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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.

With the continuous upgrading of the production mode of the manufacturing system, the characteristics of multi-variety, small batch and mixed fluidization are presented, and the production environment becomes more and more complex. To improve the efficiency of solving multi-objective flexible job shop scheduling problem (FJSP), an improved hybrid particle swarm optimization algorithm (IH-PSO) is proposed.

After reviewing literatures on FJSP, an IH-PSO algorithm for solving FJSP is developed. First, IH-PSO algorithm draws on the crossover and mutation operations of genetic algorithm (GA) algorithm and proposes a new method for updating particles, which makes the offspring particles inherit the superior characteristics of the parent particles. Second, based on the improved simulated annealing (SA) algorithm, the method of updating the individual best particles expands the search scope of the domain and solves the problem of being easily trapped in local optimum. Finally, analytic hierarchy process (AHP) is used in this paper to solve the optimal solution satisfying multi-objective optimization.

Through the benchmark experiment and the production example experiment, it is verified that the proposed algorithm has the advantages of high quality of solution and fast speed of convergence.

This method does not consider the unforeseen events that occur during the process of scheduling and cause the disruption of normal production scheduling activities, such as machine breakdown.

IH-PSO algorithm combines PSO algorithm with GA and SA algorithms. This algorithm retains the advantage of fast convergence speed of traditional PSO algorithm and has the characteristic of inheriting excellent genes. In addition, the improved SA algorithm is used to solve the problem of falling into local optimum.

This research provides an efficient scheduling method for solving the FJSP problem.

This research proposes an IH-PSO algorithm to solve the FJSP more efficiently and meet the needs of multi-objective optimization.

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 cut down energy consumption and eliminate production waste on mixed-model assembly lines. Therefore, a supermarket integrated dynamic cyclic kitting system with the application of electric vehicles (EVs) is introduced. The system resorts to just-in-time (JIT) and segmented sub-line assignment strategies, with the objectives of minimizing line-side inventory and energy consumption.

Hybrid opposition-based learning and variable neighborhood search (HOVMQPSO), a multi-objective meta-heuristics algorithm based on quantum particle swarm optimization is proposed, which hybridizes opposition-based learning methodology as well as a variable neighborhood search mechanism. Such algorithm extends the search space and is capable of obtaining more high-quality solutions.

Computational experiments demonstrated the outstanding performance of HOVQMPSO in solving the proposed part-feeding problem over the two benchmark algorithms non-dominated sorting genetic algorithm-II and quantum-behaved multi-objective particle swarm optimization. Additionally, using modified real-life assembly data, case studies are carried out, which imply HOVQMPSO of having good stability and great competitiveness in scheduling problems.

The feeding problem is based on static settings in a stable manufacturing system with determined material requirements, without considering the occurrence of uncertain incidents. Current study contributes to assembly line feeding with EV assignment and could be modified to allow cooperation between EVs.

The dynamic cyclic kitting problem with sub-line assignment applying EVs and supermarkets is solved by an innovative HOVMQPSO, providing both novel part-feeding strategy and effective intelligent algorithm for industrial engineering.

The purpose of this paper is to realize a multi‐objective location‐routing network optimization in reverse logistics using particle swarm optimization based on grey relational analysis with entropy weight.

Real world network design problems are often characterized by multi‐objective in reverse logistics. This has recently been considered as an additional objective for facility location problem or vehicle routing problem in reverse logistics network design. Both of them are shown to be NP‐hard. Hence, location‐routing problem (LRP) with multi‐objective is more complicated integrated problem, and it is NP‐hard too. Due to the fact that NP‐hard model cannot be solved directly, grey relational analysis and entropy weight were added to particle swarm optimization to decision among the objectives. Then, a mathematics model about multi‐objective LRP of reverse logistics has been constructed, and a proposed hybrid particle swarm optimization with grey relational analysis and entropy weight has been developed to resolve it. An example is also computed in the last part of the paper.

The results are convincing: not only that particle swarm optimization and grey relational analysis can be used to resolve multi‐objective location‐routing model, but also that entropy and grey relational analysis can be combined to decide weights of objectives.

The method exposed in the paper can be used to deal with multi‐objective LRP in reverse logistics, and multi‐objective network optimization result could be helpful for logistics efficiency and practicability.

The paper succeeds in realising both a constructed multi‐objective model about location‐routing of reverse logistics and a multi‐objective solution algorithm about particle swarm optimization and future stage by using one of the newest developed theories: grey relational analysis.

The purpose of this paper is to propose a multi-objective particle swarm optimization (MOPSO) algorithm based design optimization of Brushless DC (BLDC) motor with a view to mitigate cogging torque and enhance the efficiency.

The suitability of MOPSO algorithm is tested on a 120 W BLDC motor considering magnet axial length, stator slot opening and air gap length as the design variables. It avails the use of MagNet 7.5.1, a Finite Element Analysis tool, to account for the geometry and the non-linearity of material for assuaging an improved design framework and operates through the boundaries of generalized regression neural network (GRNN) to advocate the optimum design. The results of MOPSO are compared with Multi-Objective Genetic Algorithm and Non-dominated Sorting Genetic Algorithm-II based formulations for claiming its place in real world applications.

