Multi-objective Design Problem Research Articles

Topology Optimisation Using MPBILs and Multi-Grid Ground Element

This paper aims to study the comparative performance of original multi-objective population-based incremental learning (MPBIL) and three improvements of MPBIL. The first improvement of original MPBIL is an opposite-based concept, whereas the second and third method enhance the performance of MPBIL using the multi and adaptive learning rate, respectively. Four classic multi-objective structural topology optimization problems are used for testing the performance. Furthermore, these topology optimization problems are improved by the method of multiple resolutions of ground elements, which is called a multi-grid approach (MG). Multi-objective design problems with MG design variables are then posed and tackled by the traditional MPBIL and its improved variants. The results show that using MPBIL with opposite-based concept and MG approach can outperform other MPBIL versions.

A model for multi-class road network recovery scheduling of regional road networks

In this paper, an optimisation model for recovery planning of road networks is presented in which both social and economic resilience is aimed to be achieved. The model is formulated as a bi-level multi-objective discrete network design problem which forms a non-convex mixed integer non-linear problem. Solved by a Branch and Bound method, the solution algorithm employs an outer approximation method to estimate the lower bound of each node in the Branch and Bound search tree. The solution algorithm exploits a unique approach for lower-bound computation dealing with a disrupted multi-class network that may not be able to satisfy the demand between all OD pairs due to damaged links. The model is assessed by applying it on the Sioux Falls network. It is also illustrated how the Pareto-optimal solutions achieved by the multi-objective optimisation can vary depending on the emphasis placed on different classes of vehicles.

A novel multi-criteria self-organising migrating algorithm for engineering problems

Solving engineering design and resources optimisation via multi-objective evolutionary algorithms has attracted much attention in the last few years. In this study, an improved Self-Organising Migrating Algorithm (MOSOMA) is developed and investigated to solve multi-objective engineering design problems. The proposed MOSOMA algorithm uses a migration approach for the search of optima. In order to obtain a uniform distribution of Pareto optimal solutions, the crowding distance method is introduced. Pareto dominance is incorporated into the algorithm in order to allow this heuristic to handle problems with several objective functions. The performance of the MOSOMA algorithm is assessed by applying it to a set of multi-objective standard test functions and constrained engineering design problems. The results show that the proposed approach is competitive and effective compared to other algorithms contemplated in this work and it can also find the result with greater precision.

On the Effect of Mate Selection Scheme of Multi-objective Evolutionary Algorithms with Large Population on Constrained Multi-objective Optimization Problems

Multi-objective evolutionary algorithms (MOEAs) are active research topics for multi-objective design problems. MOEAs are population-based global optimization algorithms and it is said that the performance of the MOEAs depends on the population size. Meanwhile, one of the recent trends of computer development is in the large-scale many-core architectures and massive parallel computation is getting feasible in more companies and laboratories. One of the simple yet effective ways of MOEAs for utilizing the large-scale computational resources would be to increase the population size. This study examines the effect of the population size on MOEAs' performance on a real-world-derived benchmarking optimization problem, with large population size. In this paper, three mate selection schemes with different degree of elitist strategy are adapted to M2M-decomposed NSGA-II. The experimental results show that the elitist strategy can efficiently make use of the effect of the large population size, therefore can reduce the turn-around time of an MOEA.

Multi-Fidelity Multi-Objective Efficient Global Optimization Applied to Airfoil Design Problems

In this study, efficient global optimization (EGO) with a multi-fidelity hybrid surrogate model for multi-objective optimization is proposed to solve multi-objective real-world design problems. In the proposed approach, a design exploration is carried out assisted by surrogate models, which are constructed by adding a local deviation estimated by the kriging method and a global model approximated by a radial basis function. An expected hypervolume improvement is then computed on the basis of the model uncertainty to determine additional samples that could improve the model accuracy. In the investigation, the proposed approach is applied to two-objective and three-objective optimization test functions. Then, it is applied to aerodynamic airfoil design optimization with two objective functions, namely minimization of aerodynamic drag and maximization of airfoil thickness at the trailing edge. Finally, the proposed method is applied to aerodynamic airfoil design optimization with three objective functions, namely minimization of aerodynamic drag at cruising speed, maximization of airfoil thickness at the trialing edge and maximization of lift at low speed assuming a landing attitude. XFOILis used to investigate the low-fidelity aerodynamic force, and a Reynolds-averaged Navier–Stokes simulation is applied for high-fidelity aerodynamics in conjunction with a high-cost approach. For comparison, multi-objective optimization is carried out using a kriging model only with a high-fidelity solver (single fidelity). The design results indicate that the non-dominated solutions of the proposed method achieve greater data diversity than the optimal solutions of the kriging method. Moreover, the proposed method gives a smaller error than the kriging method.

