Maintain Population Diversity Research Articles

Optimal deployment strategy of airships for near‐space communication system using multiobjective advanced evolutionary algorithm

SummaryThis paper presents a near‐space communication system (NSCS) using advanced deployment strategies to gain high throughput. The airships are deployed according to the user's location, assuming robust backbone network characteristics such as signal path loss, fading factor, routing efficiency, and safety issues among bi‐connected airships. Due to the independent flying nature of airships, it is very attractive to deploy them as aerial base stations and construct airborne networks to provide service for on‐ground users. However, it is quite challenging to optimally deploy multiple airships for on‐demand coverage while maintaining the connectivity among airships. A balance between the network parameters, i.e., capacity and coverage area, should be maintained for optimal deployment of the airships. We have derived the maximum throughput of NSCS, including system parameters, as a multiobjective optimization problem subjected to efficient routing protocol and safety constraints. A decomposition‐based advanced multiobjective evolutionary algorithm (AMOEA/D) is adopted to solve the deployment optimization problem. The proposed algorithm is motivated by the non‐dominated solutions that maintain population diversity over the variable space. Two designed test problems, that is, the L‐shaped hotspot problem and nine hotspot problems, are also investigated. Numerical results show that the proposed method improves the system performance compared with benchmark external archive‐guided MOEA/D (EGA‐MOEA/D) and non‐dominated sorted genetic algorithms (NSGA‐II) by 10.46% and 3.84%, respectively.

Parallel dynamic NSGA-II with multi-population search for rescheduling of Seru production considering schedule changes under different dynamic events

Seru production is usually accompanied by various dynamic events in the real world, such as worker tool breakdowns, new batch arrivals, batch cancellations, and batch size changes. Therefore, dynamic Seru production is proposed. To cope with the dynamic seru production, we adopt an event-driven predictive-reactive scheduling method, i.e., when a dynamic event occurs, rescheduling is triggered to produce a new schedule with good efficiency. However, the new schedule may deviate significantly from the previous schedule. Therefore, it is critical to minimize schedule changes while maximizing efficiency (e.g. makespan) simultaneously. First, we formulate a multi-objective dynamic seru production model that applies to various dynamic events to minimize both schedule changes and makespan. Then, we develop dynamic NSGA-II to produce a new schedule. To effectively respond to dynamic events, a population re-initialization strategy is proposed to fast-track non-dominated solutions by making use of the characteristics of dynamic events, and a communication mechanism is designed to accelerate the convergence speed. However, these two mechanisms may lead to reducing its diversity. To maintain population diversity, a multi-population search strategy based on hyper-heuristic is adopted. The hyper-heuristic algorithm is incorporated to evolve an additional seru rescheduling population, which employs NSGA-ΙΙ as the high-level strategy to manipulate several low-level heuristics to generate efficient local search heuristic sequences. However, this approach also results in a longer computation time. Therefore, a parallel mechanism is designed to save computational time. Finally, we have conducted extensive experiments to demonstrate that our algorithm outperforms existing algorithms and provides several management insights.

Multiobjective-Based Constraint-Handling Technique for Evolutionary Constrained Multiobjective Optimization: A New Perspective

Multiobjective-based constraint-handling techniques are popular in evolutionary constrained single-objective optimization. However, most of these techniques run into troubles when dealing with constrained multiobjective optimization problems (CMOPs). That is, they have difficulty optimizing too many objective functions, are ineffective in maintaining population diversity, or are challenged in establishing appropriate additional objective functions. As a remedy to these limitations, we propose a novel technique called NRC for handling CMOPs. The novelty of NRC lies in its three sorting procedures: nondominated sorting, reversed nondominated sorting, and constrained crowding distance sorting, which are performed in sequence to provide driving forces toward the Pareto front (PF) of a transformed unconstrained multiobjective optimization problem (treating the overall constraint violation as an additional objective function), the boundary front, and the constrained PF, respectively. With the combination of these three different forces, NRC can conveniently approach the desired PF from diverse search directions. The effectiveness of NRC is experimentally verified. Also, we incorporate NRC into a two-archive mechanism and develop a novel constrained multiobjective evolutionary algorithm, called NRC2. Comprehensive experiments on 49 benchmark CMOPs and 21 real-world ones demonstrate that NRC2 is significantly superior or comparable to six state-of-the-art constrained evolutionary multiobjective optimizers on most test instances.

