Inverted Generational Distance Research Articles

A Hybrid and Light Weight Metaheuristic Approach with Clustering for Multi-Objective Resource Scheduling and Application Placement in Fog Environment

Fog computing is receiving considerable attention in the research community to deliver computing resources for Internet of Things (IoT) devices. With rapid advancements in IoT, it is necessary to cater to the applications closer to the user using fog which acts as a potential complement to the cloud. In practice, scheduling of fog devices and allocation of IoT applications to fog play a key role, if improperly done, IoT applications in a fog environment may not be deployed effectively. As a result, there is a wastage of resources, an increase in network latency, and a burden on Quality of Service (QoS) on the fog nodes, resulting in a multi-objective optimization problem. To analyze the scheduling and allocation problem of fog nodes this work proposes a combinatorial novel model based on a metaheuristic approach called Enhanced Multi-Objective Particle Swarm Optimization with Clustering (EMOPSOC) and Fog Picker. The proposed EMOPSOC is alightweight algorithmthat dynamically schedules the fog nodes based on a multi-objective optimization problem. The model usesthe application of machine learning techniques to enhance the evolutionary computation algorithmby minimizing the latency between the IoT and fog devices, resource wastage, and load imbalances, as well as making efficient use of the resources and reducing turnaround time. In addition, the Fog Picker deployed in the model allocates the IoT components to the fog nodes based on QoS attributes. The proposed approach is simulated and tested using iFogSim and jMetal. The performance of the proposed algorithm was tested on several benchmark test functions using Inverted Generational Distance (IGD) and Hypervolume (HV) indicators. The experimental results show that EMOPSOC in combination with Fog Picker has outperformed the variants of Multi-Objective Particle Swarm Optimization (MOPSO) algorithms and state-of-the-art algorithms such as Non-Dominated Sorting Genetic Algorithm-II (NSGA-II), Strength Pareto Evolutionary Algorithm-II (SPEA-II) by maintaining meritoriously distributed populations, converging quickly, and maintaining steady performance without forfeiting steadiness. Finally, the numerical results verify, that the optimal solution set has improved convergence and divergence over the relative methods. The experimental results of the Fog Picker have increased by 80%, indicating that the efficiency is greatly improved even when the fog nodes and IoT application components are increased.

Performance Analysis of Multi-Objective Simulated Annealing Based on Decomposition

Simulated annealing is a metaheuristic that balances exploration and exploitation to solve global optimization problems. However, to deal with multi- and many-objective optimization problems, this balance needs to be improved due to diverse factors such as the number of objectives. To deal with this issue, this work proposes MOSA/D, a hybrid framework for multi-objective simulated annealing based on decomposition and evolutionary perturbation functions. According to the literature, the decomposition strategy allows diversity in a population while evolutionary perturbations add convergence toward the Pareto front; however, a question should be asked: What is the effect of such components when included as part of a multi-objective simulated annealing design? Hence, this work studies the performance of the MOSA/D framework considering in its implementation two widely used perturbation operators: classical genetic operators and differential evolution. The proposed algorithms are MOSA/D-CGO, based on classical genetic operators, and MOSA/D-DE, based on differential evolution operators. The main contribution of this work is the performance analysis of MOSA/D using both perturbation operators and identifying the one most suitable for the framework. The approaches were tested using DTLZ on two and three objectives and CEC2009 benchmarks on two, three, five, and ten objectives; the performance analysis considered diversity and convergence measured through the hypervolume (HV) and inverted generational distance (IGD) indicators. The results pointed out that there is a promising improvement in performance in favor of MOSA/D-DE.

Tourism Route Recommendation Based on A Multi-Objective Evolutionary Algorithm Using Two-Stage Decomposition and Pareto Layering

