Multi-objective Particle Swarm Optimization Research Articles

A switching competitive swarm optimizer for multi-objective optimization with irregular Pareto fronts

In the past two decades, multi-objective particle swarm optimization, as a powerful swarm intelligence paradigm, has been widely used to solve multi-objective optimization problems. By further exploring the competition mechanism among particles in the swarm, some particle update strategies have been proposed, which are effective in improving convergence performance and search speed. However, these strategies encounter difficulties in properly approximating irregular Pareto fronts (PFs), as their geometric structures are complex, leading to get trapped in local optima. To address this issue, a switching competitive swarm optimizer for multi-objective optimization with irregular PFs is proposed. In comparison with existing approaches that utilize reference vectors to guide the search or selection process, the proposed approach introduces a competition-based learning strategy with a novel winner determination mechanism. Within this strategy, independent neighborhoods are constructed for each winner to learn the structure of irregular PFs. To take advantage of the potential knowledge of winners, the switching competitive swarm optimizer is designed to provide more diverse search directions. The experimental results demonstrate the superiority of the proposed algorithm over several state-of-the-art evolutionary algorithms in tackling multi-objective optimization problems with irregular PFs.

Two Improved Multiobjective Fractional-Order Particle Swarm Optimization Algorithms for True Temperature Inversion of Multiwavelength Pyrometer

Two Improved Multiobjective Fractional-Order Particle Swarm Optimization Algorithms for True Temperature Inversion of Multiwavelength Pyrometer

Global Path Planning Algorithm for Unmanned Vehicles Based on Multi-Objective Particle Swarm Optimization Strategy

To overcome the limitations of unmanned vehicle global path planning with the sole objective of distance, a multi-objective particle swarm optimization strategy is proposed for indoor unmanned vehicle path planning. This strategy integrates objectives related to travel distance and cumulative turning angle. The traditional distance function is enhanced to accelerate algorithm convergence, and cumulative turning angle is introduced to construct a comprehensive function, meeting the demands of multi-objective navigation. The Pareto solution set concept is incorporated, and through the multi-objective particle swarm optimization algorithm, optimal paths for different travel objectives are identified, enhancing solution comprehensiveness. Experimental results validate the feasibility and effectiveness of the improved algorithm.

New Methods for Optimal Power Allocation and Joint Resource Scheduling in 5G Network which Use Mobile Edge Computing

Mobile Edge Computing (MEC) is considered one of the enabling and promising technologies in 5G networks, especially with the massive data movement of various devices and the increased demand for computing. Here, computational offloading of tasks to edge clouds provides an effective, flexible, low-latency solution for mobile users in the network. However, the limited computing resources in edge clouds and the dynamic demands of mobile users make it difficult to schedule computing requests to appropriate edge clouds, and make the offloading process energetically expensive for devices. Therefore, it is very important to design an energy-efficient offloading strategy. To this end, we first formulate the transmission power allocation (PA) problem for mobile phone users to minimize power consumption. Using a quasi-convex technique, we address the (PA) problem using a (Hybrid GAPSO) algorithm resulting from combining the Genetic Algorithm (GA) with the Particle Swarm Optimization (PSO) algorithm. Next, we model the joint request offloading and resource scheduling (JRORS) problem as a mixed- nonlinear program to minimize the response delay of requests. The (JRORS) problem can be divided into two problems, namely the request offloading (RO) problem and the computing resource scheduling (RS) problem. Therefore, we analyze the JRORS problem as a dual decision problem and propose a multi-objective particle swarm optimization algorithm referred as (MO-PSO). The simulation results show that (HGAPSO) can save transmission power consumption and has good convergence property, and (MO-PSO) outperforms existing methods in terms of response rate and can maintain good performance in a dynamic network.