Integration of Fuzzy Analytic Hierarchy Process into multi-objective Computer Aided Molecular Design

In this paper, a novel Computer Aided Molecular Design (CAMD) framework is developed to solve multi-objective molecular design problems. CAMD can be formulated as a multi-objective optimisation problem when there are multiple target properties to be optimised simultaneously. A major obstacle faced by multi-objective CAMD problems is the difficulty in assigning weighting factors to the target properties, since the relative importance of these factors is not always defined. It is particularly difficult to compare target properties which belong to different categories, such as physicochemical, safety, health and environmental properties, on a common scale. This paper presents a systematic CAMD algorithm built on Fuzzy Analytic Hierarchy Process (FAHP) to deal with the ambiguity involved in evaluating the weights of target properties in multi-objective CAMD problem. Instead of using exact numerical values, FAHP approach expresses the pairwise comparison of target properties through triangular fuzzy numbers, which allow the degree of confidence of decision maker to be quantified. Hence, the proposed approach can address the uncertainties arising from ambiguity involved during value judgement elicitation in multi-objective CAMD problems. The solutions generated provide a better balance of performance for a set of identified target properties. The proposed methodology is illustrated through a case study on designing a better solvent for extracting residual oil from palm pressed fibre.

An optimization tool for coaxial magnetic gears

PurposeThis paper aims to show a complete optimization tool that can be used for the design of coaxial magnetic gears. In the first part, the paper deals with the semi-analytic modelling of these machines and also discusses how to reduce the computational efforts. In the second part, an optimization algorithm is adopted for finding the Pareto optimal geometries.Design/methodology/approachThe machine is subdivided into a set of domains according to their physical and geometrical properties, and the potential distribution is found semi-analytically in them under some simplifying hypothesis. A loss estimation is performed for both ferromagnetic and permanent magnet regions. A stochastic differential evolution (DE) algorithm for multi-objective constrained problems is then applied.FindingsIt is shown that the presented design tool gives results in accordance to finite element method (FEM)-based analysis keeping the advantages of robustness and simplicity of the analytical methods. The DE-based strategy performs well on the magnetic gear optimization problem.Practical implicationsThe proposed tool appears to be a good starting point when designing coaxial magnetic gears. The optimal Pareto points can be used as initial seeds of FEM-based optimizations, resulting in a cheaper computational method with respect to a full FEM optimization.Originality/valueThis paper takes inspiration from recent works on magnetic gear modelling and completes the design procedure with a suitable efficiency estimation. The paper also shows how to use mature optimization strategies to solve the constrained multi-objective magnetic gear design problem.

A Lagrangian relaxation approach to fuzzy robust multi-objective facility location network design problem

This study considers a multi-objective combined budget constrained facility location/network design problem (FL/NDP) in which the system uncertainty is considered. The most obvious practical examples of the problem are territorial designing and locating of academies, airline networks, and medical service centers. In order to assure the network reliability versus uncertainty, an efficient robust optimization approach is applied to model the proposed problem. The formulation is minimizing the total expected costs, including, transshipment costs, facility location (FL) costs, fixed cost of road/link utilization as well as minimizing the total penalties of uncovered demand nodes. Then, in order to consider of several system uncertainty, the proposed model is changed to a fuzzy robust model by suitable approaches. An efficient Sub-gradient based Lagrangian relaxation algorithm is applied. In addition, a practical example is studied. At the following, a series of experiments, including several test problems, is designed and solved to evaluate of the performance of the algorithm. The obtained results emphasize that considering of practical factors (e.g., several uncertainties, system disruptions, and customer satisfaction) in modelling of the problem can lead to significant improvement of the system yield and subsequently more efficient utilization of the established network.

