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In order to optimize SCSWIRC, the simplification and further optimization method is proposed. SCSWIRC's optimization includes two levels. The first level refers to simplifying structural system from the perspective of components; the second level refers to optimizing components' sectional areas from the perspective of mechanics. The first level aims to remove redundant components, and the second level aims to reduce structural self-weight based on the first level. The purpose of the paper is to simplify SCSWIRC's structural system and optimize structural self-weight and reduce construction forming difficulty.

Grid-jumping layout and multi-objective optimization method is used to simplify and further optimize Spatial cable-truss structure without inner ring cables (SCSWIRC). Grid-jumping layout is used to simplify remove redundant components, and multi-objective optimization method is used to reduce structural self-weight. The detailed solving process is given based on grid-jumping layout and multi-objective optimization method.

Take SCSWIRC with a span of 100m as an example to verify the feasibility and correctness of the simplification and further optimization method. The optimization results show that 12 redundant components are removed and the self-weight reduces by 3.128t from original scheme to grid-jumping layout scheme 1. The self-weight reduces from 36.007t to 28.231t and feasible coefficient decreases from 1.0 to 0.627 from grid-jumping layout scheme 1 to multi-objective optimization scheme. The simplification and further optimization can not only remove the redundant components and simplify structural system to reduce construction forming difficulty, but also optimize structural self-weight under considering structural stiffness to reduce project costs.

The proposed method firstly simplifies SCSWIRC and then optimizes the simplified SCSWIRC, which can solve the optimization problem from the perspective of components and mechanics. Meanwhile, the optimal section solving method can be used to obtain circular steel tube size with the optimal stiffness of the same areas. The proposed method successfully solves the problem of construction forming and project cost, which promotes the application of SCSWIRC in practical engineering.

The purpose of this paper is to present a newly developed multi-objective optimization method for the time, cost and work interruptions for repetitive scheduling while considering uncertainties associated with different input parameters.

The design of the developed method is based on integrating six modules: uncertainty and defuzzification module using fuzzy set theory, schedule calculations module using the integration of linear scheduling method (LSM) and critical chain project management (CCPM), cost calculations module that considers direct and indirect costs, delay penalty, and work interruptions cost, multi-objective optimization module using Evolver © 7.5.2 as a genetic algorithm (GA) software, module for identifying multiple critical sequences and schedule buffers, and reporting module.

For duration optimization that utilizes fuzzy inputs without interruptions or adding buffers, duration and cost generated by the developed method are found to be 90 and 99 percent of those reported in the literature, respectively. For cost optimization that utilizes fuzzy inputs without interruptions, project duration generated by the developed method is found to be 93 percent of that reported in the literature after adding buffers. The developed method accelerates the generation of optimum schedules.

Unlike methods reported in the literature, the proposed method is the first multi-objective optimization method that integrates LSM and the CCPM. This method considers uncertainties of productivity rates, quantities and availability of resources while utilizing multi-objective GA function to minimize project duration, cost and work interruptions simultaneously. Schedule buffers are assigned whether optimized schedule allows for interruptions or not. This method considers delay and work interruption penalties, and bonus payments.

The optimality objectives are the structure weight and embodied energy as well as calculating the cost and embodied carbon of the resulting optimum options. Three optimality algorithms developed in MATLAB, namely, genetic algorithms (GA), particle swarm optimisation (PSO) and harmony search algorithm (HSA), were used for structural optimisation to compare the effectiveness of the algorithms. Two life-cycle stages were considered, production and construction stages, which include three boundaries: materials, transportation and erection. In the formulation of the optimum design problem, 107 universal steel beams (UKB) and 64 columns (UKC) sections were considered for the discrete design variables. The imposed behavioural constraints in the optimum design process were set according to the provision of Eurocode 3 (EC3). The study aims to find the optimum solution of 2D steel frames whilst considering weight and embodied energy, investigate the performance of the analysis integrated with MATLAB and provide three examples to which all these are applied to.

Undoubtedly, in structural engineering, the best design of any structure aims at the most economical and environmental option, without impairing the functional and its structural integrity. In the paper, multi-objective stochastic search methods are proposed for optimum design of three two-dimensional multi-story frames.