Tourism route planning is widely applied in the smart tourism field. The Pareto-optimal front obtained by the traditional multi-objective evolutionary algorithm exhibits long tails, sharp peaks and disconnected regions problems, which leads to uneven distribution and weak diversity of optimization solutions of tourism routes. Inspired by these limitations, we propose a multi-objective evolutionary algorithm for tourism route recommendation (MOTRR) with two-stage and Pareto layering based on decomposition. The method decomposes the multi-objective problem into several subproblems, and improves the distribution of solutions through a two-stage method. The crowding degree mechanism between extreme and intermediate populations is used in the two-stage method. The neighborhood is determined according to the weight of the subproblem for crossover mutation. Finally, Pareto layering is used to improve the updating efficiency and population diversity of the solution. The two-stage method is combined with the Pareto layering structure, which not only maintains the distribution and diversity of the algorithm, but also avoids the same solutions. Compared with several classical benchmark algorithms, the experimental results demonstrate competitive advantages on five test functions, hypervolume (HV) and inverted generational distance (IGD) metrics. Using the experimental results of real scenic spot datasets from two famous tourism social networking sites with vast amounts of users and large-scale online comments in Beijing, our proposed algorithm shows better distribution. It proves that the tourism routes recommended by our proposed algorithm have better distribution and diversity, so that the recommended routes can better meet the personalized needs of tourists.

Multi-objective SHADE with manta ray foraging optimizer for structural design problems

This paper presents a hybrid multi-objective success history-based parameter adaptive differential evolution (SHADE) with manta ray foraging optimizer (MRFO) for structural design problems, called MO-SHADE-MRFO. In the proposed algorithm, the updating rules of SHADE, a variant of differential evolution with great performance, are combined with the operators from MRFO, a recent swarm-based metaheuristic algorithm inspired from the manta ray with cyclone, chain and somersault foraging behaviors, which can balance the exploration and exploitation of the algorithm for structural design problems. Furthermore, MO-SHADE-MRFO utilizes the external archive to save and update the obtained Pareto fronts during the optimization process. The proposed algorithm is verified by multi-objective truss optimization problems with two objectives of minimizing the structural weight and the compliance, including 10-bar, 25-bar, 37-bar, 120-bar, 200-bar and 942-bar truss problems. Moreover, 9 different multi-objective metaheuristic algorithms are implemented to compare with the proposed algorithm, where three metrics are used to measure the performance of the algorithms, including hypervolume (HV), inverted generational distance (IGD), and spacing-to-extent (STE). According to the experimental results, MO-SHADE-MRFO can provide the best statistical values of HV, IGD and STE in most cases, ranking the first among the compared algorithms. Besides, the proposed algorithm also gives well-distributed Pareto solutions for the tested problems, illustrating the effectiveness of the hybrid updating rules of SHADE and MRFO.

SONG: A Multi-Objective Evolutionary Algorithm for Delay and Energy Aware Facility Location in Vehicular Fog Networks.

With the emergence of delay- and energy-critical vehicular applications, forwarding sense-actuate data from vehicles to the cloud became practically infeasible. Therefore, a new computational model called Vehicular Fog Computing (VFC) was proposed. It offloads the computation workload from passenger devices (PDs) to transportation infrastructures such as roadside units (RSUs) and base stations (BSs), called static fog nodes. It can also exploit the underutilized computation resources of nearby vehicles that can act as vehicular fog nodes (VFNs) and provide delay- and energy-aware computing services. However, the capacity planning and dimensioning of VFC, which come under a class of facility location problems (FLPs), is a challenging issue. The complexity arises from the spatio-temporal dynamics of vehicular traffic, varying resource demand from PD applications, and the mobility of VFNs. This paper proposes a multi-objective optimization model to investigate the facility location in VFC networks. The solutions to this model generate optimal VFC topologies pertaining to an optimized trade-off (Pareto front) between the service delay and energy consumption. Thus, to solve this model, we propose a hybrid Evolutionary Multi-Objective (EMO) algorithm called Swarm Optimized Non-dominated sorting Genetic algorithm (SONG). It combines the convergence and search efficiency of two popular EMO algorithms: the Non-dominated Sorting Genetic Algorithm (NSGA-II) and Speed-constrained Particle Swarm Optimization (SMPSO). First, we solve an example problem using the SONG algorithm to illustrate the delay-energy solution frontiers and plotted the corresponding layout topology. Subsequently, we evaluate the evolutionary performance of the SONG algorithm on real-world vehicular traces against three quality indicators: Hyper-Volume (HV), Inverted Generational Distance (IGD) and CPU delay gap. The empirical results show that SONG exhibits improved solution quality over the NSGA-II and SMPSO algorithms and hence can be utilized as a potential tool by the service providers for the planning and design of VFC networks.

