Multi-objective Optimisation, Sensitivity and Robustness Analysis in FBA Modelling

There is an increasing trend in the use of multi-objective evolutionary algorithms (MOEAs) to solve multi-objective optimization problems of the allocation of water resources. However, typically the outcome is a set of Pareto optimal solutions which make up a trade-off surface between the objective functions. For decision makers to choose a satisfactory alternative from a set of Pareto-optimal solutions, this paper suggests a new method based on least squares support vector machine (LSSVM) and k-means clustering for ranking the optimal solutions for the multi-objective allocation of water resources. First, the k-means clustering method was adopted to reduce the large set of solutions to a few representative solutions. Then, to capture and represent the decision maker's preferences as well as to select the most desirable alternative, the LSSVM method was applied to obtain the utility value for each representative solution. According to the magnitude of the utility values, the final priority orders of the representative solutions were determined. Finally, this methodology was applied to rank the Pareto optimal solution set obtained from the multi-objective optimization problems of water resources allocation for the water-receiving areas of the South-to-North Water Transfer Project in Hebei Province, China. Moreover, the comparisons of the proposed method with the information entropy method and the artificial neural network (ANN) model were given. The results of the comparison indicate that the proposed method has the ability to rank the non-dominated solutions of the multi-objective operation optimization model and that it can be employed for decision-making on water allocation and management in a river basin.

Selection of optimum machining parameters is vital to the machining processes in order to ensure the quality of the product, reduce the machining cost, increasing the productivity and conserve resources for sustainability. Hence, in this work a posteriori multi-objective optimization algorithm named as Non-dominated Sorting Teaching–Learning-Based Optimization (NSTLBO) is applied to solve the multi-objective optimization problems of three machining processes namely, turning, wire-electric-discharge machining and laser cutting process and two micro-machining processes namely, focused ion beam micro-milling and micro wire-electric-discharge machining. The NSTLBO algorithm is incorporated with non-dominated sorting approach and crowding distance computation mechanism to maintain a diverse set of solutions in order to provide a Pareto-optimal set of solutions in a single simulation run. The results of the NSTLBO algorithm are compared with the results obtained using GA, NSGA-II, PSO, iterative search method and MOTLBO and are found to be competitive. The Pareto-optimal set of solutions for each optimization problem is obtained and reported. These Pareto-optimal set of solutions will help the decision maker in volatile scenarios and are useful for real production systems.

In optimizing the propagation paths of automotive product design changes, we applied the complex network theory to automotive product structure modeling and established a directed weighted auto part network model. In this model, we defined the parts as the nodes, the physical connections between the parts as the edges, and the impacts of change propagation as the weights of the edges. According to the characteristics of change propagation, we constructed a multiobjective optimization model that simultaneously considered the development time, development cost, and change risk. Using a multiobjective particle swarm optimization (MOPSO) algorithm, we solved the model and obtained the Pareto set of optimal solutions, which provided a basis for designers to choose the optimal design change plan. We conducted the multiobjective optimization of the air-conditioning system design change propagation path in a car model to verify the feasibility and effectiveness of the method.

Recently, the flexible cryogenic hose has been preferred as an alternative to exploit offshore liquefied natural gas (LNG), in which helical corrugated steel pipe is the crucial component with C-shaped corrugation. Parametric finite element models of the LNG cryogenic helical corrugated pipe are established using a three-dimensional shell element in this paper. Considering the nonlinearity of cryogenic material and large geometric structural deformation, mechanical behaviors are simulated under axial tension, bending, and internal pressure loads. In addition, design parameters are determined to optimize the shape of flexible cryogenic hose structures through sectional dimension analysis, and sensitivity analysis is performed with changing geometric parameters. A multi-objective optimization to minimize stiffness and stress is formulated under operation conditions. Full factorial experiment and radial basis function (RBF) neural network are applied to establish the approximated model for structure analysis. The set of Pareto optimal solutions and value range of parameters are obtained through nondominated sorting genetic algorithm II (NSGA-II) under manufacturing and stiffness constraints, thereby providing a feasible optimal approach for the structural design of LNG cryogenic corrugated hose.

Optimizing multiple conflicting black-box objectives simultaneously is a prevalent occurrence in many real-world applications, such as neural architecture search, and machine learning. These problems are known as expensive multi-objective optimization problems (EMOPs) when the function evaluations are computationally or financially costly. Multi-objective Bayesian optimization (MOBO) offers an efficient approach to discovering a set of Pareto optimal solutions. However, the data deficiency issue caused by limited function evaluations has posed a great challenge to current optimization methods. Moreover, most current methods tend to prioritize the quality of candidate solutions, while ignoring the quantity of promising samples. In order to tackle these issues, our paper proposes a novel multi-objective Bayesian optimization algorithm with a data augmentation strategy that provides ample high-quality samples for Pareto set learning (PSL). Specifically, it utilizes Generative Adversarial Networks (GANs) to enrich data and a dominance prediction model to screen out high-quality samples, mitigating the predicament of limited function evaluations in EMOPs. Additionally, we adopt the regularity model to expensive multi-objective Bayesian optimization for PSL. Experimental results on both synthetic and real-world problems demonstrate that our algorithm outperforms several state-of-the-art and classical algorithms.