A systematic methodology for multi-objective molecular design via Analytic Hierarchy Process

Abstract This paper presents a novel methodology for solving multi-objective Computer Aided Molecular Design (CAMD) problems. One of the major challenges in multi-objective CAMD problems is the subjectivity involved in assigning the weighting factors to each property that is optimised. It is difficult to define the relative importance of each property in CAMD problems as target properties that belong to different categories cannot be compared on a common scale. It is crucial to solve this issue as distinct solutions will be generated due to different weighting factors of each property. In this work, a systematic framework that combines CAMD and Analytic Hierarchy Process (AHP) is developed to deal with the ambiguities involved in assessing the relative importance weightings of target properties in multi-objective molecular design problem. Through AHP, molecular design problems can be approached as a hierarchical decision structure and different categories of target properties are combined in the same analysis. Besides, AHP has the ability to generate numerical priorities from the subjective knowledge in evaluating the relative importance of properties using pairwise comparison. A case study on solvent design for oil extraction from palm pressed fibre is solved to illustrate the proposed methodology.

Optimal Design of Nonlinear Multimaterial Structures for Crashworthiness Using Cluster Analysis

This study presents an efficient multimaterial design optimization algorithm that is suitable for nonlinear structures. The proposed algorithm consists of three steps: conceptual design generation, clustering, and metamodel-based global optimization. The conceptual design is generated using a structural optimization algorithm for linear models or a heuristic design algorithm for nonlinear models. Then, the conceptual design is clustered into a predefined number of clusters (materials) using a machine learning algorithm. Finally, the global optimization problem aims to find the optimal material parameters of the clustered design using metamodels. The metamodels are built using sampling and cross-validation and sequentially updated using an expected improvement function until convergence. The proposed methodology is demonstrated using examples from multiple physics and compared with traditional multimaterial topology optimization (MTOP) method. The proposed approach is applied to a nonlinear, multi-objective design problems for crashworthiness.

A Hybrid Estimation of Distribution Algorithm for Multi-Objective Multi-Sourcing Intermodal Transportation Network Design Problem Considering Carbon Emissions

The increasing concern on global warming is prompting transportation sector to take into account more sustainable operation strategies. Among them, intermodal transportation (IT) has already been regarded as one of the most effective measures on carbon reductions. This paper focuses on the model and algorithm for a certain kind of IT, namely multi-objective multi-sourcing intermodal transportation network design problem (MO_MITNDP), in which carbon emission factors are specially considered. The MO_MITNDP is concerned with determining optimal transportation routes and modes for a series of freight provided by multiple sourcing places to find good balance between the total costs and time efficiencies. First, we establish a multi-objective integer programming model to formulate the MO_MITNDP with total cost (TTC) and maximum flow time (MFT) criteria. Specifically, carbon emission costs distinguished by the different transportation mode and route are included in the cost function. Second, to solve the MO_MITNDP, a hybrid estimation of distribution algorithm (HEDA) combined with a heterogeneous marginal distribution and a multi-objective local search is proposed, in which the from the Pareto dominance scenario. Finally, based on randomly generated data and a real-life case study of Jilin Petrochemical Company (JPC), China, simulation experiments and comparisons are carried out to demonstrate the effectiveness and application value of the proposed HEDA.

∊-constraint heat transfer search (∊-HTS) algorithm for solving multi-objective engineering design problems

Abstract In this paper, an effective ∊-constraint heat transfer search (∊-HTS) algorithm for the multi-objective engineering design problems is presented. This algorithm is developed to solve multi-objective optimization problems by evaluating a set of single objective sub-problems. The effectiveness of the proposed algorithm is checked by implementing it on multi-objective benchmark problems that have various characteristics of Pareto front such as discrete, convex, and non-convex. This algorithm is also tested for several distinctive multi-objective engineering design problems, such as four bar truss problem, gear train problem, multi-plate disc brake design, speed reducer problem, welded beam design, and spring design problem. Moreover, the numerical experimentation shows that the proposed algorithm generates the solution to represent true Pareto front. Highlights A novel multi-objective optimization (MOO) algorithm is proposed. Proposed algorithm is presented to obtain the Pareto-optimal solutions. The multi-objective optimization algorithm compared with other work in the literature. Test performance of proposed algorithm on MOO benchmark/design engineering problems.