Chaos-enhanced multi-objective tunicate swarm algorithm for economic-emission load dispatch problem

Climate change and environmental protection have a significant impact on thermal plants. So, the main principles of combined economic-emission dispatch (CEED) problem are indeed to reduce greenhouse gas emissions and fuel costs. Many approaches have demonstrated their efficacy in addressing CEED problem. However, designing a robust algorithm capable of achieving the Pareto optimal solutions under its multimodality and non-convexity natures caused by valve ripple effects is a true challenge. In this paper, chaos-enhanced multi-objective tunicate swarm algorithm (CMOTSA) for CEED problem. To promote the exploration and exploitation abilities of the basic tunicate swarm algorithm (TSA), an exponential strategy based on chaotic logistic map (ESCL) is incorporated. Based on ESCL in CMOTSA, it can improve the possibility of diversification feature to search different areas within the solution space, and then, gradually with the progress of iterative process it converts to emphasize the intensification ability. The efficacy of CMOTSA is approved by applying it to some of multi-objective benchmarking functions which have different Pareto front characteristics including convex, discrete, and non-convex. The inverted generational distance (IGD) and generational distance (GD) are employed to assess the robustness and the good quality of CMOTSA against some successful algorithms. Additionally, the computational time is evaluated, the CMOTSA consumes less time for most functions. The CMOTSA is applied to one of the practical engineering problems such as combined economic and emission dispatch (CEED) with including the valve ripples. By using three different systems (IEEE 30-bus with 6 generators system, 10 units system and IEEE 118-bus with 14 generating units), the methodology validation is made. It can be stated for the large-scale case of 118-bus systems that the results of the CMOTSA are equal to 8741.3 $/h for the minimum cost and 2747.6 ton/h for the minimum emission which are very viable to others. It can be pointed out that the cropped results of the proposed CMOTSA based methodology as an efficient tool for CEED is proven.

A novel approach of many-objective particle swarm optimization with cooperative agents based on an inverted generational distance indicator

Most evolutionary algorithms, including particle swarm optimization (PSO), use Pareto dominance as a major selection criterion and face significant challenges when dealing with many-objective problems. To tackle this issue, this paper proposes a novel algorithm, termed: Many- Objective PSO with Cooperative Agents (MaOPSO-CA). This exploits an Inverted Generational Distance (IGD) indicator in two innovative ways: firstly, as a leader selection method to select the preferable solution in terms of convergence and diversity, and, secondly, as an archiving method to decide which non-dominated solutions are kept in a bounded archive. The proposed strategy significantly promotes selection pressure toward the Pareto front. The results indicate that the IGD-based selection circumvents the issue of a large ratio of non-dominated solutions that exist in MaOPs. Moreover, a multi-swarm is investigated and modeled as a Multi-Agent System (MAS), so that knowledge sharing among different sub-swarms is easily improved through automated negotiation. The effectiveness of our proposed algorithm is validated with numerous experimental studies in solving 110 benchmark testing instances with up to twenty objectives. Experimental results demonstrate the effectiveness of the new algorithm compared to recent state-of-the-art methods. Finally, the application of MaOPSO-CA to a challenging, real-world water resource-management problem is shown to produce very encouraging results, demonstrating its potential as a benchmark resource for the research community.

Multi-objective scheduling of a single mobile robot based on the grey wolf optimization algorithm

During the last decades, intelligent mobile robots have been recognized as one of the most promising and emerging solutions used for fulfilling material transport demands in intelligent manufacturing systems. One of the most significant characteristics of those demands is their multi-objectivity, where identified objectives might usually conflict. Therefore, obtaining the optimally scheduled robotic-based material transport system that is simultaneously facing several conflicting objectives is a highly challenging task. To address such a challenge, this paper proposes a novel multi-objective Grey Wolf Optimizer (MOGWO) methodology to efficiently schedule material transport systems based on an intelligent single mobile robot. The proposed optimization methodology includes the comprehensive analysis and the mathematical formulation of 13 novel fitness functions combined to form a Pareto front of the multi-objective optimization problem and a novel strategy for optimal exploration of multi-objective search space. Moreover, four metrics, i.e., Generational Distance (GD), Inverted Generational Distance (IGD), Spacing (SP), and Maximum Spread (MS), are employed to quantitively evaluate and compare the effectiveness of the proposed enhanced MOGWO algorithm with three state-of-the-art metaheuristic methods (MOGA, MOAOA, and MOPSO) on 25 benchmark problems. The results achieved through two experimental scenarios indicate that the enhanced MOGWO algorithm outperforms other algorithms in terms of convergence, coverage, and the robust optimal Pareto solution. Finally, transportation paths based on obtained scheduling plans are experimentally corroborated by the mobile robot RAICO (Robot with Artificial Intelligence based Cognition) within a physical model of the intelligent manufacturing environment. The achieved experimental results successfully demonstrate the efficiency of the proposed methodology for optimal multi-objective scheduling of material transport tasks based on a single mobile robotic system.

