Stochastic Multi-objective Optimization Research Articles

Stochastic multi-objective performance optimization of an in-stream woodchip denitrifying bioreactor

Woodchip denitrifying bioreactors (WDBs) that target filtration of nitrate from farm drainage water are gaining recognition as a tool for tackling the issue of diffuse nitrate pollution from agricultural landscapes. Whilst the hydraulic regime and concentration of nitrate in the drainage water constitute two fundamental environmental variables that determine the size of a denitrifying bioreactor, the issue of over- or under-treatment of water that might otherwise promote undesirable pollution swapping phenomena and construction costs also need to be factored into the overall design process. Conventional methods for optimizing the design of denitrifying bioreactors generally rely on deterministic models, even though many of the design parameters are not known with confidence. In this work we apply an alternative design philosophy and demonstrate how the bioreactor design process can be improved through application of stochastic methods. The design aspect of an ‘in-stream’ WDB planned for installation on a farm in New Zealand is structured as a multi-objective performance optimization problem that is solved in a stochastic framework, using freely available open source tools. Uncertainty considerations regarding values of physical parameters that govern bioreactor performance are incorporated into the assessment, from which a Pareto set of optimal designs was obtained. A 75 m long bioreactor of 1.5 m height was selected as the preferred choice from the optimal set of design solutions. Assuming a 10-year operational life, it is predicted the cost of nitrate removal by the planned denitrifying bioreactor will be NZ$9.70/kg-N (approx.US$6.60/kg-N).

Asymptotic convergence of stationary points of stochastic multiobjective programs with parametric variational inequality constraint via SAA approach

We consider the sample average approximation method for a stochastic multiobjective programming problem constrained by parametric variational inequalities. The first order necessary conditions for the original problem and its sample average approximation (SAA) problem are established under constraint qualifications. By graphical convergence of set-valued mappings, the stationary points of the SAA problem converge to the stationary points of the true problem when the sample size tends to infinity. Under proper assumptions, the convergence of optimal solutions of SAA problems is also obtained. The numerical experiments on stochastic multiobjective optimization problems with variational inequalities are given to illustrate the efficiency of SAA estimators.

Wind turbine blade geometry design based on multi-objective optimization using metaheuristics

The application of evolutionary algorithms to wind turbine blade design can be interesting, by reducing the number of aerodynamic-to-structural design loops in the conventional design process, hence reducing the design time and cost. Recent developments showed satisfactory results with this approach, mostly combining genetic algorithms with the blade element momentum theory. The general objective of the present work is to define and evaluate a design methodology for the rotor blade geometry in order to maximize the energy production of wind turbines and minimize the mass of the blade itself, using for that purpose stochastic multi-objective optimization methods. An optimization benchmark problem was proposed, which represents the wind conditions and present wind turbine concepts found in Brazil. A variable speed pitch-controlled 2.5 MW direct-drive synchronous generator turbine with a rotor diameter of 120 m was chosen as concept. Four different multi-objective evolutionary algorithms were selected for evaluation in solving this benchmark problem: Non-dominated Sorting Genetic Algorithm version II (NSGA-II), Quantum-inspired Multi-objective Evolutionary Algorithm (QMEA), Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D), and Multi-objective Optimization Differential Evolution Algorithm (MODE). Detailed analysis of the best compromise blade design showed that the output of the design methodology is feasible for manufacturing.

A stochastic multi-objective location-allocation-routing problem for tire supply chain considering sustainability aspects and quantity discounts

Abstract Sustainable supply chain is widely studied and investigated in various papers due to the presence of increasing environmental pollution and social risks caused by manufactories, transportation vehicles, and unused and defective products spilled into the nature; e.g. tires. This paper designs a closed loop supply chain network taking into consideration sustainability aspects and quantity discounts under uncertainty. To this end, a stochastic multi-objective optimization for supplier selection and location-allocation-routing problems is formulated. The first and second objectives of the model attempt to minimize total costs and environmental emission effects, respectively. The third objective seeks to maximize the responsiveness of the integrated network. Also, ɛ-constraint method is applied to solve the proposed framework. To verify the model, a real-world case study placed in Iran is provided and a sensitivity analysis is performed to measure the efficiency of the proposed framework. Results confirm the efficiency of the proposed approach, showing the practicability of the proposed approach for managers. Finally, future research directions are discussed.