Improving Performance of Differential Evolution Using Multi-Population Ensemble Concept

Differential evolution (DE) stands out as a straightforward yet remarkably powerful evolutionary algorithm employed for real-world problem-solving purposes. In the DE algorithm, few parameters are used, and the population is evolved by applying various operations. It is difficult in evolutionary computation algorithms to maintain population diversity. The main issue is the sub-population of the DE algorithm that helps improve convergence speed and escape from the local optimum. Evolving sub-populations by maintaining diversity is an important issue in the literature that is considered in this research. A solution is proposed that uses sub-populations to promote greater diversity within the population and improve the algorithm performance. DE, heterogeneous distributed differential evolution (HDDE), multi-population ensemble differential evolution (MPEDE), and the proposed improved multi-population ensemble differential evolution (IMPEDE) are implemented using parameter settings; population sizes of 100 NP, 150 NP, and 200 NP; and dimensions of 10D, 30D, and 50D for performance comparison. Different combinations of mutations are used to generate the simulated results. The simulation results are generated using 1000, 3000, and 5000 iterations. Experimental outcomes show the superior results of the proposed IMPEDE over existing algorithms. The non-parametric significance Friedman test confirms that there is a significant difference in the performance of the proposed algorithm and other algorithms used in this study by considering a 0.05 level of significance using six benchmark functions.

An Enhanced Hunger Games Search Optimization with Application to Constrained Engineering Optimization Problems.

The Hunger Games Search (HGS) is an innovative optimizer that operates without relying on gradients and utilizes a population-based approach. It draws inspiration from the collaborative foraging activities observed in social animals in their natural habitats. However, despite its notable strengths, HGS is subject to limitations, including inadequate diversity, premature convergence, and susceptibility to local optima. To overcome these challenges, this study introduces two adjusted strategies to enhance the original HGS algorithm. The first adaptive strategy combines the Logarithmic Spiral (LS) technique with Opposition-based Learning (OBL), resulting in the LS-OBL approach. This strategy plays a pivotal role in reducing the search space and maintaining population diversity within HGS, effectively augmenting the algorithm's exploration capabilities. The second adaptive strategy, the dynamic Rosenbrock Method (RM), contributes to HGS by adjusting the search direction and step size. This adjustment enables HGS to escape from suboptimal solutions and enhances its convergence accuracy. Combined, these two strategies form the improved algorithm proposed in this study, referred to as RLHGS. To assess the efficacy of the introduced strategies, specific experiments are designed to evaluate the impact of LS-OBL and RM on enhancing HGS performance. The experimental results unequivocally demonstrate that integrating these two strategies significantly enhances the capabilities of HGS. Furthermore, RLHGS is compared against eight state-of-the-art algorithms using 23 well-established benchmark functions and the CEC2020 test suite. The experimental results consistently indicate that RLHGS outperforms the other algorithms, securing the top rank in both test suites. This compelling evidence substantiates the superior functionality and performance of RLHGS compared to its counterparts. Moreover, RLHGS is applied to address four constrained real-world engineering optimization problems. The final results underscore the effectiveness of RLHGS in tackling such problems, further supporting its value as an efficient optimization method.