A multi-objective agile project planning model and a comparative meta-heuristic approach

Agile software development methodologies are used to meet the changing needs in the market. The most popular framework among these methodologies is the Scrum framework. In Scrum planning, the assignment of user stories to sprints requires the consideration of multiple objectives to use the limited resources more effectively. In this paper, a multi-objective mixed-integer programming model is developed which considers three objectives: maximizing the sprint capacity usage, maximizing the assignment of user stories with high priority to primary sprints, and maximizing the assignment of affine user stories to the same sprint. The aim is to contribute to both theory and practice of Scrum planning considering multiple objectives. Additionally, different from the existing literature of Scrum planning, alternative user stories are also taken into account. The proposed model is applied to the small, medium, and big-sized instances of the problem taken from a real-life system. Non-dominated Sorting Genetic Algorithm (NSGA-II) and Strong Pareto Evolutionary Algorithm (SPEA2) are used as heuristic approaches since big-sized instances of the problem could not be solved using optimization approaches. To analyze the performances of these algorithms, Hypervolume (HV), Epsilon (ϵ), Generational Distance (GD), Inverted Generational Distance (IGD), Inverted Generational Distance Plus (IGD+), and Spread (Δ) indicators are used. Results showed that NSGA-II performs better than SPEA2 according to ϵ indicator for big-sized instance. On the other hand, SPEA2 performs better than NSGA-II according to HV, GD, IGD, IGD+, and Δ indicators. However, the results are very close to each other for HV, ϵ, IGD, and IGD+ indicators. In conclusion, both algorithms can be used to deal with the multi-objective Scrum planning problem.

A constrained multiobjective evolutionary algorithm with the two-archive weak cooperation

The significant issue to solve constrained multiobjective optimization problems (CMOPs) is to keep the balance between objectives and constraints, but the existing evolutionary algorithms are in the face of challenges for solving CMOPs with complex feasible regions. Based on this purpose, a constrained multiobjective evolutionary algorithm with the two-archive weak cooperation (CMOEA-TWC) is proposed in this article. In CMOEA-TWC, two archives are evolved, which are denoted as driving archive and normal archive, respectively. Besides, the weak cooperation of two archives is designed for sharing valuable information between archives. Specifically, the driving archive only considers objectives, while the normal archive considers both objectives and constraints. In addition, the minimum shift-based density estimation-based (SDE) distance is adopted to enhance the diversity of solutions in the driving archive, and a strict constrained dominance principle is designed to improve the feasibility of solutions in the normal archive. The proposed algorithm is tested on 47 CMOPs of 4 benchmark suites with the comparison of 4 state-of-the-art algorithms. The experimental results demonstrate that the average ranks in terms of inverted generational distance (IGD) outperform those of existing state-of-the-art competitors.

A multi-objective multi-tasking evolutionary algorithm based inverse mapping and adaptive transformation strategy: IM-MFEA

Multi-tasking optimization algorithm attracts much attention because the knowledge transfer between tasks enables the algorithm to process multiple related tasks simultaneously. However, negative knowledge transfer occasionally occurs, which may weaken the performance of the algorithm. To reduce the impact of negative knowledge transfer, a multi-objective multi-tasking optimization algorithm (IM-MFEA) based on inverse model mapping and an objective transformation strategy is proposed. First, correlation analysis is applied in an inverse mapping strategy to improve the accuracy of the inverse mapping model. Then, following the pattern of using the source domain solutions to assist the optimization of the target domain, the adaptive transformation strategy is used to improve the quality of the source domain solution in the objective space. These transformed solutions are reconstructed through the inverse mapping strategy. Finally, these reconstructed source domain solutions are mated with the target domain solutions to generate competitive offspring individuals for the target domain. To verify the effectiveness of the IM-MFEA, comprehensive experiments were conducted on nine multi-objective multi-factorial optimization (MFO) benchmark problems. Empirical results demonstrate that IM-MFEA is superior to other algorithms in 90% of test instances by inverted generational distance (IGD) and hypervolume (HV) value indicators.