Stochastic multi-objective optimisation of the cure process of thick laminates

A stochastic multi-objective cure optimisation methodology is developed in this work and applied to the case of thick epoxy/carbon fibre laminates. The methodology takes into account the uncertainty in process parameters and boundary conditions and minimises the mean values and standard deviations of cure time and temperature overshoot. Kriging is utilised to construct a surrogate model of the cure substituting Finite Element (FE) simulation for computational efficiency reasons. The surrogate model is coupled with Monte Carlo and integrated into a stochastic multi-objective optimisation framework based on Genetic Algorithms. The results show a significant reduction of about 40% in temperature overshoot and cure time compared to standard cure profiles. This reduction is accompanied by a reduction in variability by about 20% for both objectives. This highlights the opportunity of replacing conventional cure schedules with optimised profiles achieving significant improvement in both process efficiency and robustness.

Multi-Objective Programming for Supplier Selection and Order Allocation Under Disruption Risk and Demand, Quality, and Delay Time Uncertainties

The purpose of this article is to develop a new stochastic multi objective optimization model to mitigate disruption risks while simultaneously addressing operational risks as well. Indeed, this model considers five objective functions for selecting a set of suppliers considering disruption risk and stochastic demand, quality, and delay time. The authors use two types of risk evaluation models: value-at-risk (VaR) and conditional value-at-risk (CVaR). Two examples are given to illustrate our model and two solution methods are compared and tested.

Multi-Objective Optimal Design of a Building Envelope and Structural System Using Cyber-Physical Modeling in a Wind Tunnel

This paper explores the use of a cyber-physical systems (CPS) “loop-in-the-model” approach to optimally design the envelope and structural system of low-rise buildings subject to wind loads. Both the components and cladding (C&C) and the main wind force resisting system (MWFRS) are considered through multi-objective optimization. The CPS approach combines the physical accuracy of wind tunnel testing and efficiency of numerical optimization algorithms to obtain an optimal design. The approach is autonomous: experiments are executed in a boundary layer wind tunnel (BLWT), sensor feedback is monitored and analyzed by a computer, and optimization algorithms dictate physical changes to the structural model in the BLWT through actuators. To explore a CPS approach to multi-objective optimization, a low-rise structure with a parapet wall of variable height is considered. In the BLWT, servo-motors are used to adjust the parapet to a particular height. Parapet walls alter the location of the roof corner vortices, reducing suction loads on the windward facing roof corners and edges, a C&C design load. At the same time, parapet walls increase the surface area of the building, leading to an increase in demand on the MWFRS. A combination of non-stochastic and stochastic optimization algorithms were implemented to minimize the magnitude of suction and positive pressures on the roof of a low-rise building model, followed by stochastic multi-objective optimization to simultaneously minimize the magnitude of suction pressures and minimize base shear. Experiments were conducted at the University of Florida Experimental Facility (UFEF) of the National Science Foundation’s (NSF) Natural Hazard Engineering Research Infrastructure (NHERI) program.

A stochastic multi-objective model based on the classical optimal search model for searching for the people who are lost in response stage of earthquake

Although after an earthquake the injured person should be equipped with food, shelter and hygiene activities, before anything must be searched and rescued. But disaster management (DM) has focused heavily on emergency logistics and developing an effective strategy for search operations has been largely ignored. In this study, we suggest a stochastic multi-objective optimization model to allocate resource and time for searching the individuals who are trapped in disaster regions. Since in disaster conditions the majority of information is uncertain, our model assumes ambiguity for the locations where the missing people may exist. Fortunately, the suggested model fits nicely into the structure of the classical optimal search model. Hence, we use a stochastic dynamic programming approach to solve this problem. On the other hand, through a computational experiment, we have observed that this model needs heavy computation. Therefore, we reformulate the suggested search model as a multi-criteria decision making (MCDM) problem and employ two efficient MCDM techniques, i.e. TOPSIS and COPRAS to tackle this ranking problem. Consequently, the computational effort is decreased significantly and a promising solution is produced.