A MOPSO design optimization procedure has been enlivened to escalate the performance of the BLDC motor. The optimality in design has been out reached through minimizing the cogging torque, maximizing the average torque and reducing the total losses to claim an increase in the efficiency. The results have been fortified in well-distributed Pareto-optimal planes to arrive at trade-off solutions between different objectives.

The rhetoric theory of multi objective formulations has been reinforced to provide a decisive solution with regard to the choice of the design obtained from Pareto-optimal planes.

The incorporation of a larger number of design variables together with an orientation to thermal and vibration analysis will still go a long way in bringing on board new dimensions to the fold of optimality in the design of BLDC motors.

The proposal offers a new perspective to the design of BLDC motor in the sense it be-hives the facility of a swarm based approach to optimize the parameters in order that it serves to improve its performance. The results of a 120 W motor in terms of lowering the losses, minimizing the cogging torque and maximizing the average torque emphasize the benefits of the GRNN based multi-objective formulation and establish its viability for use in practical applications.

The paper aims at the bi‐objective optimization of a two‐echelon distribution network model for facility location and capacity allocation where in a set of customer locations with demands and a set of candidate facility locations will be known in advance. The problem is to find the locations of the facilities and the shipment pattern between the facilities and the distribution centers (DCs) to minimize the combined facility location and shipment costs subject to a requirement that maximum customer demands be met.

To optimize the two objectives simultaneously, the location and distribution two‐echelon network model is mathematically represented in this paper considering the associated constraints, capacity, production and shipment costs and solved using hybrid multi‐objective particle swarm optimization (MOPSO) algorithm.

This paper shows that the heuristic based hybrid MOPSO algorithm can be used as an optimizer for characterizing the Pareto optimal front by computing well‐distributed non‐dominated solutions. These aolutions represent trade‐off solutions out of which an appropriate solution can be chosen according to industrial requirement.

Very few applications of hybrid MOPSO are mentioned in literature in the area of supply chain management. This paper addresses one of such applications.

The purpose of this paper is to introduce a hybrid, metaheuristic, multimodal and multi-objective optimization tool that is needed for aerospace propulsion engineering problems.

Multi-objective hybrid optimization code is integrated with various benchmark and test functions that are selected suitable to the difficulty level of the aero propulsion performance problems.

Ant colony and particle swarm optimization (ACOPSO) has performed satisfactorily with benchmark problems.

ACOPSO is able to solve multi-objective and multimodal problems. Because every optimization problem has specific features, it is necessary to search their general behavior using other algorithms.

In addition to the optimization solving, ACOPSO enables an alternative methodology for turbine engine performance calculations by using generic components maps. The user is flexible for searching various effects of component designs along with the compressor and turbine maps.

A hybrid optimization code that has not been used before is introduced. It is targeted use is propulsion systems optimization and design such as Turboshaft or turbofan by preparing the necessary engine functions. A number of input parameters and objective functions can be modified accordingly.

The purpose of this paper is to present an approach for the decentralization of swarm intelligence algorithms that run on computing systems with autonomous components that are connected by a network. The approach is applied to a particle swarm optimization (PSO) algorithm with multiple sub‐swarms. PSO is a nature inspired metaheuristic where a swarm of particles searches for an optimum of a function. A multiple sub‐swarms PSO can be used for example in applications where more than one optimum has to be found.

In the studied scenario the particles of the PSO algorithm correspond to data packets that are sent through the network of the computing system. Each data packet contains among other information the position of the corresponding particle in the search space and its sub‐swarm number. In the proposed decentralized PSO algorithm the application specific tasks, i.e. the function evaluations, are done by the autonomous components of the system. The more general tasks, like the dynamic clustering of data packets, are done by the routers of the network.

Simulation experiments show that the decentralized PSO algorithm can successfully find a set of minimum values for the used test functions. It was also shown that the PSO algorithm works well for different type of networks, like scale‐free network and ring like networks.

The proposed decentralization approach is interesting for the design of optimization algorithms that can run on computing systems that use principles of self‐organization and have no central control.

During the 3D printing process, the model needs to add a support structure to ensure structural stability. Excessive support structure reduces printing efficiency and results in material cost. A flexible support platform for 3 D printing has been designed. It can form an external support structure to replace the original support structure. This paper aims to study the influence of a model’s build orientation on properties when the model is printed on the platform, aiming to provide users with suitable solutions.

A fitness function for estimating the support structure with a support length is constructed. The particle swarm optimization (PSO) algorithm is modified and applied to find the build orientation that minimizes the support structure. However, when the model is printed on the platform, the build orientation of the minimum support structure enhances the complexity of the working path, resulting in an increase of printing time, which needs to be avoided. This paper applies a multi-objective particle swarm optimization (MOPSO) algorithm to minimize the support structure while minimizing printing time. The Pareto solution is obtained by the algorithm.

It is found that the model that has the cantilever structure can reduce more support structure after optimization on the platform, when there is surface quality requirement. When there is no limit, the modified algorithm can minimize the support structure of each model. Considering support structure and printing time, the MOPSO algorithm can easily get optimization results to guide the practical work.

This paper optimizes the model’s build orientation on the flexible support platform by PSO, thereby reducing material cost and improving work efficiency.