A novel adaptive weight algorithm based on decomposition and two-part update strategy for many-objective optimization

Decomposition-based multi-objective evolutionary algorithm (MOEA/D) has good performance in solving multi-objective problems (MOPs) but poor performance in solving many-objective optimization problems (MaOPs). The weight vectors in MOEA/D are relatively fixed, which results in poor performance when dealing with complex MaOPs. In this paper, random and adaptive weights are introduced into MOEA/D to break the limitation of fixed weight vectors. And the moth search algorithm (MSA) is used as an operator to improve global search ability. The updating strategies in MSA are more consistent with the neighborhood learning strategy adopted in MOEA/D. In addition, to enable MSA to find the optimal solution in the neighborhood on the MaOPs to update other individuals. This paper introduces mutual evaluation value for evaluating the optimal individual in the neighborhood, and the proposed algorithm is abbreviated as MOEA/DMS. In comparative experiments on the MaF test suite, hypervolume (HV) and inverted generational distance (IGD) are used to measure MOEA/DMS and other many-objective evolutionary algorithms (MaOEAs). The results show that MOEA/DMS has an excellent performance in dealing with MaOPs. Besides, MOEA/DMS is compared with other state-of-the-art MaOEAs on two combinatorial MaOPs. The results show that MOEA/DMS also has significant advantages in dealing with combinatorial MaOPs.

Combining modified inverted generational distance indicator with reference-vector-guided selection for many-objective optimization

Combining modified inverted generational distance indicator with reference-vector-guided selection for many-objective optimization

DPb-MOPSO: A Dynamic Pareto bi-level Multi-objective Particle Swarm Optimization Algorithm

Particle Swarm Optimization (PSO) system based on the distributed architecture over multiple sub-swarms is very efficient for static multi-objective optimization but has not been considered for solving dynamic multi-objective problems (DMOPs). Tracking the most effective solutions over time and ensuring good exploitation and exploration are the main challenges of solving DMOP. This study proposes a Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization (DPb-MOPSO) algorithm including two parallel optimization levels. At the first level, all solutions are managed in a single search space. When a dynamic change is successfully detected in the objective values, the Pareto ranking operator is used to enable multiple sub-swarm’ subdivisions and processing which drives the second level of enhanced exploitation. A dynamic handling strategy based on random detectors is used to track the changes in the objective function due to time-varying parameters. A response strategy consisting in reevaluating all unimproved solutions and replacing them with newly generated ones is also implemented. The DPb-MOPSO system is tested on DMOPs with different types of time-varying Pareto Optimal Set (POS) and Pareto Optimal Front (POF). Inverted generational distance (IGD), mean inverted generational distance (MIGD), hypervolume difference (HVD), Robust IGD (RIGD), and Robust General Distance (RGD) metrics are used to assess the DPb-MOPSO performance. Quantitative results are analyzed using Friedman’s analysis of variance, and the Wilcoxon sum ranks test, while the stability is analyzed using Lyapunov’s theorem. The DPb-MOPSO is more robust than several dynamic multi-objective evolutionary algorithms in solving 21 complex problems over a range of changes in both the POS and POF. On IGD and HVD, DPb-MOPSO can solve 8/13 and 8/13 of the 13 UDF and ZJZ functions with moderate changes. DPb-MOPSO can resolve 7/8 FDA and DMOP benchmarks with severe changes to the MIGD, and 6/8 with moderate changes. DPb-MOPSO assumes 7/8, 6/8, and 5/8 for solving FDA, and dMOP functions on IGD and 6/8, 5/8, and 5/8 on HVD metrics considering severe, moderate, and slight environmental changes respectively. Also, it is the winner for solving 8 DMOPs based on RIGD, and RGD metrics.