PID2018 Benchmark Challenge: Multi-Objective Stochastic Optimization Algorithm

This paper presents a multi-objective stochastic optimization method for tuning of the controller parameters of Refrigeration Systems based on Vapour Compression. Stochastic Multi Parameter Divergence Optimization (SMDO) algorithm is modified for minimization of the Multi Objective function for optimization process. System control performance is improved by tuning of the PI controller parameters according to discrete time model of the refrigeration system with multi objective function by adding conditional integral structure that is preferred to reduce the steady state error of the system. Simulations are compared with existing results via many graphical and numerical solutions.

Stochastic multi-objective optimization of combined heat and power economic/emission dispatch

Abstract In this paper, an optimization technique based on time-varying acceleration particle swarm optimization (TVAC-PSO) is applied for optimizing economic dispatch and emission reduction problems in a system consisting of CHP units. At first algorithm is used for deterministic model that for comparison with previous works. Besides, its convergence speed is adequately high. Then Monte Carlo method is implemented to solve the stochastic model providing real situation. In the Monte Carlo simulation you have a range of values as a result, and you are able to understand the risk and uncertainty in the model. Deterministic models used for conventional economic dispatch problems are not able to address some real conditions in practical applications. Deterministic models of power system applications are incapable to express the uncertainties that come from energy demand and supply of intermittent renewable systems. Due to the presence of these various uncertain variables stochastic attitude is inevitable in practical applications. Therefore, solving economic dispatch and emission reduction problems simultaneously and stochastically that is the main objective of this paper has a great level of importance. For modeling accurately, both power transmission losses and nonlinear fuel cost function are considered. The proposed method is applied to a 7-unit test system.

Mathematical Methods for the Multi-Criteria Optimization of Structure and Management of Energy Efficient Gas Supply Chains

While the problem of the optimal operation of gas networks has been the object of a large amount of research work, the inclusion of market mechanisms and environmental issues, leading to more complex models resulting in stochastic multiobjective optimization algorithms, has not been considered in its generality. The goal of this article is double: to identify the most general models and algorithms, capable of providing a complete decision support tool, and to show how simplified models can be obtained from them if the complexity of the network makes it necessary to reduce the computational burden.

Balancing exploration, uncertainty and computational demands in many objective reservoir optimization

Abstract Reservoir operations are central to our ability to manage river basin systems serving conflicting multi-sectoral demands under increasingly uncertain futures. These challenges motivate the need for new solution strategies capable of effectively and efficiently discovering the multi-sectoral tradeoffs that are inherent to alternative reservoir operation policies. Evolutionary many-objective direct policy search (EMODPS) is gaining importance in this context due to its capability of addressing multiple objectives and its flexibility in incorporating multiple sources of uncertainties. This simulation-optimization framework has high potential for addressing the complexities of water resources management, and it can benefit from current advances in parallel computing and meta-heuristics. This study contributes a diagnostic assessment of state-of-the-art parallel strategies for the auto-adaptive Borg Multi Objective Evolutionary Algorithm (MOEA) to support EMODPS. Our analysis focuses on the Lower Susquehanna River Basin (LSRB) system where multiple sectoral demands from hydropower production, urban water supply, recreation and environmental flows need to be balanced. Using EMODPS with different parallel configurations of the Borg MOEA, we optimize operating policies over different size ensembles of synthetic streamflows and evaporation rates. As we increase the ensemble size, we increase the statistical fidelity of our objective function evaluations at the cost of higher computational demands. This study demonstrates how to overcome the mathematical and computational barriers associated with capturing uncertainties in stochastic multiobjective reservoir control optimization, where parallel algorithmic search serves to reduce the wall-clock time in discovering high quality representations of key operational tradeoffs. Our results show that emerging self-adaptive parallelization schemes exploiting cooperative search populations are crucial. Such strategies provide a promising new set of tools for effectively balancing exploration, uncertainty, and computational demands when using EMODPS.

Whole blood or apheresis donations? A multi-objective stochastic optimization approach

In the blood supply chain, several alternative technologies are available for collection and processing. These technologies differ in cost and efficiency: for example, collection by apheresis requires very expensive machines but the yield of blood products is considerably greater than whole blood collection. Blood centre managers are faced with the difficult strategic problem of choosing the best combination of technologies, as well as the equally difficult operational problem of assigning donors to collection methods. These decisions are complex since so many factors have to be taken into account, including stochastic demand, blood group compatibilities, donor availability, the proportions of blood types in both donor and recipient populations, fixed and variable costs, and process efficiencies. The use of deterministic demand forecasts is rarely adequate and a robust decision must consider uncertainty and variability in demand as well as trade-offs between several potentially conflicting objectives. This paper presents a multi-objective stochastic integer linear programming model to support such decisions. The model treats demand as stochastic and seeks to optimize two objectives: the total cost and the number of donors required. To solve this problem, we apply a novel combination of Sample Average Approximation and the Augmented Epsilon-Constraint algorithm. This approach is illustrated using real data from Bogota, Colombia.

