A two-stage approach for multi-objective decision making with applications to system reliability optimization

This paper proposes a two-stage approach for solving multi-objective system reliability optimization problems. In this approach, a Pareto optimal solution set is initially identified at the first stage by applying a multiple objective evolutionary algorithm (MOEA). Quite often there are a large number of Pareto optimal solutions, and it is difficult, if not impossible, to effectively choose the representative solutions for the overall problem. To overcome this challenge, an integrated multiple objective selection optimization (MOSO) method is utilized at the second stage. Specifically, a self-organizing map (SOM), with the capability of preserving the topology of the data, is applied first to classify those Pareto optimal solutions into several clusters with similar properties. Then, within each cluster, the data envelopment analysis (DEA) is performed, by comparing the relative efficiency of those solutions, to determine the final representative solutions for the overall problem. Through this sequential solution identification and pruning process, the final recommended solutions to the multi-objective system reliability optimization problem can be easily determined in a more systematic and meaningful way.     

Multi-objective genetic algorithm for solving N-version program design problem

N-version programming (NVP) is a programming approach for constructing fault tolerant software systems. Generally, an optimization model utilized in NVP selects the optimal set of versions for each module to maximize the system reliability and to constrain the total cost to remain within a given budget. In such a model, while the number of versions included in the obtained solution is generally reduced, the budget restriction may be so rigid that it may fail to find the optimal solution. In order to ameliorate this problem, this paper proposes a novel bi-objective optimization model that maximizes the system reliability and minimizes the system total cost for designing N-version software systems. When solving multi-objective optimization problem, it is crucial to find Pareto solutions. It is, however, not easy to obtain them. In this paper, we propose a novel bi-objective optimization model that obtains many Pareto solutions efficiently.We formulate the optimal design problem of NVP as a bi-objective 0–1 nonlinear integer programming problem. In order to overcome this problem, we propose a Multi-objective genetic algorithm (MOGA), which is a powerful, though time-consuming, method to solve multi-objective optimization problems. When implementing genetic algorithm (GA), the use of an appropriate genetic representation scheme is one of the most important issues to obtain good performance. We employ random-key representation in our MOGA to find many Pareto solutions spaced as evenly as possible along the Pareto frontier. To pursue improve further performance, we introduce elitism, the Pareto-insertion and the Pareto-deletion operations based on distance between Pareto solutions in the selection process.The proposed MOGA obtains many Pareto solutions along the Pareto frontier evenly. The user of the MOGA can select the best compromise solution among the candidates by controlling the balance between the system reliability and the total cost.     

Two-stage hybrid flow shop scheduling with preventive maintenance using multi-objective tabu search method

This paper investigates an integrated bi-objective optimisation problem with non-resumable jobs for production scheduling and preventive maintenance in a two-stage hybrid flow shop with one machine on the first stage and m identical parallel machines on the second stage. Sequence-dependent set-up times and preventive maintenance (PM) on the first stage machine are considered. The scheduling objectives are to minimise the unavailability of the first stage machine and to minimise the makespan simultaneously. To solve this integrated problem, three decisions have to be made: determine the processing sequence of jobs on the first stage machine, determine whether or not to perform PM activity just after each job, and specify the processing machine of each job on the second stage. Due to the complexity of the problem, a multi-objective tabu search (MOTS) method is adapted with the implementation details. The method generates non-dominated solutions with several parallel tabu lists and Pareto dominance concept. The performance of the method is compared with that of a well-known multi-objective genetic algorithm, in terms of standard multi-objective metrics. Computational results show that the proposed MOTS yields a better approximation.     

Explicit consideration of multiple objectives in cellular manufacturing

Although many methodologies have been proposed for solving the cell-formation problem, few of them explicitly consider the existence of multiple objectives in the design process. In this article, the development of multi-objective genetic programming single-linkage cluster analysis (GP-SLCA), an evolutionary methodology for the solution of the multi-objective cell-formation problem, is described. The proposed methodology combines an existing algorithm for the solution of single-objective cell-formation problems with NSGA-II, an elitist evolutionary multi-objective optimization technique. Multi-objective GP-SLCA is able to generate automatically a set of non-dominated solutions for a given multi-objective cell-formation problem. The benefits of the proposed approach are illustrated using an example test problem taken from the literature and an industrial case study.     

MONSS: A multi-objective nonlinear simplex search approach

This article presents a novel methodology for dealing with continuous box-constrained multi-objective optimization problems (MOPs). The proposed algorithm adopts a nonlinear simplex search scheme in order to obtain multiple elements of the Pareto optimal set. The search is directed by a well-distributed set of weight vectors, each of which defines a scalarization problem that is solved by deforming a simplex according to the movements described by Nelder and Mead's method. Considering an MOP with n decision variables, the simplex is constructed using n+1 solutions which minimize different scalarization problems defined by n+1 neighbor weight vectors. All solutions found in the search are used to update a set of solutions considered to be the minima for each separate problem. In this way, the proposed algorithm collectively obtains multiple trade-offs among the different conflicting objectives, while maintaining a proper representation of the Pareto optimal front. In this article, it is shown that a well-designed strategy using just mathematical programming techniques can be competitive with respect to the state-of-the-art multi-objective evolutionary algorithms against which it was compared.     