Shuffled ARSH-FATI: A Novel Meta-Heuristic for Lifetime Maximization of Range-Adjustable Wireless Sensor Networks

Wireless Sensor Network (WSN) is an essential component of the Internet-of-Things (IoT), enabling the creation of a vast network of interconnected devices and systems that can interact with each other and with the physical world. WSNs are widely used for a variety of applications, including environmental monitoring, healthcare, industry 4.0, agriculture, transportation, and surveillance. WSN consists of devices with limited residual energy therefore, the lifetime improvement of WSN is critical for achieving the full potential of IoT and enabling the creation of more robust and reliable connected systems. This paper explores the problem of Lifetime Maximization of Range Adjustable Sensors (LM-RAS). The goal is to optimize the lifetime of the WSN consisting of range-adjustable sensors while satisfying two constraints. Firstly, all targets in the network must be monitored simultaneously. Secondly, the activation time of each sensor should be limited by its battery energy. A novel meta-heuristic called Shuffled ARSH-FATI has been proposed that embeds ARSH-FATI into a multi-population method. Shuffled ARSH-FATI solves the LM-RAS problem by splitting it into two sub-problem. The first sub-problem deals with the creation of energy-efficient coverage schemes and the second sub-problem deal with the schedule of these schemes. Shuffled ARSH-FATI utilizes a Linear Programming (LP) model to generate an optimal schedule for the coverage schemes but its performance greatly depends on the quality of the coverage schemes. Shuffled ARSH-FATI simultaneously explores several regions of the search space by partitioning the coverage schemes in population into several sub-populations. It evolves each sub-population (in this problem a sub-set of coverage schemes) independently using ARSH-FATI. It incorporates the shuffling process via Merge, Shuffle, and Partition (MSP) algorithm that merges the sub-populations, shuffles, and then partitions the merged population into new sub-populations. The shuffling process along with the strategy to fine-tune the coverage scheme into energy-efficient coverage schemes maintains population diversity throughout the optimization. The diverse high-quality coverage scheme improves the performance of the LP model.

Thermal-economic optimization design of shell and tube heat exchanger using an improved sparrow search algorithm

Optimal design of heat exchangers is challenging, since complex non-linear relationship exists among the various design parameters. This study aims to construct a full-dimensional thermal-economic model for shell-and-tube heat exchanger using two commonly (i.e., Kern and Bell-Delaware) methods based on Logarithmic-Mean-Temperature-Difference (LMTD) or ε-Number-of-Transfer-Units (ε-NTU) method and proposes a novel solving mechanism based on improved sparrow search algorithm to achieve thermal-economic optimization design of heat exchanger. The improved method organically combines nonlinear gradient descent weight factor, elite reverse strategy, selection-mutation operator to maintain population diversity, enhance convergence speed and avoid being stuck in local optima. Firstly, the constructed model’s accuracy is verified by numerical analysis. Then, the improved sparrow search algorithm is applied to four examples after algorithm parameter tuning, and the results show that the area decreases by 15.62%∼49.30% and total annual cost is reduced by 27.93% compared to the literature. It can also identify feasible solutions at a lower total cost than the metaheuristic method, with reductions of 7.56%∼59.42%(Kern) and 6.26%∼60.19%(Bell-Delaware). Moreover, a multi-objective optimization algorithm is obtained by adding fast non-dominated sorting mechanism and archival gene pool, and the superiority is verified by standard test functions. Finally, a multi-objective optimization scheme with the higher effectiveness-economic benefit is conducted to achieve cost-effectiveness tradeoff for two real-world cases. The results show that total cost of the most economic-efficient scheme decreases by 53.73% and effectiveness increases by 2.33%, while the runtime decreases by 35%. Furthermore, sensitivity analysis of effectiveness and total cost varying with crucial variables is performed and discussed.