This paper presents a simultaneous multiobjective optimization of a direct-drive permanent magnet synchronous generator and a three-blade horizontal-axis wind turbine for a large scale wind energy conversion system. Analytical models of the generator and the turbine are used along with the cost model for optimization. Three important characteristics of the system i.e., the total cost of the generator and blades, the annual energy output and the total mass of generator and blades are chosen as objective functions for a multi-objective optimization. Genetic algorithm (GA) is then employed to optimize the value of eight design parameters including seven generator parameters and a turbine parameter resulting in a set of Pareto optimal solutions. Four optimal solutions are then selected by applying some practical restrictions on the Pareto front. One of these optimal designs is chosen for finite element verification. A circuit-fed coupled time stepping finite element method is then performed to evaluate the no-load and the full load performance analysis of the system including the generator, a rectifier and a resistive load. The results obtained by the finite element analysis (FEA) verify the accuracy of the analytical model and the proposed method.

This article is devoted to the synergistic design of the thermal management and signal integrity for 3-D integrated chips. The structure parameters of the micro-fin and interconnected components are optimized to obtain a balanced performance of chip heat dissipation and signal integrity. The 3-D integrated chip flows heat transfer model under the action of electrothermal coupling is developed. A full-wave electromagnetic simulation model of the signal interconnection components is proposed with the same structural parameters. The effects of various structural factors on the heat transfer performance and signal integrity of 3-D integrated chips are investigated. A multiobjective optimization algorithm is carried out to simultaneously reduce the total thermal resistance of the 3-D integrated chip and the signal transmission losses of the critical interconnect components. The results show that the total thermal resistance of the 3-D IC becomes lower with a larger through-silicon via (TSV) diameter, micro-fins height and micro-fin radius, and smaller oxide thickness. When the TSV diameter and oxide thickness increase, the height and radius of the micro-fins are reduced to facilitate the signal transmission of the chip's interconnected components. The response surface analysis method was used to design the experimental combination and thus obtain the fit function for the performance of the two objectives. Hundred sets of Pareto optimal solutions are obtained by multiobjective optimization. The technique for order preference by similarity to ideal solution (TOPSIS) method is used to select the weights of the two optimization objectives to determine the optimal solution. When thermal resistance and signal transmission are given equal weight in the chip design, thermal resistance is reduced by 13.8%, and signal transmission efficiency is improved by 9.74%. The study has important implications for chip thermal management and signal integrity.

Multimodal multiobjective optimization problems (MMOPs) have attracted wide attention in recent years. This kind of problem is very challenging since they need to locate different Pareto-optimal solution sets (PSs) that correspond to the same Pareto front. To resolve it, this article proposes a novel multimodal multiobjective differential evolution (DE) algorithm with species conservation, which develops a new way of locating different PSs. Specifically, the proposed algorithm adopts species conservation to determine different PSs in known areas, while it uses a variant of DE as the basic optimizer to explore new areas. There are three operators in species conservation: 1) species division; 2) seed determination; and 3) seed conservation. Species division mainly partitions the joint population of parents and children into various species in the decision space for retaining different PSs. Seed determination selects superior solutions from each species as seeds that need to be kept in the next generation. Seed conservation is to ensure that all species seeds are retained in the new generation by substituting no promising solutions with them, thereby guarantee not missing some known areas that may contain different PSs. Besides, the DE variant is utilized to produce diverse solutions to find new areas in the decision space where PSs may exist. The comparative experiments with ten state-of-the-art algorithms have been performed on the CEC 2019 MMOPs test set and two real-world problems. The experimental results have verified that the proposed algorithm has a competitive performance for MMOPs.

