Abstract:This article presents a robust optimization reformulation of the dual response problem developed in response surface methodology. The dual response approach fits separate models for the mean and the variance, and analyzes these two models in a mathematical optimization setting.We use metamodels estimated from experiments with both controllable and environmental inputs.These experiments may be performed with either real or simulated systems; we focus on simulation experiments. For the environmental inputs, clas… Show more
“…This is reasonable, as the economic data are all influenced from the same market developments [63]. Then, the uncertainty set can be assumed as ellipsoidal (for other Φ-divergence uncertainty sets see [62,64]). The constraint can be written as:…”
Coarse woody debris (deadwood) serves as a dwelling space for many rare species, and is therefore a most important factor to ensure diversity in forest ecosystems. However, wood from forest ecosystems is also needed for construction and heating. Therefore, a forest enterprise has to simultaneously incorporate the provision of suitable habitats, as well as the production of wood into their long-term management plans. If the owner wants to fulfil such multiple objectives in an effective way, the providing of ecosystem services can be included in economic planning. Applying computer aided robust optimization techniques, we optimized the provision of deadwood for two exemplary enterprises in East Bavaria, Germany. The results show that high amounts of deadwood provision can cause severe opportunity costs for the forest owner. These costs highly depend on the tree species, the sorting strategy and the time horizon, in which the deadwood objective is reached. Low deadwood targets up to 5 m 3 h a − 1 can be provided most cost-effectively with crown material, while higher targets (20 m 3 h a − 1 and more) are better achieved with heavy timber grades or the provision of total trees. The novelty of our research is the inclusion of deadwood targets in a risk-considering optimization tool on enterprise level. Instead of calculating the economic loss of commercially not-used timber assortments we show a way of deriving the impact of such decisions at stand level on the economic performance of the whole forest enterprise. We were able to derive optimized opportunity costs. These costs can be used as guidelines for necessary incentives to encourage forest owners to incorporate the provision of deadwood into their management.
“…This is reasonable, as the economic data are all influenced from the same market developments [63]. Then, the uncertainty set can be assumed as ellipsoidal (for other Φ-divergence uncertainty sets see [62,64]). The constraint can be written as:…”
Coarse woody debris (deadwood) serves as a dwelling space for many rare species, and is therefore a most important factor to ensure diversity in forest ecosystems. However, wood from forest ecosystems is also needed for construction and heating. Therefore, a forest enterprise has to simultaneously incorporate the provision of suitable habitats, as well as the production of wood into their long-term management plans. If the owner wants to fulfil such multiple objectives in an effective way, the providing of ecosystem services can be included in economic planning. Applying computer aided robust optimization techniques, we optimized the provision of deadwood for two exemplary enterprises in East Bavaria, Germany. The results show that high amounts of deadwood provision can cause severe opportunity costs for the forest owner. These costs highly depend on the tree species, the sorting strategy and the time horizon, in which the deadwood objective is reached. Low deadwood targets up to 5 m 3 h a − 1 can be provided most cost-effectively with crown material, while higher targets (20 m 3 h a − 1 and more) are better achieved with heavy timber grades or the provision of total trees. The novelty of our research is the inclusion of deadwood targets in a risk-considering optimization tool on enterprise level. Instead of calculating the economic loss of commercially not-used timber assortments we show a way of deriving the impact of such decisions at stand level on the economic performance of the whole forest enterprise. We were able to derive optimized opportunity costs. These costs can be used as guidelines for necessary incentives to encourage forest owners to incorporate the provision of deadwood into their management.
“…Notably, there are different optimization approaches available on dual response methodology where some of them are referenced in (Ardakani & Noorossana, 2008;Beyer & Sendhoff, 2007;Nha et al, 2013;Yanikoglu et al, 2016), so here just for instance some common methods of them are mentioned in Table 3.…”
Nowadays, process optimization has been an interest in engineering design for improving the performance and reducing cost. In practice, in addition to uncertainty or noise parameters, a comprehensive optimization model must be able to attend other circumstances which might be imposed in problems under real operational conditions such as dynamic objectives, multiresponses, various probabilistic distribution, discrete and continuous data, physical constraints to design parameters, performance cost, computational complexity and multi-process environment. The main goal of this paper is to give a general overview on topics with brief systematic review and concise discussions about the recent development on comprehensive robust design optimization methods under hybrid aforesaid circumstances. Both optimization methods of mathematical programming based on Taguchi approach and robust optimization based on scenario sets are briefly described. Metamodels hybrid robust design is discussed as an appropriate methodology to decrease computational complexity in problems under uncertainty. In this context, the authors' policy is to choose important topics for giving a systematic picture to those who wish to be more familiar with recent studies about robust design optimization hybrid metamodels, also by attending real circumstances in practice. In particular, production and project management are considered as two important methodologies that could be improved by applications of advanced robust design combining with metamodel methods.
“…As a consequence, it searches for an optimal set of input variables to optimize the response by using a set of designed experiments. In the past few years, several robust DRSO techniques have been developed [12,13]. Yanikoglu et al (2016) introduced Taguchi's Robust Parameter Design approach into DRSO to develop a method that uses only experimental data, and it can yield a solution that is robust against ambiguity in the probability of inputs [12].…”
This paper proposes a novel statistical approach for blending source waters in a public water distribution system to improve water quality (WQ) by minimizing the release of heavy metals (HMR). Normally, introducing a new source changes the original balanced environment and causes adverse effects on the WQ in a water distribution system. One harmful consequence of blending source water is the release of heavy metals, including lead, copper and iron. Most HMR studies focus on the forecasting of unfavorable effects using precise and complicated nonlinear equations. This paper uses a statistical multiple objectives optimization, namely Multiple Source Waters Blending Optimization (MSWBO), to find optimal blending ratios of source waters for minimizing three HMRs in a water supply system. In this paper, three response surface equations are applied to describe the reaction kinetics of HMR, and three dual response surface equations are used to track the standard deviations of the three response surface equations. A weighted sum method is performed for the multi-objective optimization problem to minimize three HMRs simultaneously. Finally, the experimental data of a pilot distribution system is used in the proposed statistical approach to demonstrate the model's applicability, computational efficiency, and robustness.Keywords: water quality (WQ); blending; release of heavy metals (HMR); dual response surface optimization (DRSO); multiple source waters blending optimization (MSWBO)
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.