Unintentional drifts during quiet stance and voluntary body

Estimation of low failure probabilities in high dimensional structural reliability problems generally involves a trade-off between computational effort and accuracy of the estimate, whether efficient sampling techniques have been employed or not. While a substantial effort continues to be made by the community to develop and benchmark new and efficient sampling schemes, the limits of performance of a given algorithm, e.g., what is the best attainable accuracy of the method for a fixed computational effort and if that is good enough, have not received comparable attention. However, such insights could prove valuable in making the right choice in solving a computationally demanding reliability problem. In a multi-objective stochastic optimization formulation, these questions yield the so-called Pareto front or the set of non-dominated solutions: solutions that cannot be further improved without worsening at least one objective. Posteriori user defined preferences can then be applied to rank members of the Pareto set and obtain the best strategy. We take up two classes of variance-reducing algorithms – importance sampling (IS) and subset simulations (SS) – and apply them to a range of benchmarked reliability problems of various size and complexity to bring out the issue of optimality and trade-off between accuracy and effort. The design variables are variously of categorical, discrete as well as continuous types and the stochastic multi-objective optimization without recourse is solved using Genetic Algorithms. In each case, we ascertain the best possible accuracies that a given method can achieve and identify the corresponding design variables. We find that the proposal pdf does have an effect on the efficiency of SS, the FORM design point is not always the best sampling location in IS and setting the sensitivity parameter associated with Adaptive Importance Sampling at 0.5 does not guarantee optimal performance. In addition to this the benefits of using SS for high dimensional problems are reinforced. We also show that the Pareto fronts corresponding to different methods can intersect indicating that more is not always better and different solution techniques for the same problem may be required in different computational regimes.

Addressing design preferences via auto-associative connectionist models: Application in sustainable architectural Façade design

Abstract Truly successful designs are characterized by both satisfaction of design goals and the presence of desirable physical features. Experienced design professionals are able to exercise their cognition to satisfy both aspects to a high degree. However, complex design tasks represent challenges for human cognition, and as such computational decision support systems emerge as a relevant topic. We present a computational decision support framework for treating preferences related to physical design features. The proposed framework is based on auto-associative machine learning models that inductively learn relationships between design features characterizing highly performing designs. The knowledge matter to be learned is derived through multi-objective stochastic optimization. The resulting auto-associative models are excited with a preference vector containing a favorable composition of design features. The models are able to alleviate those relationships that result in shortcomings of performance. The model thus outputs well performing design solution, where preferences pertaining to physical features are also satisfied, to the extent possible. The paper focuses on the applicability of the proposed approach in architectural design, as an exceptional example of complex design, discusses methods to evaluate model performance, and validates the proposed method through an application focusing on the design of a sustainable facade.

Stochastic optimization methods for ship resistance and operational efficiency via CFD

Hull-form stochastic optimization methods are presented and evaluated for resistance reduction and operational efficiency (operability), addressing stochastic sea state and operations. The cost/benefit analysis of the optimization procedure is presented by comparison of four hierarchical problems, from stochastic most general to deterministic least general. The parent hull is a high-speed catamaran, with geometrical constraints for maximum variation of length, beam, draft, and displacement. Problem 1 is used as a benchmark for the evaluation of the other problem formulations and is defined as a multi-objective stochastic optimization for resistance and operability, considering stochastic sea state and speed, but limited to head waves. Problem 2 is a multi-objective stochastic optimization for resistance and motions at fixed sea state and speed. Problem 3 is a multi-objective deterministic optimization for resistance and motions using a single regular wave at fixed speed. Problem 4 is a single-objective deterministic optimization for calm-water resistance at fixed speed. The design optimization is based on hull-form modifications by the Karhunen-Loeve expansion of a free-form deformation, URANS-based CFD simulations, regular wave approximations for irregular waves, metamodels and multi-objective particle swarm. The design optimization achieves an 8.7, 23, 53, and 10% average improvements for problems 1, 2, 3, and 4, respectively. Comparing to problem 1, problem 2, 3, 4 optimized designs have average performances 1, 2.1 and 1.7% worse, respectively. The most efficient problem, from the computational cost/benefit viewpoint, is problem 3. Nevertheless, problem 1 is needed to evaluate and compare the stochastic performance of the designs and finally assess the optimization cost/benefit.