Multi-objective sine-cosine algorithm (MO-SCA) for multi-objective engineering design problems

This paper proposes a novel and an effective multi-objective optimization algorithm named multi-objective sine-cosine algorithm (MO-SCA) which is based on the search technique of sine-cosine algorithm (SCA). MO-SCA employs the elitist non-dominated sorting and crowding distance approach for obtaining different non-domination levels and to preserve the diversity among the optimal set of solutions, respectively. The effectiveness of the method is measured by implementing it on multi-objective benchmark problems that have various characteristics of Pareto front such as convex, non-convex and discrete. This proposed algorithm is also checked for the multi-objective engineering design problems with distinctive features. Furthermore, we show the proposed algorithm effectively generates the Pareto front and is easy to implement and algorithmically simple.

Incorporating Light Beam Search in a Vector Normal Boundary Intersection Method for Linear Antenna Array Optimization

An high directivity and low side lobe level antenna array is essential in wireless communication systems. Currently, the array design is often based on the experience of the designer. To combine the preferences of a decision maker into the evolution process of a multi-objective linear antenna array design problem, the light beam search method is proposed to be incorporated into a vector normal boundary intersection method to find an arbitrary fraction of the Pareto front. To adapt different preferences, a new transformed projection mechanism is introduced. To enhance the diversity of the algorithm, a dynamic transitional sub-domain strategy is proposed and used. Typical mathematical test functions and a ten-element linear antenna array optimization problem are used to testify the effectiveness of the proposed method.

Non-dominated sorting moth flame optimization (NS-MFO) for multi-objective problems

This paper proposes an effective non-dominated moth-flame optimization algorithm (NS-MFO) method for solving multi-objective problems. Most of the multi-objective optimization algorithms use different search techniques inspired by different optimization techniques such as genetic algorithms, differential evolutions, particle swarm optimization, cuckoo search etc., but search techniques of recently developed metaheuristics have hardly been investigated. Non-dominated moth-flame optimization algorithm (NS-MFO) is based on the search technique of moth-flame optimization algorithm (MFO) algorithm and utilizes the elitist non-dominated sorting and crowding distance approach for obtaining different non domination levels and to preserve the diversity among the optimal set of solutions respectively. The effectiveness of the method is measured by implementing it on multi-objective benchmark problems and multi-objective engineering design problems with distinctive features. It is shown in this paper that this method effectively generates the Pareto front and also, this method is easy to implement and algorithmically simple.

Resilience-based optimal design of water distribution network

Optimal design of water distribution network is generally aimed to minimize the capital cost of the investments on tanks, pipes, pumps, and other appurtenances. Minimizing the cost of pipes is usually considered as a prime objective as its proportion in capital cost of the water distribution system project is very high. However, minimizing the capital cost of the pipeline alone may result in economical network configuration, but it may not be a promising solution in terms of resilience point of view. Resilience of the water distribution network has been considered as one of the popular surrogate measures to address ability of network to withstand failure scenarios. To improve the resiliency of the network, the pipe network optimization can be performed with two objectives, namely minimizing the capital cost as first objective and maximizing resilience measure of the configuration as secondary objective. In the present work, these two objectives are combined as single objective and optimization problem is solved by differential evolution technique. The paper illustrates the procedure for normalizing the objective functions having distinct metrics. Two of the existing resilience indices and power efficiency are considered for optimal design of water distribution network. The proposed normalized objective function is found to be efficient under weighted method of handling multi-objective water distribution design problem. The numerical results of the design indicate the importance of sizing pipe telescopically along shortest path of flow to have enhanced resiliency indices.