Results showed that the optimised designs obtained by HSA are better than those found by the GA and PSO with an average difference of 16% from GA and PSO, where this difference increases at larger frame structures. It was, therefore, concluded that the integration of the analysis, design and optimisation methods employed in MATLAB can be effective in obtaining prompt optimum results during the decision-making stage.

There may be some possible limitations in the study. Due to the time constraints, only three meta-heuristic approaches were investigated, where more methods should be investigated to fully understand their effectiveness in multi-objective problems.

Investigating the performance of three optimisation methods in multi-objective problems developed in MATLAB. More importantly, developing optimisation models for evaluation of embodied energy, embodied carbon and cost for steel structures to assist designers, during the initial stages, to evaluate design decisions against their energy consumption and carbon impacts.

There are process uncertainties and material property variations during laminated steel sheet forming, and those fluctuations may result in non-reliable forming quality issues such as fracture and delamination. Additionally, the optimization of sheet forming process is a typical multi-objective optimization problem. The target is to find a multi-objective design optimization and improve the process design reliability for laminated sheet metal forming. The paper aims to discuss these issues.

Desirability function approach is adopted to conduct deterministic multi-objective optimization, and response surface is used as meta-model. Reliability analysis is conducted to evaluate the robustness of the multi-objective design optimization. The proposed method is implemented in a step-bottom square cup drawing process. First, forming process parameters and three noise factors are assumed as probability variables to conduct reliability assessment of the laminated steel sheet forming process using Monte Carlo simulation. Next, only two forming process parameters, blank holding force and frictional coefficient, are considered as probability variables to investigate the influence of the forming parameter deviation on the variance of the response using the first-order second-moment method.

The results indicate that multi-objective design optimization using desirability function method has high efficiency, and an optimized robust design can be obtained after reliability assessment.

The proposed design procedure has potential as a simple and practical approach in the laminated steel sheet forming process.

The purpose of this paper is to propose an optimal energy management (OEM) method using intelligent optimization techniques applied to implement an optimally hybrid heat and power isolated microgrid. The microgrid investigated combines renewable and conventional power generation.

Five bio-inspired optimization methods include an advanced proposed multi-objective particle swarm optimization (MOPSO) approach which is comparatively applied for OEM of the implemented microgrid with other bio-inspired optimization approaches via their comparative simulation results.

Optimal multi-objective solutions through Pareto front demonstrate that the advanced proposed MOPSO method performs quite better in comparison with other meta-heuristic optimization methods. Moreover, the proposed MOPSO is successfully applied to perform 24-h OEM microgrid. The simulation results also display the merits of the real time optimization along with the arbitrary of users’ selection as to satisfy their power requirement.

This paper focuses on the OEM of a designed microgrid using a newly proposed modified MOPSO algorithm. Optimal multi-objective solutions through Pareto front demonstrate that the advanced proposed MOPSO method performs quite better in comparison with other meta-heuristic optimization approaches.

The purpose of this paper is to propose the selection guide of the multi-objective optimization methods for the ergonomic design. The proposed guide enables designers to select an appropriate method for optimizing the human characteristics composed of the engineering characteristics (e.g. users’ height, weight and muscular strength) and the physiological characteristics (e.g. brain wave, pulse-beat and myoelectric signal) in the trade-off relationships.

This paper focuses on the types of the relationships between engineering or physiological characteristics and their psychological characteristics (e.g. comfort and usability). Using these relationships and the characteristics of the multi-objective optimization methods, this paper classified them and constructed a flow chart for selecting them.

This paper applied the proposed selection guide to a geometric design of a comfortable seat and confirmed its applicability. The selected multi-objective optimization method optimized the contact area of seat back (engineering characteristic associated with the comfortable fit of the seat backrest) and the blood flow volume (physiological characteristic associated with the numbness in the lower limb) on the basis of each design intent such as a deep-vein thrombosis after long flight.

Because of the lack of the selection guide of the multi-objective optimization methods, an inappropriate method is often applied in industry. This paper proposed the selection guide applied in the ergonomic design having a lot of the multi-objective optimization problem.