Multi-objective process planning and scheduling using controlled elitist non-dominated sorting genetic algorithm

The integration of process planning and scheduling is considered as a critical component in manufacturing systems. In this paper, a multi-objective approach is used to solve the planning and scheduling problem. Three different objectives considered in this work are minimisation of makespan, machining cost and idle time of machines. To solve this integration problem, we propose an improved controlled elitist non-dominated sorting genetic algorithm (NSGA) to take into account the computational intractability of the problem. An illustrative example and five test cases have been taken to demonstrate the capability of the proposed model. The results confirm that the proposed multi-objective optimisation model gives optimal and robust solutions. A comparative study between proposed algorithm, controlled elitist NSGA and NSGA-II show that proposed algorithm significantly reduces scheduling objectives like makespan, cost and idle time, and is computationally more efficient.     

A new multi-objective optimization model for preventive maintenance and replacement scheduling of multi-component systems

In this article, a new multi-objective optimization model is developed to determine the optimal preventive maintenance and replacement schedules in a repairable and maintainable multi-component system. In this model, the planning horizon is divided into discrete and equally-sized periods in which three possible actions must be planned for each component, namely maintenance, replacement, or do nothing. The objective is to determine a plan of actions for each component in the system while minimizing the total cost and maximizing overall system reliability simultaneously over the planning horizon. Because of the complexity, combinatorial and highly nonlinear structure of the mathematical model, two metaheuristic solution methods, generational genetic algorithm, and a simulated annealing are applied to tackle the problem. The Pareto optimal solutions that provide good tradeoffs between the total cost and the overall reliability of the system can be obtained by the solution approach. Such a modeling approach should be useful for maintenance planners and engineers tasked with the problem of developing recommended maintenance plans for complex systems of components.     

MOEA/D-SQA: a multi-objective memetic algorithm based on decomposition

A multi-objective memetic algorithm based on decomposition is proposed in this article, in which a simplified quadratic approximation (SQA) is employed as a local search operator for enhancing the performance of a multi-objective evolutionary algorithm based on decomposition (MOEA/D). The SQA is used for a fast local search and the MOEA/D is used as the global optimizer. The multi-objective memetic algorithm based on decomposition, i.e. a hybrid of the MOEA/D with the SQA (MOEA/D-SQA), is designed to balance local versus global search strategies so as to obtain a set of diverse non-dominated solutions as quickly as possible. The emphasis of this article is placed on demonstrating how this local search scheme can improve the performance of MOEA/D for multi-objective optimization. MOEA/D-SQA has been tested on a wide set of benchmark problems with complicated Pareto set shapes. Experimental results indicate that the proposed approach performs better than MOEA/D. In addition, the results obtained are very competitive when comparing MOEA/D-SQA with other state-of-the-art techniques.     

外卖配送路径多目标实时优化研究

随着外卖行业的不断发展,外卖配送的路径优化问题已引起学者们的广泛关注。但现有研究未将骑手的目标考虑在内,且未考虑动态场景下多目标如何设定权重的问题。因此,本文对外卖配送路径的多目标实时优化进行深入研究。建立多目标外卖配送路径优化模型。该模型不仅考虑订单履行时间、平台利润和骑手服务质量3个常用的目标,另外增加骑手等待时间和骑手空驶距离这两个目标,充分将外卖平台、顾客和骑手的目标综合考虑。设计动态调整权重的多目标外卖配送路径启发式算法,解决动态场景下多目标权重如何设定的问题。通过外卖配送的实时数据进行算例分析。结果表明,本文提出的算法可以有效对多目标的外卖配送问题进行实时路径优化,且订单的密集程度对骑手等待时间和订单履行时间有直接的影响。     

A multi-objective scatter search for a bi-criteria no-wait flow shop scheduling problem

The flow shop problem as a typical manufacturing challenge has gained wide attention in academic fields. This article considers a bi-criteria no-wait flow shop scheduling problem (FSSP) in which weighted mean completion time and weighted mean tardiness are to be minimized simultaneously. Since a FSSP has been proved to be NP-hard in a strong sense, a new multi-objective scatter search (MOSS) is designed for finding the locally Pareto-optimal frontier of the problem. To prove the efficiency of the proposed algorithm, various test problems are solved and the reliability of the proposed algorithm, based on some comparison metrics, is compared with a distinguished multi-objective genetic algorithm (GA), i.e. SPEA-II. The computational results show that the proposed MOSS performs better than the above GA, especially for the large-sized problems.     