Optimal design of diversion dams based on Upgraded Multi-Objective Particle Swarm Optimization (UMOPSO)

In the present research, the application of the Upgraded Multi-Objective Particle Swarm Optimization (UMOPSO) algorithm is investigated with the aim of reducing concreting costs through minimizing the diversion dam weight function. At the time of using optimization algorithms, regarding the nature of such a;gorithms and the research problem, making changes in algorithm running steps is necessary. Hence, in the current study, making some changes in the UMOPSO algorithm develops it to solve multi-objective optimization problems by considering their problem restrictions. In this paper, the study diversion dam is the Nazelian dam located in Kermanshah, Province, Iran. The decision variables in the optimization problem include the height of upstream and downstream cut off walls, the length and the thickness of the upstream concrete bed and the thickness of the stilling basin. By considering the initial population (n = 15), the optimal answer is achieved in iteration 100 and after algorithm run 1500. In this study, considering that the objective function should be evaluated for five decision variables with infinite possible values on a discrete range for each variable, the general result of the present study emphasizes on the desirable efficiency and speed of the UMOPSO algorithm in finding the optimal answer of the diversion dam optimal design problem which shows the strength of this algorithm.

An Agile Approach for Adopting Sustainable Energy Solutions with Advanced Computational Techniques

In the face of the burgeoning electricity demands and the imperative for sustainable development amidst rapid industrialization, this study introduces a dynamic and adaptable framework suitable for policymakers and renewable energy experts working on integrating and optimizing renewable energy solutions. While using a case study representative model for Sub-Saharan Africa (SSA) to demonstrate the challenges and opportunities present in introducing optimization methods to bridge power supply deficits and the scalability of the model to other regions, this study presents an agile multi-criteria decision tool that pivots on four key development phases, advancing established methodologies and pioneering refined computational techniques, to select optimal configurations from a set of Policy Decision-Making Metrics (PDM-DPS). Central to this investigation lies a rigorous comparative analysis of variants of three advanced algorithmic approaches: Swarm-Based Multi-objective Particle Swarm Optimization (MOPSO), Decomposition-Based Multi-objective Evolutionary Algorithm (MOEA/D), and Evolutionary-Based Strength Pareto Evolutionary Algorithm (SPEA2). These are applied to a grid-connected hybrid system, evaluated through a comprehensive 8760-hour simulation over a 20-year planning horizon. The evaluation is further enhanced by a set of refined Algorithm Performance Evaluation Metrics (AL-PEM) tailored to the specific constraints. The findings not only underscore the robustness and consistency of the SPEA2 variant over 15 runs of 200 generations each, which ranks first on the AL-PEM scale, but the findings also validate the strategic merit of combining multiple technologies and empowering policymakers with a versatile toolkit for informed decision-making.

Dual resource constrained flexible job shop scheduling with sequence‐dependent setup time

AbstractThis study addresses the imperative need for efficient solutions in the context of the dual resource constrained flexible job shop scheduling problem with sequence‐dependent setup times (DRCFJS‐SDSTs). We introduce a pioneering tri‐objective mixed‐integer linear mathematical model tailored to this complex challenge. Our model is designed to optimize the assignment of operations to candidate multi‐skilled machines and operators, with the primary goals of minimizing operators' idleness cost and sequence‐dependent setup time‐related expenses. Additionally, it aims to mitigate total tardiness and earliness penalties while regulating maximum machine workload. Given the NP‐hard nature of the proposed DRCFJS‐SDST, we employ the epsilon constraint method to derive exact optimal solutions for small‐scale problems. For larger instances, we develop a modified variant of the multi‐objective invasive weed optimization (MOIWO) algorithm, enhanced by a fuzzy sorting algorithm for competitive exclusion. In the absence of established benchmarks in the literature, we validate our solutions against those generated by multi‐objective particle swarm optimization (MOPSO) and non‐dominated sorted genetic algorithm (NSGA‐II). Through comparative analysis, we demonstrate the superior performance of MOIWO. Specifically, when compared with NSGA‐II, MOIWO achieves success rates of 90.83% and shows similar performance in 4.17% of cases. Moreover, compared with MOPSO, MOIWO achieves success rates of 84.17% and exhibits similar performance in 9.17% of cases. These findings contribute significantly to the advancement of scheduling optimization methodologies.