The interval multi-objective optimization problems (IMOPs) are universal and vital uncertain optimization problems. In this study, an interval multi-objective grey wolf optimization algorithm (GWO) based on fuzzy system is proposed to solve IMOPs effectively.

First, the classical genetic operators are embedded into the interval multi-objective GWO as local search strategies, which effectively balanced the global search ability and local development ability. Second, by constructing a fuzzy system, an effective local search activation mechanism is proposed to save computing resources as much as possible while ensuring the performance of the algorithm. The fuzzy system takes hypervolume, imprecision and number of iterations as inputs and outputs the activation index, local population size and maximum number of iterations. Then, the fuzzy inference rules are defined. It uses the activation index to determine whether to activate the local search process and sets the population size and the maximum number of iterations in the process.

The experimental results show that the proposed algorithm achieves optimal hypervolume results on 9 of the 10 benchmark test problems. The imprecision achieved on 8 test problems is significantly better than other algorithms. This means that the proposed algorithm has better performance than the commonly used interval multi-objective evolutionary algorithms. Moreover, through experiments show that the local search activation mechanism based on fuzzy system proposed in this study can effectively ensure that the local search is activated reasonably in the whole algorithm process, and reasonably allocate computing resources by adaptively setting the population size and maximum number of iterations in the local search process.

This study proposes an Interval multi-objective GWO, which could effectively balance the global search ability and local development ability. Then an effective local search activation mechanism is developed by using fuzzy inference system. It closely combines global optimization with local search, which improves the performance of the algorithm and saves computing resources.

In this work, the multi-objective optimization shuffled complex evolution is proposed. The algorithm is based on the extension of shuffled complex evolution, by incorporating two classical operators into the original algorithm: the rank ordering and crowding distance. In order to accelerate the convergence process, a Local Search strategy based on the generation of potential candidates by using Latin Hypercube method is also proposed.

The multi-objective optimization shuffled complex evolution is used to accelerate the convergence process and to reduce the number of objective function evaluations.

In general, the proposed methodology was able to solve a classical mechanical engineering problem with different characteristics. From a statistical point of view, we demonstrated that differences may exist between the proposed methodology and other evolutionary strategies concerning two different metrics (convergence and diversity), for a class of benchmark functions (ZDT functions).

The development of a new numerical method to solve multi-objective optimization problems is the major contribution.

This paper aims to propose a double-sided switched reluctance linxear generator (DSRLG) exclusively for wave power generation. The initial dimensions are given through design experience and principles. To ameliorate comprehensive performance of the DSRLG, the multi-objective optimization design is processed.

The multi-objective optimization design of the DSRLG is processed by adopting a modified entropy technique for order of preference by similarity to ideal solution (TOPSIS) algorithm. First, sensitivity analyzes on geometric parameters of the DSRLG are conducted to determine several pivotal geometric parameters as optimization variables. Then, the multi-objective optimization is conducted on the basis of initial dimensions. After determination of synthetical evaluation value of each structure parameter, the best dimension scheme of the DSRLG is concluded.

After verification by finite element method simulation and dynamic simulation, the final dimension scheme proves to perform better than the initial scheme. Finally, experiments are conducted to verify the accuracy of both the stable finite element DSRLG model and dynamic simulation system model so that the conclusion of this paper proves to be reliable and compelling.

This paper proposes an improved structure of the DSRLG, which is superior for wave power generation. Meanwhile, a novel modified entropy TOPSIS algorithm is applied to the field of electrical machine multi-objective optimal design for the first time.

The aim of the paper is to compare two different approaches to multi‐objective optimisation in magnetostatics; in this way, the case study is investigated as a possible benchmark.

A Tabu search method modified with ε‐constraint algorithm is compared with a multi‐objective multi‐individual evolution strategy. The case study is the automated shape design of a magnetic pole. In order to reduce the computational cost of solving the direct problem, which requires repeated analyses of the magnetic field, a neural network has been used to approximate the objective functions that depend on the design variables.

An approximation of the Pareto front for each method is obtained. A twofold comparison between the two methods is made, based on both the result accuracy and the computational cost.

Two different methods were already tested on a case study proposed as a benchmark for multi‐objective optimization in magnetostatics. The paper represents a contribution to bridge the gap between analytical and numerical benchmarks in electromagnetism.