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In this work, the design problem of hydrodynamic plain journal bearings is formulated as a multi-objective optimization problem to improve bearing performance under different operating conditions.

The problem is solved using a hybrid approach combining genetic algorithm and sequential quadratic programming. The selected state variables are oil leakage flow rate, power loss and minimum oil film thickness. The selected design variables are the radial clearance, length-to-diameter ratio, oil viscosity, oil supply pressure and oil supply groove angular position. A validated empirical model is adopted to provide relatively accurate estimation of the bearing state variables with reduced computations. Pareto optimal solution sets are obtained for different operating conditions, and secondary selection criteria are proposed to choose a final optimum design.

The adopted hybrid optimization approach is a random search algorithm that generates a different solution set for each run, thus a different bearing design. For a number of runs, it is found that the key design variables that significantly affect the optimum state variables are the bearing radial clearance, oil viscosity and oil supply pressure. Additionally, oil viscosity is found to represent the significant factor that distinguishes the optimum designs obtained using the implemented secondary selection criteria. Finally, the results of the proposed optimum design framework at different operating conditions are presented and compared.

The proposed multi-objective formulation of the bearing design problem can provide engineers with a systematic approach and an important degree of flexibility to choose the optimum design that best fits the application requirements.

This chapter presents the survey of selected linear and mixed integer programming multi-objective portfolio optimization. The definitions of selected percentile risk measures are presented. Some contrasts and similarities of the different types of portfolio formulations are drawn out. The survey of multi-criteria methods devoted to portfolio optimization such as weighting approach, lexicographic approach, and reference point method is also presented. This survey presents the nature of the multi-objective portfolio problems focuses on a compromise between the construction of objectives, constraints, and decision variables in a portfolio and the problem complexity of the implemented mathematical models. There is always a trade-off between computational time and the size of an input data, as well as the type of mathematical programming formulation with linear and/or mixed integer variables.

This paper aims to investigate deterministic strategies for low-cost multi-objective design optimization of compact microwave structures, specifically, impedance matching transformers. The considered methods involve surrogate modeling techniques and variable-fidelity electromagnetic (EM) simulations. In contrary to majority of conventional approaches, they do not rely on population-based metaheuristics, which permit lowering the design cost and improve reliability.

There are two algorithmic frameworks presented, both fully deterministic. The first algorithm involves creating a path covering the Pareto front and arranged as a sequence of patches relocated in the course of optimization. Response correction techniques are used to find the Pareto front representation at the high-fidelity EM simulation level. The second algorithm exploits Pareto front exploration where subsequent Pareto-optimal designs are obtained by moving along the front by means of solving appropriately defined local constrained optimization problems. Numerical case studies are provided demonstrating feasibility of solving real-world problems involving expensive EM-simulation models of impedance transformer structures.

It is possible, by means of combining surrogate modeling techniques and constrained local optimization, to identify the set of alternative designs representing Pareto-optimal solutions, in a realistic time frame corresponding to a few dozen of high-fidelity EM simulations of the respective structures. Multi-objective optimization for the considered class of structures can be realized using deterministic approaches without defaulting to evolutionary methods.

The present study can be considered a step toward further studies on expedited optimization of computationally expensive simulation models for miniaturized microwave components.

The proposed algorithmic solutions proved useful for expedited multi-objective design optimization of miniaturized microwave structures. The problem is extremely challenging when using conventional methods, in particular evolutionary algorithms. To the authors’ knowledge, this is one of the first attempts to investigate deterministic surrogate-assisted multi-objective optimization of compact components at the EM-simulation level.

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 ever-stringent environmental regulations force power producers to produce electricity at the cheapest price and with minimum pollutant emission levels. The electrical power generation from fossil fuel releases several contaminants into the air, and this becomes excrescent if the generating unit is fed by multiple fuel sources (MFSs). Inclusion of this issue in operational tasks is a welcome perspective. This paper aims to develop a multi-objective model comprising total fuel cost and pollutant emission.