A multi-objective PSO for DC microgrids: Efficient battery management to minimize energy losses and operating costs

This article addresses the challenge of battery energy management in a Direct Current (DC) Microgrid (MG) with distributed photovoltaic generators working at their highest power point. This study adopted a multi-objective approach whose main goals is to reduce energy losses and operating costs. To mathematically model this problem, we used Multi-Objective Mixed-Integer Nonlinear Programming (MOMINLP) that incorporated two conflicting objective functions that minimize — at the same time — the energy losses and operating costs of DC MGs. To solve this problem, we followed a master–slave approach. Two multi-objective algorithms were used in the master stage: the Multi-Objective Particle Swarm Optimizer (MOPSO) and the Multi-Objective Lion Ant Optimizer (MOALO). The slave stage applied an hourly load flow analysis employing the method of Successive Approximations (SAs). To validate our methodology, the 33-bus test feeder was adapted by incorporating specific data on generated power and electricity demand from a specific region in Colombia. These data (obtained from the local network operator) are projections of electricity demand for an average day in the region under analysis. The methodology was implemented in the MATLAB environment, and each algorithm was run 100 times to assess standard deviations, maximum reductions, average reductions, and processing times. The two algorithms were compared to identify which one exhibited the best performance when they solved the problem examined here. The results proved that the MOPSO was the most effective approach in terms of minimizing operating costs and significantly reducing energy losses compared to the benchmark scenario.

A Pacesetter-Lévy multi-objective particle swarm optimization with Arnold Chaotic Map with opposition-based learning

To accelerate the convergence of multi-objective optimization algorithm and achieve an optimization solution set with good diversity, this paper proposes the Pacesetter-Lévy Multi-Objective Particle Swarm Optimization using Arnold Chaotic Map with Opposition-Based Learning algorithm (PLMOPSOCO). Firstly, the Arnold Chaotic Map with Opposition-based Learning is proposed to generate some valuable particles in the stage of initialization while maintaining the diversity of population, which can speed up exploration. Secondly, a competition mechanism with k-means clustering is integrated to categorize particles into losers and winners. The flight direction of the loser particles is adjusted according to the Pacesetter-Lévy kinetic equation, an innovative approach to effectively enhance the population’s exploitative ability. Thirdly, a crossover mutation is implemented to assist particles to escape local optima and prevent population stagnation. Comparative studies on benchmark functions demonstrate that this new algorithm is more competitive in terms of both diversity and convergence when compared to several advanced multi-objective algorithms.

Two-stage particle swarm optimization with dual-indicator fusion ranking for multi-objective problems

Elite solutions guiding population evolution are often used as one of main ideas to improve the performance of multi-objective particle swarm optimization (MOPSO). However, in most research work, sole Pareto dominance criterion is often used to evaluate solutions. This sole criterion may easily cause some problems, such as the premature convergence. In this study, we propose an MOPSO variant with dual-indicator fusion ranking (TPSO-DF), to evaluate elite solutions and to guide search without sacrificing diversity. In TPSO-DF, two indicators are introduced by using the convergence and diversity information, respectively. Both indicators are then fusioned in a ranking measure to focus on valuable information and to filter out solutions with these valuable information. Meanwhile, an adaptive global leader selection strategy is introduced to take full advantage of valuable information and to guide population evolution toward the optimal direction. As another contribution of this study, a two-stage hybrid mutation strategy is designed by utilizing the valuable information differently in different evolutionary states of the algorithm to enhance performance. Compared to eight representative multi-objective evolutionary algorithms, the performance of TPSO-DF is validated by extensive experiments on ZDT and DTLZ test suites, as well as one practical problem. Experimental results show that TPSO-DF can achieve competitive performance on most of the test functions.

Multi-Objective Plum Tree Algorithm and Machine Learning for Heating and Cooling Load Prediction

The prediction of heating and cooling loads using machine learning algorithms has been considered frequently in the research literature. However, many of the studies considered the default values of the hyperparameters. This manuscript addresses both the selection of the best regressor and the tuning of the hyperparameter values using a novel nature-inspired algorithm, namely, the Multi-Objective Plum Tree Algorithm. The two objectives that were optimized were the averages of the heating and cooling predictions. The three algorithms that were compared were the Extra Trees Regressor, the Gradient Boosting Regressor, and the Random Forest Regressor of the sklearn machine learning Python library. We considered five hyperparameters which were configurable for each of the three regressors. The solutions were ranked using the MOORA method. The Multi-Objective Plum Tree Algorithm returned a root mean square error value for heating equal to 0.035719 and a root mean square error for cooling equal to 0.076197. The results are comparable to the ones obtained using standard multi-objective algorithms such as the Multi-Objective Grey Wolf Optimizer, Multi-Objective Particle Swarm Optimization, and NSGA-II. The results are also performant concerning the previous studies, which considered the same experimental dataset.