Identification of photovoltaic module parameters by implementing a novel teaching learning based optimization with unique exemplar generation scheme (TLBO-UEGS)

The performance evaluation of a Photovoltaic (PV) system heavily relies on accurately estimating the parameters based on its current—voltage relationships. However, due to the PV model’s inherent complexity, obtaining these parameters with precision and efficiency is a challenging task. In this study, a new variant known as teaching learning-based optimization with unique exemplar generation schemes (TLBO-UEGS) is proposed to address PV module parameter estimation problems with robustness and effectiveness. To enhance the performance of TLBO-UEGS, a modified initialization scheme that leverages the strengths of chaotic maps and dynamic oppositional based learning is introduced. This scheme ensures the generation of an initial population with improved solution quality. Furthermore, both the modified teacher phase and modified learner phase are integrated within the TLBO-UEGS optimization framework. This integration allows for different learning strategies to be employed based on the fitness values of each learner, effectively updating their search trajectories. Within the modified teacher phase, two unique exemplar generation schemes are designed to facilitate more effective guidance for learners in the first half of the population while maintaining population diversity. Meanwhile, the modified learner phase emulates a realistic knowledge acquisition process by enabling learners in the second half of the population to engage in collaborative learning with multiple peer learners or retain valuable knowledge from previous learning processes. Extensive simulations demonstrate that TLBO-UEGS achieves superior results, with the minimum root mean square error (RMSE) values of 3.5644 × 10−04 ± 0.0014, 1.3237 × 10−04± 0.0043, and 6.6016 × 10−06± 0.00011 obtained for Photowatt-PWP201, Leibold Solar (LSM 20), and Leybold Solar (STE 4/100) PV modules, respectively.

An integrated differential evolution of multi-population based on contribution degree

The differential evolution algorithm based on multi-population mainly improves its performance through mutation strategy and grouping mechanism. However, each sub-population plays a different role in different periods of iterative evolution. If each sub-population is assigned the same computing resources, it will waste a lot of computing resources. In order to rationally distribute computational resources, an integrated differential evolution of multi-population based on contribution degree (MDE-ctd) is put forth in this work. In MDE-ctd, the whole population is divided into three sub-populations according to different update strategies: archival, exploratory, and integrated sub-populations. MDE-ctd dynamically adjusts computing resources according to the contribution degree of each sub-population. It can effectively use computing resources and speed up convergence. In the updating process of integrated sub-populations, a mutation strategy pool and two-parameter value pools are used to maintain population diversity. The experimental results of CEC2005 and CEC2014 benchmark functions show that MDE-ctd outperforms other state-of-art differential evolution algorithms based on multi-population, especially when it deals with highly complex optimization problems.Graphical abstractAn integrated differential evolution of multi-population based on contribution degree

A Multi-Objective Optimization Method for a Tractor Driveline Based on the Diversity Preservation Strategy of Gradient Crowding

This study presents a multi-objective optimization method for a tractor driveline based on the diversity maintenance strategy of gradient crowding. The objective was to address the trade-off between high power and low fuel consumption rates in a tractor driveline by optimizing the distribution of driveline ratios, aiming to enhance overall driving performance and reduce fuel consumption. This method introduces a strategy for evaluating gradient crowding to reduce non-inferior solution sets during selection to ensure the uniform and wide distribution of solutions while maintaining population diversity. The transmission ratio of a tractor is optimized by varying the input of the transmission ratios in each gear, constraining the theoretical tractor driving rate, common transmission ratio, and drive adhesion limit, and introducing the diversity maintenance strategy of gradient crowding. The goal is to reduce the loss rate of driving power and specific fuel consumption as much as possible. The analysis results demonstrate that the GC_NSGA-II algorithm, incorporating the evaluation strategy of gradient crowding, achieves greater diversity and a more uniform distribution in the front end. After verifying the algorithm, the optimized tractor showed a reduction of 41.62 (±S.D. 0.44)% in the theoretical loss rate of driving power and 62.8 (±S.D. 0.56)% in the loss rate of specific fuel consumption, indicating that the tractor’s drive performance significantly improved, accompanied by a substantial reduction in the fuel consumption rate. These findings affirm the feasibility of the proposed optimization method and provide valuable research insights for enhancing the overall performance of tractors.

