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Multi-objective is a complex problem that appears in real life while these objectives are conflicting. The swarm intelligence algorithm is often used to solve such multi-objective problems. Due to its strong search ability and convergence ability, particle swarm optimization algorithm is proposed, and the multi-objective particle swarm optimization algorithm is used to solve multi-objective optimization problems. However, the particles of particle swarm optimization algorithm are easy to fall into local optimization because of their fast convergence. Uneven distribution and poor diversity are the two key drawbacks of the Pareto front of multi-objective particle swarm optimization algorithm. Therefore, this paper aims to propose an improved multi-objective particle swarm optimization algorithm using adaptive Cauchy mutation and improved crowding distance.

In this paper, the proposed algorithm uses adaptive Cauchy mutation and improved crowding distance to perturb the particles in the population in a dynamic way in order to help the particles trapped in the local optimization jump out of it which improves the convergence performance consequently.

In order to solve the problems of uneven distribution and poor diversity in the Pareto front of multi-objective particle swarm optimization algorithm, this paper uses adaptive Cauchy mutation and improved crowding distance to help the particles trapped in the local optimization jump out of the local optimization. Experimental results show that the proposed algorithm has obvious advantages in convergence performance for nine benchmark functions compared with other multi-objective optimization algorithms.

In order to help the particles trapped in the local optimization jump out of the local optimization which improves the convergence performance consequently, this paper proposes an improved multi-objective particle swarm optimization algorithm using adaptive Cauchy mutation and improved crowding distance.

This paper aims to use the crankshaft-bearing system of a four-cylinder internal combustion engine as the studying object, and develop a multi-objective optimization design of the crankshaft-bearing. In the current optimization design of engine crankshaft-bearing, only the crankshaft-bearing was considered as the studying object. However, the corresponding relations of major structure dimensions exist between the crankshaft and the crankshaft-bearing in internal combustion engine, and there are the interaction effects between the crankshaft and the crankshaft-bearing during the operation of internal combustion engine.

The crankshaft mass and the total frictional power loss of crankshaft-bearing s are selected as the objective functions in the optimization design of crankshaft-bearing. The Particle Swarm Optimization algorithm based on the idea of decreasing strategy of inertia weight with the exponential type is used in the optimization calculation.

The total frictional power loss of crankshaft-bearing and the crankshaft mass are decreased, respectively, by 26.2 and 5.3 per cent by the multi-objective optimization design of crankshaft-bearing, which are more reasonable than the ones of single-objective optimization design in which only the crankshaft-bearing is considered as the studying object.

The crankshaft-bearing system of a four-cylinder internal combustion engine is taken as the studying object, and the multi-objective optimization design of crankshaft-bearing based on the crankshaft-bearing system is developed. The results of this paper are helpful to the design of the crankshaft-bearing for engine. There is universal significance to research the multi-objective optimization design of crankshaft-bearing based on the crankshaft-bearing system. The research method of the multi-objective optimization design of crankshaft-bearing based on the crankshaft-bearing system can be used to the optimization design of the bearing in the shaft-bearing system of ordinary machinery.

In line with computational technological advances, obtaining optimal solutions for engineering problems has become attractive research topics in various disciplines and real engineering systems having multiple objectives. Therefore, it is aimed to ensure that the multiple objectives are simultaneously optimized by considering them among the trade-offs. Furthermore, the practical means of solving those problems are principally concentrated on handling various complicated constraints. The purpose of this paper is to suggest an algorithm based on symbiotic organisms search (SOS), which mimics the symbiotic reciprocal influence scheme adopted by organisms to live on and breed within the ecosystem, for constrained multi-objective engineering design problems.

Though the general performance of SOS algorithm was previously well demonstrated for ordinary single objective optimization problems, its efficacy on multi-objective real engineering problems will be decisive about the performance. The SOS algorithm is, hence, implemented to obtain the optimal solutions of challengingly constrained multi-objective engineering design problems using the Pareto optimality concept.

Four well-known mixed constrained multi-objective engineering design problems and a real-world complex constrained multilayer dielectric filter design problem are tackled to demonstrate the precision and stability of the multi-objective SOS (MOSOS) algorithm. Also, the comparison of the obtained results with some other well-known metaheuristics illustrates the validity and robustness of the proposed algorithm.

The algorithmic performance of the MOSOS on the challengingly constrained multi-objective multidisciplinary engineering design problems with constraint-handling approach is successfully demonstrated with respect to the obtained outperforming final optimal designs.

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.