Application of Health Education Program based on Intelligent Recommendation Algorithm in the Development of School-age Children's Hand Hygiene Behavior

The cultivation of hand hygiene behavior among school-age children is an important way to prevent the spread of diseases and ensure children’s health. However, traditional health education methods lack personalized programs tailored to each child, which cannot effectively improve their hand hygiene awareness and behavior. In response to this issue, the study combines multi-objective particle swarm optimization algorithm to provide personalized hand hygiene behavior development recommendations for school-age children, improving their hand hygiene awareness and behavioral level. The study adopted multi-objective particle swarm optimization algorithm and convolutional neural network, combined with the personalized needs of school-age children and the goal of cultivating hand hygiene behavior, and proposed a health education plan based on intelligent recommendation algorithm. Through deep learning, match the hand hygiene needs of school-age children with corresponding health education plans to achieve personalized recommendations. The average accuracy of the health education recommendation plan for hand hygiene behavior cultivation of school-age children based on multi-objective particle swarm optimization algorithm reaches 99.07%. Meanwhile, after introducing convolutional neural networks, the feature matching error between the recommended scheme and school-age children ranges from 10-1 to 10-2. After testing, the designed algorithm performs more stably and has less fluctuations under different sparsity conditions. Health education solutions based on intelligent recommendation algorithms can provide personalized solutions for school-age children, effectively cultivate their hand hygiene behavior, and meet various health needs.

Multi-objective optimization and sensitivity analysis of offset strip fin compact heat exchangers

In this study, the aerothermal performance of Offset Strip Fin Compact Heat Exchangers (OSF-CHE) is optimized with the multi-objective Particle Swarm Optimization method. Available empirical correlations for the Fanning factor and Colburn factor are utilized in the optimization process. Selected off-design Pareto-optimal solutions for compact heat exchanger configurations are reconstructed and simulated by Computational Fluid Dynamics simulations at various boundary conditions after extensive validation processes. Optimized OSF-CHE designs are shown to have improved aerothermal performances among comparable designs in the literature. It has been shown that a high Reynolds number in the range of 1,500–2,000 as a flow attribute provides the Fanning factor ranging from 0.0228 to 0.0619 and the Colburn factor between 0.0067 and 0.0122 and Re is more dominant than geometric design variables on the objective functions. Low and moderate Reynolds number flows at 500 and 1,000 offer a wider selection range for both objective functions on the Pareto-front.

Multi-objective optimization of solar-driven hollow fiber membrane dehumidification system based on MOPSO

The solar-driven hollow fiber membrane dehumidification (SHFMD) system is a renewable, energy-saving, and highly effective dehumidification system. It provides an effective solution to the problem of air-entrained liquid droplets during the traditional solution dehumidification process. The system's mathematical model was established and the reliability of the mathematical model was verified by experimental data. To enhance the comprehensive performance of the system, the multi-objective particle swarm optimization (MOPSO) algorithm is used in this paper to optimize the multi-objective parameters of the system. The objective function is the total exergy destruction of the system and the dehumidification capacity of the system. The optimization variables are cold water temperature, cold water flow rate, solution flow rate, air flow rate, and hot water flow rate. The optimization is performed using the multi-objective particle swarm optimization (MOPSO) algorithm to obtain the Pareto front, and the points of the Pareto front are normalized. Finally, the optimal trade-off point of the Pareto frontier is obtained. Each operating parameter of the optimal point of the Pareto front is also analyzed. The results show that the air flow rate and cold water flow rate have the most influence on the conflict between the total exergy destruction of the system and the dehumidification capacity of the system.