Analysis, control and design of speed control of electric vehicles delayed model: multi‐objective fuzzy fractional‐order controller

The purpose of this study is to suggest an optimal multi-objective fuzzy fractional-order controller (MOFFOPID) for the speed control of EV systems with time-delay. It is presumed that while the EV is in movement, the armature winding resistance of the direct current (DC) motor varies with time due to temperature changes and this makes it impossible to develop an accurate dynamic model for an EV system. Consequently, in order to have a fast and accurate tracking of the set-point, besides a smooth control signal, a new multi-objective stochastic optimisation is used for the online adjustment of the parameters of MOFFOPID controller. Moreover, a comparison is made between the results of the current study and those of some of the most recent studies on the same topic, which have used online multi-objective PI and online multi-objective fuzzy PI, to assess the efficiency of the suggested controller. Finally, the experimental results based on a TMS320F28335 DSP are implemented on a DC motor to verify the effectiveness of the proposed MOFFOPID controller in controlling the speed of the DC motor which has non-linear features. The results of the simulation confirm the desirable performance of suggested controller.

Multiobjective Stochastic Optimization Approach Applied to a Hybrid Process Production–Separation in the Production of Biobutanol

Acetone, butanol, and ethanol are produced in an acetobutylic fermentation, butanol being the main interest product because of its superior properties making it a feasible substitute for fuels coming from fossil sources. In this work we have simulated and optimized under a rigorous scheme an integrated process to produce acetone, butanol, and ethanol from lignocellulosic biomass. Since ABE fermentation presents several hurdles such as low concentration broths or inhibitory effects during fermentation, here is proposed a hybrid simultaneous system of saccharification–fermentation–separation in which inhibition products during both fermentation and enzymatic hydrolysis are limited. A liquid–liquid extraction step is selected as the recovery technique. The reactor was modeled and simulated using Matlab software coupled with Aspen Plus which simulated the separation step. The entire optimization was developed taking into consideration several objective targets such as the total annual cost and some bioindexes...

Scalable modeling and solution of stochastic multiobjective optimization problems

Abstract We present a scalable computing framework for the solution stochastic multiobjective optimization problems. The proposed framework uses a nested conditional value-at-risk (nCVaR) metric to find compromise solutions among conflicting random objectives. We prove that the associated nCVaR minimization problem can be cast as a standard stochastic programming problem with expected value (linking) constraints. We also show that these problems can be implemented in a modular and compact manner using PLASMO (a Julia -based structured modeling framework) and can be solved efficiently using PIPS-NLP (a parallel nonlinear solver). We apply the framework to a CHP design study in which we seek to find compromise solutions that trade-off cost, water, and emissions in the face of uncertainty in electricity and water demands.

Design under uncertainty of carbon capture and storage infrastructure considering cost, environmental impact, and preference on risk

We present a stochastic decision-making algorithm for the design and operation of a carbon capture and storage (CCS) network; the algorithm incorporates the decision-maker’s tolerance of risk caused by uncertainties. Given a set of available resources to capture, store, and transport CO2, the algorithm provides an optimal plan of the CCS infrastructure and a CCS assessment method, while minimizing annual cost, environmental impact, and risk under uncertainties. The model uses the concept of downside risk to explicitly incorporate the trade-off between risk and either economic or environmental objectives at the decision-making level. A two-phase-two-stage stochastic multi-objective optimization problem (2P2SSMOOP) solving approach is implemented to consider uncertainty, and the ε-constraint method is used to evaluate the interaction between total annual cost with financial risk and an Eco-indicator 99 score with environmental risk. The environmental impact is measured by Life Cycle Assessment (LCA) considering all contributions made by operation and installation of a CCS infrastructure. A case study of power-plant CO2 emission in Korea is presented to illustrate the application of the proposed modeling and solution method.