Multi-objective binary grey wolf optimization for feature selection based on guided mutation strategy

Feature selection aims to choose a subset of features with minimal feature-feature correlation and maximum feature-class correlation, which can be considered as a multi-objective problem. Grey wolf optimization mimics the leadership hierarchy and group hunting mechanism of grey wolves in nature. However, it can easily fall into local optimization in multi-objective optimization. To address this, a novel multi-objective binary grey wolf optimization based on a guided mutation strategy (GMS), called MOBGWO-GMS, is proposed. In the initialization phase, the population is initialized based on feature correlation, and features are selected using a uniform operator. The proposed GMS uses the Pearson correlation coefficient to provide direction for local search, improving the local exploration ability of the population. Moreover, a dynamic agitation mechanism is used for perturbation to prevent population stagnation due to the use of a single strategy. The strategy is dynamically adjusted to maintain population diversity and improve detection ability. To evaluate the classification ability of quasi-optimal subsets, a wrapper-based k-nearest neighbor classifier was employed. The effectiveness of the proposed algorithm was demonstrated through an extensive comparison with eight well-known algorithms on fourteen benchmark datasets. Experimental results showed that the proposed approach is superior in the optimal trade-off between the two fitness evaluation criteria and can easily jump out of local optima compared to other algorithms.

Hierarchical learning particle swarm optimization using fuzzy logic

Particle swarm optimization (PSO) has been used extensively in numerical and engineering optimization problems in the last decades. However, due to drawbacks such as a single learning sample, PSO has the problems of loss of population diversity and easily falls into local optimum. To enhance optimization capability, a PSO based on fuzzy logic and hierarchical learning mechanism (FHPSO) is proposed. In FHPSO, the parameters are dynamically adjusted through fuzzy logic. The purpose of the fuzzy system is to generate appropriate parameters based on the performance metrics at each iteration, which better balances exploration and exploitation capability. Then particles are classified into different layers in terms of their fitness, and the particles in different layers perform different learning mechanisms. Each layer divides the particles into high-energy particles and low-energy particles. The high-energy particles in each layer are qualified to learn from the particles in the upper layer and the low-energy particles learn from the high-energy particles in their layer. This learning mechanism avoids all individuals to learn the global optimal individual at each iteration which will effectively reduce the speed and possibility of premature convergence and maintain population diversity. The FHPSO was compared with 8 well-known algorithms and 6 state-of-the-art PSO variants in the CEC 2022 and CEC 2021 test suites, respectively. The experimental results show significant performance of FHPSO. Simulation results for 5 complex engineering optimization problems and 3D path planning problem also show that the FHPSO can provides more competitive optimization results.

Problem-specific knowledge MOEA/D for energy-efficient scheduling of distributed permutation flow shop in heterogeneous factories

With the development of the global economy and the enhancement of environmental awareness, energy-efficient permutation flow shop scheduling gets more attention. Nevertheless, research on distributed scheduling with heterogeneous factories is scarce. In this paper, a knowledge-driven MOEA/D (KMOEA/D) is proposed to address the energy-efficient scheduling of distributed permutation flow shop problem in heterogeneous factories (DPFSP-HF) with the criteria of minimizing the makespan (Cmax) and total energy consumption (TEC). First, an efficient energy-saving strategy is proposed to reduce the TEC criteria. Second, a constructive heuristic is designed to generate a high-quality solution set. Third, an ingenious genetic operator is utilized to maintain population diversity. Fourth, the knowledge-driven local search operator combined the problem-specific knowledge is constructed according to the properties of DPFSP-HF. Additionally, the Taguchi approach is used to calibrate the parameter configuration of KMOEA/D. We evaluate the effectiveness of each improvement of KMOEA/D and compare it to other well-known multi-objective optimization algorithms on different instances. The results indicate the effectiveness of each improvement of KMOEA/D, and verify that KMOEA/D is an efficient approach to address DPFSP-HF.