Multi-objective unrelated parallel machine scheduling: a Tabu-enhanced iterated Pareto greedy algorithm

This work proposes a high-performance algorithm for solving the multi-objective unrelated parallel machine scheduling problem. The proposed approach is based on the iterated Pareto greedy (IPG) algorithm but exploits the accessible Tabu list (TL) to enhance its performance. To demonstrate the superior performance of the proposed Tabu-enhanced iterated Pareto greedy (TIPG) algorithm, its computational results are compared with IPG and existing algorithms on the same benchmark problem set. Experimental results reveal that incorporating the accessible TL can eliminate ineffective job moves, causing the TIPG algorithm to outperform state-of-the-art approaches in the light of five multi-objective performance metrics. This work contributes a useful theoretical and practical optimisation method for solving this problem.     

A surrogate-based multiobjective metaheuristic and network degradation simulation model for robust toll pricing

Robust transportation network design problems generally rely on systems engineering methods that share common research gaps. First, problem sizes are constrained due to the use of multi-objective solution algorithms that are notoriously inefficient due to computationally expensive function evaluations. Second, link disruptions at a network level are difficult to model realistically. In this paper, a stochastic search metaheuristic based on radial basis functions is proposed for constrained multiobjective problems. It is proven to converge, and compared with conventional metaheuristics for four representative test problems. A scenario simulation method based on multivariate Bernoulli random variables that accounts for correlations between link failures is proposed to sample scenarios for a mean-variance toll pricing problem. Four tests are conducted on the classical Sioux Falls network to gain some insights into the algorithm, the simulation model, and to the robust toll pricing problem. The first test empirically measures the efficiency of the simulation algorithm and approximate Pareto set by obtaining a standard error in the ε-indicator measure for a given number of scenarios and iterations. The second test compares the dominance of the proposed heuristic’s solutions with a conventional multiobjective genetic algorithm by comparing the average ε-indicator. The third test quantifies the gap due to falsely assuming that link failures are independent of each other when they are not. The last test quantifies the value of having the flexibility to adapt a Pareto set of toll pricing solutions to changing probability regimes such as peak and off-peak hurricane or snow seasons.     

An optimal autonomous microgrid cluster based on distributed generation droop parameter optimization and renewable energy sources using an improved grey wolf optimizer

Microgrid (MG) clustering is regarded as an important driver in improving the robustness of MGs. However, little research has been conducted on providing appropriate MG clustering. This article addresses this shortfall. It proposes a novel multi-objective optimization approach for finding optimal clustering of autonomous MGs by focusing on variables such as distributed generation (DG) droop parameters, the location and capacity of DG units, renewable energy sources, capacitors and powerline transmission. Power losses are minimized and voltage stability is improved while virtual cut-set lines with minimum power transmission for clustering MGs are obtained. A novel chaotic grey wolf optimizer (CGWO) algorithm is applied to solve the proposed multi-objective problem. The performance of the approach is evaluated by utilizing a 69-bus MG in several scenarios.     

Reliability-based robust multi-objective optimization applied to engineering system design

ABSTRACT

Probabilistic and non-probabilistic methods have been proposed to deal with design problems under uncertainties. Reliability-based design and robust design are probabilistic strategies traditionally used for this purpose. In the present contribution, reliability-based robust design optimization (RBRDO) is formulated as a multi-objective problem considering the interaction of both approaches. The proposed methodology is based on the differential evolution algorithm associated with two strategies to deal with reliability and robustness, respectively, namely inverse reliability analysis and the effective mean concept. This multi-objective optimization problem considers the maximization of reliability and robustness coefficients as additional objective functions. The effectiveness of the methodology is illustrated by two classical test cases and a rotor-dynamics application. The results demonstrate that the proposed methodology is an alternative method to solve RBRDO problems.     

Bi-objective reentrant hybrid flowshop scheduling: an iterated Pareto greedy algorithm

The multi-objective reentrant hybrid flowshop scheduling problem (RHFSP) exhibits significance in many industrial applications, but appears under-studied in the literature. In this study, an iterated Pareto greedy (IPG) algorithm is proposed to solve a RHFSP with the bi-objective of minimising makespan and total tardiness. The performance of the proposed IPG algorithm is evaluated by comparing its solutions to existing meta-heuristic algorithms on the same benchmark problem set. Experimental results show that the proposed IPG algorithm significantly outperforms the best available algorithms in terms of the convergence to optimal solutions, the diversity of solutions and the dominance of solutions. The statistical analysis manifestly shows that the proposed IPG algorithm can serve as a new benchmark approach for future research on this extremely challenging scheduling problem.     

