimization (MOBGO) itself is still too long, even though it only requires a few function evaluations. The reason for the high cost of MOBGO is two-fold: on the one hand, MOBGO requires an infill criterion to be calculated many times, but the computational complexity of an infill criterion has so far been very high. Another reason is that the optimizer, which aims at searching for an optimal solution according to the surrogate models, is not sufficiently efficient. The main contributions of this thesis consist of 1. Decreased the computational complexity of a well-known infill criteria, Expected Hypervolume Improvement, into $n log (n)$ both in 2-D and 3-D cases; 2. Proposed a new criterion, Truncated Expected Hypervolume Improvement, to make full use of a-priori knowledge of objective functions, whenever it is available; 3. Proposed another infill criterion, Expected Hypervolume Improvement Gradient, to improve the convergence of the optimizer in MOBGO. Show less