The cost-effective and environmentally responsive power system operations in the presence of MFSs can be recognised as a multi-objective constrained optimisation problem with conflicting operational objectives. The complexity of the problem requires a suitable optimisation tool. Ant lion algorithm (ALA), the most recent nature-inspired algorithm, was used as the main optimisation tool because of its salient characteristics. The fuzzy decision-making mechanism has been integrated to determine the best compromised solution in the multi-objective framework.

This paper is the first to propose a more precise and practical operational model for studying a multi-fuel power dispatch scenario considering valve-point effects and CO₂ emission. The modern meta-heuristic algorithm ALA is applied for the first time to address the economic operation of thermal power systems with multiple fuel options.

Power companies aim to make profit by abiding by the norms of the regulatory board. To achieve economic benefits, the power system must be analysed using an accurate operational model. The proposed model integrates total fuel cost, valve-point loadings and CO₂ emission, which are prevailing power system operational objectives. The economic advantages of the operational model can be observed through economic deviation indices, and the performed analysis validates that the developed model corresponds to the actual power operation.

The realistic operational model is proposed by considering total fuel and pollutant emission, and the ALA is applied for the first time to address the proposed multi-objective problem. To validate the effectiveness of ALA, it is implemented in standard test systems with varying generating units (10-100) and the IEEE 30 bus system, and various kinds of power system operations are performed. Moreover, the comparison and performance analysis confirm that the current proposal is found enhanced in terms of solution quality.

The purpose of this paper is to consider the concept of Fuzzy Radial Basis Function Neural Networks with Information Granulation (IG‐FRBFNN) and their optimization realized by means of the Multiobjective Particle Swarm Optimization (MOPSO).

In fuzzy modeling, complexity, interpretability (or simplicity) as well as accuracy of the obtained model are essential design criteria. Since the performance of the IG‐RBFNN model is directly affected by some parameters, such as the fuzzification coefficient used in the FCM, the number of rules and the orders of the polynomials in the consequent parts of the rules, the authors carry out both structural as well as parametric optimization of the network. A multi‐objective Particle Swarm Optimization using Crowding Distance (MOPSO‐CD) as well as O/WLS learning‐based optimization are exploited to carry out the structural and parametric optimization of the model, respectively, while the optimization is of multiobjective character as it is aimed at the simultaneous minimization of complexity and maximization of accuracy.

The performance of the proposed model is illustrated with the aid of three examples. The proposed optimization method leads to an accurate and highly interpretable fuzzy model.

A MOPSO‐CD as well as O/WLS learning‐based optimization are exploited, respectively, to carry out the structural and parametric optimization of the model. As a result, the proposed methodology is interesting for designing an accurate and highly interpretable fuzzy model.

The main motive behind framing this paper is to provide a compromised solution for trapezoidal fuzzy number–multi-objective fully quadratic fractional optimisation model (TrFN-MOFQFOM) by avoiding ambiguities and confusion of decision-makers (DMs). Many researchers have used Taylor's series and parametric approach to transform fractional objective function into non-fractional ones, but Taylor's series expansion is valid only up to a neighbourhood. To avoid these extra efforts, this article suggests a methodology in which numerator of objective function is optimised under the condition of optimising denominator.

This paper suggests an efficient procedure to search for compromised solution of MOFQFOM with fuzzy coefficients using α-level set and FGP approach. Incomplete data in model is dealt with α-level set. Then after defuzzification, non-fractional models are built from fractional model to get optimal solution of every objective. Finally, the linear weighted sum of negative deviational variables is minimised to satisfy all objective functions up to maximum possible extent.

On applying suggested approach to the example given in end, the authors arrived at compromised solution having μO1(O1(x))=1 and μO2(O2(x))=0.71. The applied procedure requires less computational efforts and provides the preferred compromised solution.

This work has not been done previously by anyone. The idea being developed here of constructing non-fractional model by dealing numerators and denominators separately is completely new. 10; In the end, an algorithm, flowchart and numerical are also given to clarify the applicability of the suggested approach.