New insights on multi-state component criticality and importance

In this paper, new importance measures for multi-state systems with multi-state components are introduced and evaluated. These new measures complement and enhance current work done in the area of multi-state reliability. In general, importance measures are used to evaluate and rank the criticality of component or component states with respect to system reliability. The focus of the study is to provide intuitive and clear importance measures that can be used to enhance system reliability from two perspectives: (1) how a specific component affects multi-state system reliability and (2) how a particular component state or set of states affects multi-state system reliability. The first measure unsatisfied demand index, provides insight regarding a component or component state contribution to unsatisfied demand. The second measure multi-state failure frequency index, elaborates on an approach that quantifies the contribution of a particular component or component state to system failure. Finally, the multi-state redundancy importance identifies where to allocate component redundancy as to improve system reliability. The findings of this study indicate that both perspectives can be used to complement each other and as an effective tool to assess component criticality. Examples illustrate and compare the proposed measures with previous multi-state importance measures.     

Multi-objective integrated acyclic crew rostering and vehicle assignment problem in public bus transportation

In this study, we try to solve a real planning problem faced in public bus transportation. It is a multi-objective integrated crew rostering and vehicle assignment problem. We model this problem as a multi-objective set partitioning problem. Most of the time, crew rostering problem with a single-objective function is considered, and the output may not satisfy some transport companies. To minimize the cost and maximize the fairness of the workload among the drivers, we define many criteria. Although crew rostering problem and its integrated versions appear in the literature, it is the first time these two problems are integrated. We propose a new multi-objective tabu search algorithm to obtain near Pareto-optimal solutions. The algorithm works with a set of solutions using parallel search. We test our algorithm for the case with ten objectives and define a method to choose solutions from the approximated efficient frontier to present to the user. We discuss the performance of our meta-heuristic approach.

     

Scenario-based multi-objective robust scheduling for a semiconductor production line

Scheduling problems of semiconductor manufacturing systems (SMS) with the goal of optimising some classical performance indices (NP-hard), tend to be increasingly complicated due to stochastic uncertainties. This paper targets the robust scheduling problem of an SMS with uncertain processing times. A three-stage multi-objective robust optimisation (MORO) approach is proposed, that can collaboratively optimise the performance indices and their robustness measures. In the first stage, this paper studies the scheduling problem in the deterministic environment and obtains feasible scheduling strategies that perform well in four performance indices (the average cycle time (CT), the on-time delivery rate (ODR), the throughput (TP), and the total movement amount of wafers (MOV)). Then, in the second stage, the uncertainties are introduced into the production system. In the third stage, this paper proposes a hybrid method consisting of scenario planning, discrete simulation, and multi-objective optimisation to obtain an approximately and more robust optimal solution from the feasible scheduling strategy set. The proposed MORO approach is tested in a semiconductor experiment production line and makes a full analysis to illustrate the effectiveness of our method. The results show that our MORO is superior concerning the total robustness with multi-objective.     

Pareto-based multi-objective node placement of industrial wireless sensor networks using binary differential evolution harmony search

The reliability and real time of industrial wireless sensor networks (IWSNs) are the absolute requirements for industrial systems, which are two foremost obstacles for the large-scale applications of IWSNs. This paper studies the multi-objective node placement problem to guarantee the reliability and real time of IWSNs from the perspective of systems. A novel multi-objective node deployment model is proposed in which the reliability, real time, costs and scalability of IWSNs are addressed. Considering that the optimal node placement is an NP-hard problem, a new multi-objective binary differential evolution harmony search (MOBDEHS) is developed to tackle it, which is inspired by the mechanism of harmony search and differential evolution. Three large-scale node deployment problems are generated as the benCHmarks to verify the proposed model and algorithm. The experimental results demonstrate that the developed model is valid and can be used to design large-scale IWSNs with guaranteed reliability and real-time performance efficiently. Moreover, the comparison results indicate that the proposed MOBDEHS is an effective tool for multi-objective node placement problems and superior to Pareto-based binary differential evolution algorithms, nondominated sorting genetic algorithm II (NSGA-II) and modified NSGA-II.     

Pricing and location decisions in multi-objective facility location problem with M/M/m/k queuing systems

This article presents a new multi-objective model for a facility location problem with congestion and pricing policies. This model considers situations in which immobile service facilities are congested by a stochastic demand following M/M/m/k queues. The presented model belongs to the class of mixed-integer nonlinear programming models and NP-hard problems. To solve such a hard model, a new multi-objective optimization algorithm based on a vibration theory, namely multi-objective vibration damping optimization (MOVDO), is developed. In order to tune the algorithms parameters, the Taguchi approach using a response metric is implemented. The computational results are compared with those of the non-dominated ranking genetic algorithm and non-dominated sorting genetic algorithm. The outputs demonstrate the robustness of the proposed MOVDO in large-sized problems.