Multi-objective seismic design optimization of steel frames by a chaotic meta-heuristic algorithm

In this study, multi-objective optimization is applied to implement performance-based design of steel moment-resisting frame (SMRF) structures. In order to efficiently achieve this purpose, a chaotic multi-objective firefly algorithm (CMOFA) is proposed to find the Pareto optimal front for the multi-objective performance-based optimum design (MO-PBOD) problem of SMRFs. The structural weight and the maximum inter-story drift at performance levels are taken as the conflicting objective functions of the MO-PBOD problem which should be optimized simultaneously subject to serviceability and ultimate limit-state constraints. In order to illustrate the efficiency of the proposed CMOFA meta-heuristic, two benchmark truss examples and three MO-PBOD examples of SMRFs are presented. The numerical results demonstrate the better computational performance of the proposed CMOFA meta-heuristic in comparison with some existing multi-objective algorithms.

Multi-objective optimization of HVAC system using NSPSO and Kriging algorithms—A case study

In modern building design, engineers are constantly facing challenging to find an optimal design to maintain a high level of thermal comfort and indoor air quality for occupants while minimizing the system energy consumption. Over the past decades, several algorithms have been proposed and developed for optimizing the heating, ventilation and air conditioning (HVAC) system for indoor environment. Nevertheless, majority of these optimization algorithms are focused on single objective optimization procedures and require large training sample for surrogate modelling. For multi-objective HVAC design problems, previous studies introduced an arbitrary weighting factor to combine all design objectives into one single objective function. The near optimal solutions were however sensitive to the chosen value of the weighting factor. Aiming to develop a multi-objective optimization platform with minimal computational cost, this paper presents a nondominated sorting-based particle swarm optimization (NSPSO) algorithm together with the Kriging method to perform optimization for the HVAC system design of a typical office room. In addition, an adaptive sampling procedure is also proposed to enable the optimization platform to adjust the sampling point and resolution in constructing the training sample. Significant computational cost could be reduced without sacrificing the accuracy of the optimal solution. The proposed methods are applied and assessed in a typical HVAC system and the results indicate that comparing to traditional methods, the presented approach can handle multi-objective optimization in ventilation system with up to 46.6% saving of computational time.

A new iterative approach for multi-objective fault detection observer design and its application to a hypersonic vehicle

ABSTRACTThis paper addresses the multi-objective fault detection observer design problems for a hypersonic vehicle. Owing to the fact that parameters’ variations, modelling errors and disturbances are inevitable in practical situations, system uncertainty is considered in this study. By fully utilising the orthogonal space information of output matrix, some new understandings are proposed for the construction of Lyapunov matrix. Sufficient conditions for the existence of observers to guarantee the fault sensitivity and disturbance robustness in infinite frequency domain are presented. In order to further relax the conservativeness, slack matrices are introduced to fully decouple the observer gain with the Lyapunov matrices in finite frequency range. Iterative linear matrix inequality algorithms are proposed to obtain the solutions. The simulation examples which contain a Monte Carlo campaign illustrate that the new methods can effectively reduce the design conservativeness compared with the existing methods.

A multi-objective multi-echelon green supply chain network design problem with risk-averse retailers in an uncertain environment

In this paper, the multi-objective multi-echelon supply chain network design problem is investigated. The resulted problem considers uncertainty of single product demand and the downstream risk attitude simultaneously and integrate it into the greenness concept. That is, makes the model more realistic in comparison with the others. According to the related literature study, there is no specific study to design the green supply chain network based on the risk attitude of the retailer. This paper aims to deal with this research gap by formulating robust counterpart of the main proposed uncertain problem. To do this, the conditional value at risk (CVaR) method through the data-driven approach is applied to deal with demand uncertainty to makes the model to be convex and sensitive to the risk averseness level in a robust manner. In addition, uncertainty sets approach is employed to deal with the uncertainty of other three parameters according to CO2 emission. The augmented e-constraint method is used to transform the resulted multi-objective mathematical programming problem into the single objective one, to obtain the global optimal solution through the exact mathematical solution method. Finally, the model is successfully simulated and its results are illustrated through a numerical example.