Optimizing Route and Speed under the Sulfur Emission Control Areas for a Cruise Liner: A New Strategy Considering Route Competitiveness and Low Carbon

In order to reduce pollution caused by ship emissions, the International Maritime Organization (IMO) implemented sulfur emission control areas (SECAs). In comparison to ordinary vessels, cruise ships with dual attributes of transportation and tourism generate a greater amount of marine pollution, which poses a significant threat to the marine environment in both berthing ports and the sailing area. In light of the fierce competition of the cruise tourism market, cruise lines are looking for strategies, such as designing more attractive cruise routes, to maintain their core competencies under the emission control policy. In order to achieve this goal, this paper presents a mixed-integer non-linear programming (MINP) model with two objectives and is derived from the traditional route optimization problem. The primary objective is to optimize the route and speed of a cruise liner, while simultaneously enhancing route competitiveness and minimizing carbon emissions both within and outside the SECAs. Subsequently, the multi-objective particle swarm optimization (MOPSO) algorithm was used to reach the objective, and simulations were carried out to verify the effectiveness of the model and method. The results show that speed and sailing route optimization can affect carbon emissions. This paper has a certain application value and guiding significance for cruise line decision makers that will be beneficial for the environment.

A multi-objective optimisation approach with improved pareto-optimal solutions to enhance economic and environmental dispatch in power systems

This work implements the recently developed nth state Markovian jumping particle swarm optimisation (PSO) algorithm with local search (NS-MJPSOloc) awareness method to address the economic/environmental dispatch (EED) problem. The proposed approach, known as the Non-dominated Sorting Multi-objective PSO with Local Best (NS-MJPSOloc), aims to enhance the performance of the PSO algorithm in multi-objective optimisation problems. This is achieved by redefining the concept of best local candidates within the search space of multi-objective optimisation. The NS-MJPSOloc algorithm uses an evolutionary factor-based mechanism to identify the optimum compromise solution, a Markov chain state jumping technique to control the Pareto-optimal set size, and a neighbourhood’s topology (such as a ring or a star) to determine its size. Economic dispatch refers to the systematic allocation of available power resources in order to fulfill all relevant limitations and effectively meet the demand for electricity at the lowest possible operating cost. As a result of heightened public consciousness regarding environmental pollution and the implementation of clean air amendments, nations worldwide have compelled utilities to adapt their operational practises in order to comply with environmental regulations. The (NS-MJPSOloc) approach has been utilised for resolving the EED problem, including cost and emission objectives that are not commensurable. The findings illustrate the efficacy of the suggested (NS-MJPSOloc) approach in producing a collection of Pareto-optimal solutions that are evenly dispersed within a single iteration. The comparison of several approaches reveals the higher performance of the suggested (NS-MJPSOloc) in terms of the diversity of the Pareto-optimal solutions achieved. In addition, a measure of solution quality based on Pareto optimality has been incorporated. The findings validate the effectiveness of the proposed (NS-MJPSOloc) approach in addressing the multi-objective EED issue and generating a trade-off solution that is both optimal and of high quality. We observed that our approach can reduce ∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim $$\\end{document}6.4% of fuel costs and ∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim $$\\end{document}9.1% of computational time in comparison to the classical PSO technique. Furthermore, our method can reduce ∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim $$\\end{document}9.4% of the emissions measured in tons per hour as compared to the PSO approach.

Study on charge and discharge control strategy of improved PSO for EV

In view of the negative influence of electric vehicle (EV) random charging on power grid load stability and charging cost of users, on the premise of guaranteeing users' travel demand, in this paper, an improved PSO model is proposed with the objective function of optimizing the daily load variance of the power grid and minimizing the charge cost of the vehicle owner. In this model, chaotic mapping is used to initialize the position of particles so that the particles are uniformly distributed in space and the diversity of particle solutions is increased, based on the global search ability and local search ability of the improved algorithm, combined with the analysis of a numerical example, the results show that the improved multi-objective PSO algorithm converges quickly and can jump out of the local optimum, better multi-objective optimization to reduce the peak-valley load difference and charging costs.