Hybrid multi-objective Harris Hawk optimization algorithm based on elite non-dominated sorting and grid index mechanism

Pareto analysis is a broadly applicable method to model and analyze tradeoffs in multi-objective optimization problems. The set of Pareto optimal solutions is guaranteed to contain the best solution for any arbitrary cost function or selection procedure. This work introduces a method to explicitly take uncertainty into account during Pareto analysis. A solution is not modeled by a single point in the solution space, but rather by a set of such points. This is useful in settings with much uncertainty, such as during model-based design space exploration for embedded systems. A bounding-box abstraction is introduced as a finite representation of Pareto optimal solutions under uncertainty. It is shown that the set of Pareto optimal solutions in the proposed approach still captures exactly the potentially best solutions for any cost function as well as any way of reducing the amount of uncertainty. During model-based design space exploration, for instance, design and implementation choices that are made during the development process reduce the amount of uncertainty. Steps in such a refinement trajectory can render previously Pareto optimal solutions sub optimal. The presented results provide a way to ensure that early selections in the refinement process remain valid.

A systematic approach for watershed ecological restoration strategy making: An application in the Taizi River Basin in northern China

PurposeThe purpose of this study is to realize the multi-objective optimization for MRR and surface roughness in micro-milling of Inconel 718.Design/methodology/approachTaguchi method has been applied to conduct experiments, and the cutting parameters are spindle speed, feed per tooth and depth of cut. The first-order models used to predict surface roughness and MRR for micro-milling of Inconel 718 have been developed by regression analysis. Genetic algorithm has been utilized to implement multi-objective optimization between surface roughness and MRR for micro-milling of Inconel 718.FindingsThis paper implemented the multi-objective optimization between surface roughness and MRR for micro-milling of Inconel 718. And some conclusions can be summarized. Depth of cut is the major cutting parameter influencing surface roughness. Feed per tooth is the major cutting parameter influencing MRR. A number of cutting parameters have been obtained along with the set of pareto optimal solu-tions of MRR and surface roughness in micro-milling of Inconel 718.Originality/valueThere are a lot of cutting parameters affecting surface roughness and MRR in micro-milling, such as tool diameter, depth of cut, feed per tooth, spindle speed and workpiece material, etc. However, to the best our knowledge, there are no published literatures about the multi-objective optimization of surface roughness and MRR in micro-milling of Inconel 718.

To date the design of structures via topology optimisation methods has mainly focused on single-objective problems. However, real-world design problems usually involve several different objectives, most of which counteract each other. Therefore, designers typically seek a set of Pareto optimal solutions, a solution for which no other solution is better in all objectives, which capture the trade-off between these objectives. This set is known as a smart Pareto set. Currently, only the weighted sums method has been used for generating Pareto fronts with topology optimisation methods. However, the weighted sums method is unable to produce evenly distributed smart Pareto sets. Furthermore, evenly distributed weights have been shown to not produce evenly spaced solutions. Therefore, the weighted sums method is not suitable for generating smart Pareto sets. Recently, the smart normal constraints method has been shown to be capable of directly generating smart Pareto sets. This work presents an updated smart normal constraint method, which is combined with a bi-directional evolutionary structural optimisation algorithm for multi-objective topology optimisation. The smart normal constraints method has been modified by further restricting the feasible design space for each optimisation run such that dominant and redundant points are not found. The algorithm is tested on several different structural optimisation problems. A number of different structural objectives are analysed, namely compliance, dynamic and buckling objectives. Therefore, the method is shown to be capable of solving various types of multi-objective structural optimisation problems. The goal of this work is to show that smart Pareto sets can be produced for complex topology optimisation problems. Furthermore, this research hopes to highlight the gap in the literature of topology optimisation for multi-objective problems.

Uncertainty considered in robust optimization is usually treated as irreducible since it is not reduced during an optimization procedure. In contrast, uncertainty considered in sensitivity analysis is treated as partially or fully reducible in order to quantify the effect of input uncertainty on the outputs of the system. Considering this, and the usual existence of both reducible and irreducible uncertainty, an approach that can perform robust optimization and sensitivity analysis simultaneously is of much interest. This article presents such an integrated optimization model that can be used for both robust optimization and sensitivity analysis for problems that have irreducible and reducible interval uncertainty, multiple objective functions and mixed continuous-discrete design variables. The proposed model is demonstrated by two engineering examples with differing complexity to demonstrate its applicability.

Most of the engineering problems are modeled as evolutionary multiobjective optimization problems, but they always ask for only one best solution, not a set of Pareto optimal solutions. The decision maker′s subjective information plays an important role in choosing the best solution from several Pareto optimal solutions. Generally, the decision‐making processing is implemented after Pareto optimality. In this paper, we attempted to incorporate the decider′s subjective sense with Pareto optimality for chromosomes ranking. A new ranking method based on subjective probability theory was thus proposed in order to explore and comprehend the true nature of the chromosomes on the Pareto optimal front. The properties of the ranking rule were proven, and its transitivity was presented as well. Simulation results compared the performance of the proposed ranking approach with the Pareto‐based ranking method for two multiobjective optimization cases, which demonstrated the effectiveness of the new ranking approach.