An efficient hybrid optimization method for Fuzzy Flexible Job-Shop Scheduling Problem: Steady-state performance and analysis

Due to the uncertainty pervasive in manufacturing and production systems, a crisp processing time is no longer appropriate. Thus, the flexible job-shop scheduling issue comes with fuzzy processing times. Fuzzy numbers are used to depict the uncertainty associated with processing times. This paper proposes a Hybrid Fuzzy Flexible job-shop Scheduling Approach (HFFSA) for addressing the Fuzzy Flexible Job-Shop Scheduling Problem (FFJSSP). An encoding-and-decoding scheme is employed for initializing the population. HFFSA incorporates four operators to enhance the quality of solutions: the Different Positions Shuffling (DPS) operator, the Randomly Selected Positions Shuffling (RSPS) operator, the Block Shuffling (BS) operator and the Inversion Mutation (IM) operator. The DPS operator shuffles the different positions between a randomly generated solution and the current one. On the other hand, the RSPS shuffles random positions to maintain population diversity. The BS and IM work on a subset of positions from the current solution to obtain near-optimal solutions. Furthermore, we integrate the pair-wise local search strategy with HFFSA to improve the best solution. HFFSA is compared to twenty-five algorithms using Lei and remanufacturing benchmarks. Several statistical measures are employed, like the CPU time, best, average and worst fuzzy makespan values, boxplots and the Wilcoxon signed-rank test. The statistical analyses affirm the superiority of the proposed HFFSA.

CTOA: Toward a Chaotic-Based Tumbleweed Optimization Algorithm

Metaheuristic algorithms are an important area of research in artificial intelligence. The tumbleweed optimization algorithm (TOA) is the newest metaheuristic optimization algorithm that mimics the growth and reproduction of tumbleweeds. In practice, chaotic maps have proven to be an improved method of optimization algorithms, allowing the algorithm to jump out of the local optimum, maintain population diversity, and improve global search ability. This paper presents a chaotic-based tumbleweed optimization algorithm (CTOA) that incorporates chaotic maps into the optimization process of the TOA. By using 12 common chaotic maps, the proposed CTOA aims to improve population diversity and global exploration and to prevent the algorithm from falling into local optima. The performance of CTOA is tested using 28 benchmark functions from CEC2013, and the results show that the circle map is the most effective in improving the accuracy and convergence speed of CTOA, especially in 50D.

A Quantum-Based Beetle Swarm Optimization Algorithm for Numerical Optimization

The beetle antennae search (BAS) algorithm is an outstanding representative of swarm intelligence algorithms. However, the BAS algorithm still suffers from the deficiency of not being able to handle high-dimensional variables. A quantum-based beetle swarm optimization algorithm (QBSO) is proposed herein to address this deficiency. In order to maintain population diversity and improve the avoidance of falling into local optimal solutions, a novel quantum representation-based position updating strategy is designed. The current best solution is regarded as a linear superposition of two probabilistic states: positive and deceptive. An increase in or reset of the probability of the positive state is performed through a quantum rotation gate to maintain the local and global search ability. Finally, a variable search step strategy is adopted to speed up the ability of the convergence. The QBSO algorithm is verified against several swarm intelligence optimization algorithms, and the results show that the QBSO algorithm still has satisfactory performance at a very small population size.

MFO-SFR: An Enhanced Moth-Flame Optimization Algorithm Using an Effective Stagnation Finding and Replacing Strategy

Moth-flame optimization (MFO) is a prominent problem solver with a simple structure that is widely used to solve different optimization problems. However, MFO and its variants inherently suffer from poor population diversity, leading to premature convergence to local optima and losses in the quality of its solutions. To overcome these limitations, an enhanced moth-flame optimization algorithm named MFO-SFR was developed to solve global optimization problems. The MFO-SFR algorithm introduces an effective stagnation finding and replacing (SFR) strategy to effectively maintain population diversity throughout the optimization process. The SFR strategy can find stagnant solutions using a distance-based technique and replaces them with a selected solution from the archive constructed from the previous solutions. The effectiveness of the proposed MFO-SFR algorithm was extensively assessed in 30 and 50 dimensions using the CEC 2018 benchmark functions, which simulated unimodal, multimodal, hybrid, and composition problems. Then, the obtained results were compared with two sets of competitors. In the first comparative set, the MFO algorithm and its well-known variants, specifically LMFO, WCMFO, CMFO, ODSFMFO, SMFO, and WMFO, were considered. Five state-of-the-art metaheuristic algorithms, including PSO, KH, GWO, CSA, and HOA, were considered in the second comparative set. The results were then statistically analyzed through the Friedman test. Ultimately, the capacity of the proposed algorithm to solve mechanical engineering problems was evaluated with two problems from the latest CEC 2020 test-suite. The experimental results and statistical analysis confirmed that the proposed MFO-SFR algorithm was superior to the MFO variants and state-of-the-art metaheuristic algorithms for solving complex global optimization problems, with 91.38% effectiveness.