Developing a fuzzy bi-objective programming and MCDM model for bridge maintenance strategy optimization

Bridges serve as critical links in road networks, requiring continuous maintenance to ensure proper functionality throughout their lifespan. Given their pivotal role in the urban landscape, connecting various parts of a city, this research presents a multi-objective optimization model for the maintenance and repair of bridges in Babolsar, Iran. The model takes into account budget constraints and aims to minimize the total life cycle and user costs, encompassing traffic delays and vehicle expenses, while maximizing the reliability of the bridge network. Recognizing the inherent complexity of this problem, a multi-objective particle swarm optimization algorithm has been developed for an accurate solution. The study further conducts sensitivity analysis on the objective function concerning the available budget, evaluating key parameters such as hourly costs and the time value of vehicles. The results show that with an increase in the budget level, the number of repairs related to the most costly maintenance has significantly risen. In other words, as the budget expands, the model tends to favor repairs with higher costs because their impact on the bridge’s performance is more substantial.

Optimization of a photovoltaic/wind/battery energy-based microgrid in distribution network using machine learning and fuzzy multi-objective improved Kepler optimizer algorithms

In this study, a fuzzy multi-objective framework is performed for optimization of a hybrid microgrid (HMG) including photovoltaic (PV) and wind energy sources linked with battery energy storage (PV/WT/BES) in a 33-bus distribution network to minimize the cost of energy losses, minimizing the voltage oscillations as well as power purchased minimization from the HMG incorporated forecasted data. The variables are microgrid optimal location and capacity of the HMG components in the network which are determined through a multi-objective improved Kepler optimization algorithm (MOIKOA) modeled by Kepler’s laws of planetary motion, piecewise linear chaotic map and using the FDMT. In this study, a machine learning approach using a multilayer perceptron artificial neural network (MLP-ANN) has been used to forecast solar radiation, wind speed, temperature, and load data. The optimization problem is implemented in three optimization scenarios based on real and forecasted data as well as the investigation of the battery's depth of discharge in the HMG optimization in the distribution network and its effects on the different objectives. The results including energy losses, voltage deviations, and purchased power from the HMG have been presented. Also, the MOIKOA superior capability is validated in comparison with the multi-objective conventional Kepler optimization algorithm, multi-objective particle swarm optimization, and multi-objective genetic algorithm in problem-solving. The findings are cleared that microgrid multi-objective optimization in the distribution network considering forecasted data based on the MLP-ANN causes an increase of 3.50%, 2.33%, and 1.98%, respectively, in annual energy losses, voltage deviation, and the purchased power cost from the HMG compared to the real data-based optimization. Also, the outcomes proved that increasing the battery depth of discharge causes the BES to have more participation in the HMG effectiveness on the distribution network objectives and affects the network energy losses and voltage deviation reduction.

Application of Particle Swarm Optimisation in Multi-Objective Cost Optimisation of Engineering Enterprises under the Background of Digital Economy

Engineering projects must meet quality and schedule requirements during construction. This is a typical multi-objective problem and a difficult point in the management of engineering enterprises. To address these issues, a research study proposes an intelligent multi-objective optimisation technique. First, analyse the optimisation objectives of the enterprise in the context of digitalisation. Then, construct a multi-objective cost optimisation model for engineering enterprises. Second, the Multi-Objective Particle Swarm Optimisation (MOPSO) algorithm is introduced to solve multi- objective problems. To improve the multi-objective optimisation effect of the model, the inertia weight parameters and particle learning behaviour are optimised and adjusted, as the model is prone to getting stuck in local optima. In the performance test of the algorithm model, the optimised MOPSO model can accurately search for the minimum value of 0 at the position (0, 0) under the Rastrig in function, and at the same time, the number of iteration convergence is the least. The GA, ACOM, and traditional MOPSO models have more iterative convergence times, and the optimisation results are 0.10, 0.15, and 0.14, respectively. It can be seen that the performance of the optimised MOPSO model is better. In the specific example analysis, using the optimised MOPSO solution, the project cost was reduced from 31 million yuan in the contract to 30.52 million yuan, and the construction period was shortened from 588 days to 540 days, and met the environmental protection and quality requirements. The research content can provide important decision support for engineering project managers.