Fast Greedy Subset Selection From Large Candidate Solution Sets in Evolutionary Multiobjective Optimization

Subset selection plays an important role in the field of evolutionary multiobjective optimization (EMO). Especially, in an EMO algorithm with an unbounded external archive (UEA), subset selection is an essential post-processing procedure to select a prespecified number of solutions as the final result. In this article, we discuss the efficiency of greedy subset selection for the hypervolume, inverted generational distance (IGD), and IGD plus (IGD+) indicators. Greedy algorithms usually efficiently handle the subset selection. However, when a large number of solutions are given (e.g., subset selection from tens of thousands of solutions in a UEA), they often become time consuming. Our idea is to use the submodular property, which is known for the hypervolume indicator, to improve their efficiency. First, we prove that the IGD and IGD+ indicators are also submodular. Next, based on the submodular property, we propose an efficient greedy inclusion algorithm for each indicator. We demonstrate through computational experiments that the proposed algorithms are much faster than the standard greedy subset selection algorithms. The proposed algorithms also help the research on performance indicators.

A Kernel-Based Indicator for Multi/Many-Objective Optimization

How to evaluate Pareto front approximations generated by multi/many-objective optimizers is a critical issue in the field of multiobjective optimization. Currently, there exist two types of comprehensive quality indicators (i.e., volume-based and distance-based indicators). Distance-based indicators, such as inverted generational distance (IGD), are usually computed by summing up the distance of each reference point to its nearest solution. Their high computational efficiency leads to their prevalence in many-objective optimization. However, in the existing distance-based indicators, the distributions of the solution sets are usually neglected, leading to their lack of ability to well distinguish between different solution sets. This phenomenon may become even more severe in high-dimensional space. To address such an issue, a kernel-based indicator (KBI) is proposed as a comprehensive indicator. Different from other distance-based indicators, a kernel-based maximum mean discrepancy is adopted in KBI for directly measuring the difference that can characterize the convergence, spread, and uniformity of two sets, i.e., the solution set and reference set, by embedding them in reproducing kernel Hilbert space (RKHS). As a result, KBI not only reflects the distance between the solution set and the reference set but also can reflect the distribution of the solution set itself. In addition, to maintain the desirable weak Pareto compliance property of KBI, a nondominated set reconstruction approach is also proposed to shift the original solution set. The detailed theoretical and experimental analysis of KBI is provided in this article. The properties of KBI have also been analyzed by the optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> -distribution.

Multi‐objective quantum atom search optimization algorithm for electric vehicle charging station planning

This paper presents an effective planning methodology for electric vehicle (EV) fast-charging stations (CS) using a multi-objective binary version of the atom search optimization (ASO) algorithm. The proposed method uses quantum operations to binarize the algorithm and achieve a higher convergence rate than the existing binary ASO algorithm. Additionally, a modified atom selection function is used to improve the searching capability of the ASO algorithm. Furthermore, the nondominated sorting procedure and pareto concepts are infused to solve the CS location problem (CSLP) considering the EV travel time, CS costs, and grid power loss as independent multi-objectives. The efficacy of the proposed multi-objective quantum ASO (MO-QASO) algorithm is evaluated using performance metrics namely, inverted generational distance (IGD), spacing (SP), and maximum spread (MS). The MO-QASO simulation results are compared with the results of other heuristic algorithms. MO-QASO achieves the best IGD (0.0021), SP (0.0002), and MS (0.9982) values, verifying the convergence and diversity of the algorithm. Importantly, the best CS planning solution obtained from MO-QASO is similar to the true solution obtained from the exhaustive search method. The MO-QASO efficiency is further validated by solving a CSLP from literature. Thus, the MO-QASO algorithm is a promising optimization tool for solving CSLP.