This study aims to propose a new airport gate assignment method to effectively improve the comprehensive operation capacity and efficiency of hub airport. Gate assignment is one of the most important tasks for airport ground operations, which assigns appropriate airport gates with high efficiency reasonable arrangement.

In this paper, on the basis of analyzing the characteristics of airport gates and flights, an efficient multi-objective optimization model of airport gate assignment based on the objectives of the most balanced idle time, the shortest walking distances of passengers and the least number of flights at apron is constructed. Then an improved ant colony optimization (ICQACO) algorithm based on the ant colony collaborative strategy and pheromone update strategy is designed to solve the constructed model to fast realize the gate assignment and obtain a rational and effective gate assignment result for all flights in the different period.

In the designed ICQACO algorithm, the ant colony collaborative strategy is used to avoid the rapid convergence to the local optimal solution, and the pheromone update strategy is used to quickly increase the pheromone amount, eliminate the interference of the poor path and greatly accelerate the convergence speed.

The actual flight data from Guangzhou Baiyun airport of China is selected to verify the feasibility and effectiveness of the constructed multi-objective optimization model and the designed ICQACO algorithm. The experimental results show that the designed ICQACO algorithm can increase the pheromone amount, accelerate the convergence speed and avoid to fall into the local optimal solution. The constructed multi-objective optimization model can effectively improve the comprehensive operation capacity and efficiency. This study is a very meaningful work for airport gate assignment.

An efficient multi-objective optimization model for hub airport gate assignment problem is proposed in this paper. An improved ant colony optimization algorithm based on ant colony collaborative strategy and the pheromone update strategy is deeply studied to speed up the convergence and avoid to fall into the local optimal solution.

In the vast majority of published papers, the optimal reactive power dispatch (ORPD) problem is dealt as a single-objective optimization; however, optimization with a single objective is insufficient to achieve better operation performance of power systems. Multi-objective ORPD (MOORPD) aims to minimize simultaneously either the active power losses and voltage stability index, or the active power losses and the voltage deviation. The purpose of this paper is to propose multi-objective ant lion optimization (MOALO) algorithm to solve multi-objective ORPD problem considering large-scale power system in an effort to achieve a good performance with stable and secure operation of electric power systems.

A MOALO algorithm is presented and applied to solve the MOORPD problem. Fuzzy set theory was implemented to identify the best compromise solution from the set of the non-dominated solutions. A comparison with enhanced version of multi-objective particle swarm optimization (MOEPSO) algorithm and original (MOPSO) algorithm confirms the solutions. An in-depth analysis on the findings was conducted and the feasibility of solutions were fully verified and discussed.

Three test systems – the IEEE 30-bus, IEEE 57-bus and large-scale IEEE 300-bus – were used to examine the efficiency of the proposed algorithm. The findings obtained amply confirmed the superiority of the proposed approach over the multi-objective enhanced PSO and basic version of MOPSO. In addition to that, the algorithm is benefitted from good distributions of the non-dominated solutions and also guarantees the feasibility of solutions.

The proposed algorithm is applied to solve three versions of ORPD problem, active power losses, voltage deviation and voltage stability index, considering large -scale power system IEEE 300 bus.

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.

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.

The purpose of this paper is to achieve the multi-objective optimization design of novel tubular switched reluctance motor (TSRM).

First, the structure and initial dimensions of TSRM are obtained based on design criteria and requirements. Second, the sensitivity analysis rules, process and results of TSRM are performed. Third, three optimization objectives are determined by the average electromagnetic force, smoothing coefficient and copper loss ratio. The analytic hierarchy process-entropy method-a technique for order preference by similarity to an ideal solution-grey relation analysis comprehensive evaluation algorithm is used to optimize TSRM. Finally, a prototype is manufactured, a hardware platform is built and static and dynamic experimental validations are carried out.

The sensitivity analysis reveals that parameters significantly impact the performance of TSRM. The results of multi-objective optimization show that the average electromagnetic force and smoothing coefficient after optimization are better than before, and the copper loss ratio reduces slightly. The experimental and simulated results of TSRM are consistent, which verifies the accuracy of TSRM.

In this paper, only three optimization objectives are selected in the multi-objective optimization process. To improve the performance of TSRM, the heating characteristics, such as iron loss, can be considered as the optimization objective for a more comprehensive analysis of TSRM performance.

A novel motor structure is designed, combining the advantages of the TSRM and the linear motor. The established sensitivity analysis rules are scientific and suitable for the effects of various parameters on motor performance. The proposed multi-objective optimization algorithm is a comprehensive evaluation algorithm. It considers subjective weight and objective weight and fully uses the original data and the relational degree between the optimization objectives.

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.