Improved whale swarm algorithm for solving material emergency dispatching problem with changing road conditions.

To overcome the problem of easily falling into local extreme values of the whale swarm algorithm to solve the material emergency dispatching problem with changing road conditions, an improved whale swarm algorithm is proposed. First, an improved scan and Clarke-Wright algorithm is used to obtain the optimal vehicle path at the initial time. Then, the group movement strategy is designed to generate offspring individuals with an improved quality for refining the updating ability of individuals in the population. Finally, in order to maintain population diversity, a different weights strategy is used to expand individual search spaces, which can prevent individuals from prematurely gathering in a certain area. The experimental results show that the performance of the improved whale swarm algorithm is better than that of the ant colony system and the adaptive chaotic genetic algorithm, which can minimize the cost of material distribution and effectively eliminate the adverse effects caused by the change of road conditions.

A NEW PSO-BASED ALGORITHM FOR AN OPERATIONAL MANAGEMENT PROBLEM

Operational management issues represent a permanent challenge for the current economic environment and the research activity. This research will model a Travelling Salesman Problem (TSP). The complexity of this fundamental problem (np-hard) allows a chance to apply and develop heuristic methods and evolutionary algorithms along with exact methods (dynamic programming, branch & bound). This paper proposes a new discrete algorithm to solve the TSP based on the Particle Swarm Optimization (PSO) technique. The features of this method are fast determination through an iterative process of the optimal problem, the generalised search in all the solutions, and the avoidance of the local optimal. To avoid premature convergence, we have introduced a new operator with a new mathematical function, and we have proposed new techniques for measuring and maintaining population diversity. We tested the algorithm's performance by applying it to numerical instances and compared it to the solutions and performance provided by other evolutionary algorithms. By delaying the convergence process, the new algorithm PSO offers reasonable solutions in terms of quality comparable to those offered by different evolutionary algorithms tested. At the end of the research, we highlighted the conclusions, limitations, and new techniques based on the PSO algorithm.

PRETTY: A parallel transgenerational learning-assisted evolutionary algorithm for computationally expensive multi-objective optimization

Many real-world optimization problems, called computationally expensive optimization problems, often require a time-consuming fitness evaluation through computer simulation or neural network training. A persistent challenge is to obtain reasonable solutions to these problems quickly. In this study, we design a parallel transgenerational learning-assisted evolutionary algorithm, called PRETTY, to accelerate the search process using three novel mechanisms. First, we fuse the transgenerational learning mechanism with metaheuristic algorithms to reduce unnecessary fitness evaluations. Then, a Hypervolume-Cauchy (HV-Cauchy) algorithm is proposed to balance population convergence and diversity adaptively. Finally, a parallel-computing framework is proposed to fuse the transgenerational learning mechanism and the HV-Cauchy algorithm into a multipopulation evolutionary algorithm. To verify the performance of the proposed algorithm, empirical experiments are conducted on nine benchmarks and four real-world problems, including feature selection, critical node detection, flocking, and neural network training. In terms of execution time, the experimental results demonstrate that PRETTY has significant advantages over several expensive multi-objective algorithms. Furthermore, PRETTY can maintain population diversity and fast convergence while accelerating the computation. In particular, in tackling real-world problems that require expensive fitness calculations, PRETTY can reduce the execution time by more than five times while ensuring high-quality solutions.