Investigation of benchmark dataset for many-objective Multi-Skill Resource Constrained Project Scheduling Problem

The paper presents a redefinition of Multi-Skill Resource-Constrained Project Scheduling Problem (MS-RCPSP) as a many-objective optimization problem. In effect, it brings the problem closer to real-world applications. Five objectives have been defined: cost, duration, average cash flow, average usage of resources and skill overuse. To summarize MS-RCPSP usage, the paper presents a short survey (years 2015–2021) of multi- and many-objective MS–RCPSP solving methods. Moreover, results of investigation of many-objective MS–RCPSP for classic (greedy algorithm, Unified Non-dominated Sorting Genetic Algorithm III (U-NSGA-III)), single objective (decomposition-based) Differential Evolution And Greedy (DEGR) and state-of-the-art Non-dominated Tournament Genetic Algorithm (NTGA2) have been presented. Additionally, results are analysed using multi-objective quality measures (such as Pareto Front Size (PFS), Purity or Inverted Generational Distance (IGD)) to verify the efficiency of the used methods. The paper answers 4 research questions that investigate 5-objective MS-RCPSP domains, approximations of Pareto Fronts, relations between objectives and efficiency of NTGA2 compared to other methods. Finally, the paper is concluded with a summary and propositions for future work.

Stochastic optimization model for determining support system parameters of a subway station

The process of designing the support system of a subway station using a concrete arch pre-supporting system (CAPS) construction method includes an estimation of design variables based on intuition and experience. However, this process may often lead to controversial and economically unfavorable designs. In this regard, developing an optimization model to determine design variables (support system parameters) is necessary. In this study, a stochastic optimization model is developed to determine the support system parameters of a subway station constructed using CAPS. To estimate the risk of uncertainties of the soil properties, the concept of conditional value at risk (CVaR) is used. A Python script is programmed in cooperation with a 2D Finite Element Method (FEM) software to provide the dataset. Then, the results are applied to prepare multi-layer perceptron (MLP) models, which are subsequently used as meta-models and linked to a reference-point-based non-dominated sorting genetic algorithm III (NSGA-III). It should be noted that the selection of the NSGA-III algorithm was based on comparing its performance with a few other meta-heuristic algorithms such as NSGA-II, MOPSO, and MOMBIII considering metrics such as hypervolume (HV), inverted generational distance (IGD), spread, and pure diversity (PD). Finally, all optimal solutions are ranked using the ELECTRE multi-criteria decision-making method. Various weighting scenarios for the objectives are considered to evaluate the importance of the selected design criteria. The results of the numerical modeling confirm that the proposed algorithm can provide worthwhile information for a logical decision about the support system parameters of a subway station. Thus, the outcome of this study is to achieve an appropriate and economical design by minimizing four following objectives: the risk of instability, risk of the maximum surface settlement, risk of the maximum displacement throughout the station structure, and the concreting volume. The presented algorithm could also alter the prioritization of design goals based on the project's sensitivity and the designer's judgment. On the other hand, by considering the uncertainty in soil parameters, the optimal parameters of the support system are determined more accurately in comparison with an assumption of homogenous soil. Therefore, the main contribution of this article to the design of a subway station constructed by the CAPS method is to increase the accuracy of the design of support system parameters by considering the risk of uncertainties in soil parameters, the importance of the project, and goals of the designer. In this way; the overly conservative designs in practice would be avoided.

Multi-objective complex product assembly scheduling problem considering parallel team and worker skills

The flow shop scheduling problem (FSP) is a classic shop scheduling problem with a strong engineering background. As an extension of FSP, the hybrid flow shop scheduling problem (HFSP) involves parallel machine scheduling, and the worker assignment problem on assembly lines (WAPAL) involves worker allocation. Parallel machine scheduling and multi-skilled and multilevel worker allocation are both involved in the actual assembly lines of complex products, but few studies have investigated them simultaneously. This work studies a complex product assembly line scheduling problem considering multi-skilled worker assignment and parallel team scheduling and takes the maximum completion time and the imbalance degree of team workload as the optimization objective. An integer programming model is proposed, and a hybrid coding method considers the worker assignment and task order. Three improved strategies based on a multiple objective evolutionary algorithm (MOEA) are proposed in the local search. Finally, 20 test instances are generated based on actual enterprise labor data, and the results based on the three strategies are compared with six MOEAs. The results show that the three strategies are superior in terms of the quality and distribution of solutions. The inverted generational distance (IGD) index value is increased by 49.97%, 47.89%, 47.08% respectively and the hypervolume (HV) index value is increased by 39.76%, 38.19%, 38.15% respectively.