The purpose of this work is to apply and compare surrogate-assisted and multi-fidelity, multi-objective optimization (MOO) algorithms to simulation-based aerodynamic design exploration.

The three algorithms for multi-objective aerodynamic optimization compared in this work are the combination of evolutionary algorithms, design space reduction and surrogate models, the multi-fidelity point-by-point Pareto set identification and the multi-fidelity sequential domain patching (SDP) Pareto set identification. The algorithms are applied to three cases, namely, an analytical test case, the design of transonic airfoil shapes and the design of subsonic wing shapes, and are evaluated based on the resulting best possible trade-offs and the computational overhead.

The results show that all three algorithms yield comparable best possible trade-offs for all the test cases. For the aerodynamic test cases, the multi-fidelity Pareto set identification algorithms outperform the surrogate-assisted evolutionary algorithm by up to 50 per cent in terms of cost. Furthermore, the point-by-point algorithm is around 27 per cent more efficient than the SDP algorithm.

The novelty of this work includes the first applications of the SDP algorithm to multi-fidelity aerodynamic design exploration, the first comparison of these multi-fidelity MOO algorithms and new results of a complex simulation-based multi-objective aerodynamic design of subsonic wing shapes involving two conflicting criteria, several nonlinear constraints and over ten design variables.

Life cycle analysis (LCA) is more and more used in the context of electromagnetic product design. But it is often used to check a design solution regarding environmental impacts after technical and economical choices. This paper aims to investigate life cycle impact optimization (LCIO) and compare it with the classical life cycle cost optimization (LCCO).

First, a model of a dry-type transformer using different materials for windings and the magnetic core is presented. LCCO, which is a mixed continuous-discrete, multi-objective technico-economic optimization, is done using both deterministic and genetic algorithms. LCCO results and optimization performances are analyzed, and an LCA is presented for a set of optimal solutions. The final part is dedicated to LCIO, where the paper shows that these optimal solutions are close to those obtained with LCCO.

This paper investigated LCIO using an environmental impacts model that has been introduced in the optimization framework Component Architecture for the Design of Engineering Systems. The paper shows how a mixed continuous-discrete, multi-objective technico-economic optimization can be done using an efficient deterministic optimization algorithm such as Sequential Quadratic Programming. Thanks to the technico-economic-environmental model and the efficient optimization algorithm, both LCCO and LCIO were performed separately and together. It has been shown that optimal solutions are similar, leading to the conclusion that only one modeling is required (economic or environmental) but on the life cycle.

The classical sequential methodology of design is improved here by the use of a model of calculation of the environmental impacts allowing the optimization. This original optimization allowed the authors to show that an analysis of the life cycle from an economic point of view or from an environmental point of view led to quasi-equivalent technical solutions. The key is to take into account the life cycle of the product.

Developing an optimized project schedule that considers all decision criteria represents a challenge for project managers. The purpose of this paper is to provide a multi-objectives overall optimization model for project scheduling considering time, cost, resources, and cash flow. This development aims to overcome the limitations of optimizing each objective at once resulting of non-overall optimized schedule.

In this paper, a multi-objectives overall optimization model for project scheduling is developed using particle swarm optimization with a new evolutionary strategy based on the compromise solution of the Pareto-front. This model optimizes the most important decisions that affect a given project including: time, cost, resources, and cash flow. The study assumes each activity has different execution methods accompanied by different time, cost, cost distribution pattern, and multiple resource utilization schemes.

Applying the developed model to schedule a real-life case study project proves that the proposed model is valid in modeling real-life construction projects and gives important results for schedulers and project managers. The proposed model is expected to help construction managers and decision makers in successfully completing the project on time and reduced budget by utilizing the available information and resources.

The paper presented a novel model that has four main characteristics: it produces an optimized schedule considering time, cost, resources, and cash flow simultaneously; it incorporates a powerful particle swarm optimization technique to search for the optimum schedule; it applies multi-objectives optimization rather than single-objective and it uses a unique Pareto-compromise solution to drive the fitness calculations of the evolutionary process.