Multi-objective optimization for the multi-mode finance-based project scheduling problem

The finance-based scheduling problem (FBSP) is about scheduling project activities without exceeding a credit line financing limit. The FBSP is extended to consider different execution modes that result in the multi-mode FBSP (MMFBSP). Unfortunately, researchers have abandoned the development of exact models to solve the FBSP and its extensions. Instead, researchers have heavily relied on the use of heuristics and meta-heuristics, which do not guarantee solution optimality. No exact models are available for contractors who look for optimal solutions to the multi-objective MMFBSP. CPLEX, which is an exact solver, has witnessed a significant decrease in its computation time. Moreover, its current version, CPLEX 12.9, solves multi-objective optimization problems. This study presents a mixed-integer linear programming model for the multi-objective MMFBSP. Using CPLEX 12.9, we discuss several techniques that researchers can use to optimize a multi-objective MMFBSP. We test our model by solving several problems from the literature. We also show how to solve multi-objective optimization problems by using CPLEX 12.9 and how computation time increases as problem size increases. The small increase in computation time compared with possible cost savings make exact models a must for practitioners. Moreover, the linear programming-relaxation of the model, which takes seconds, can provide an excellent lower bound.     

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.     

An improved robust buffer allocation method for the project scheduling problem

Unpredictable uncertainties cause delays and additional costs for projects. Often, when using traditional approaches, the optimizing procedure of the baseline project plan fails and leads to delays. In this study, a two-stage multi-objective buffer allocation approach is applied for robust project scheduling. In the first stage, some decisions are made on buffer sizes and allocation to the project activities. A set of Pareto-optimal robust schedules is designed using the meta-heuristic non-dominated sorting genetic algorithm (NSGA-II) based on the decisions made in the buffer allocation step. In the second stage, the Pareto solutions are evaluated in terms of the deviation from the initial start time and due dates. The proposed approach was implemented on a real dam construction project. The outcomes indicated that the obtained buffered schedule reduces the cost of disruptions by 17.7% compared with the baseline plan, with an increase of about 0.3% in the project completion time.     

A Pareto block-based estimation and distribution algorithm for multi-objective permutation flow shop scheduling problem

Multi-objective flow shop scheduling plays a key role in real-life scheduling problem which attract the researcher attention. The primary concern is to find the best sequence for flow shop scheduling problem. Estimation of Distribution Algorithms (EDAs) has gained sufficient attention from the researchers and it provides prominent results as an alternate of traditional evolutionary algorithms. In this paper, we propose the pareto optimal block-based EDA using bivariate model for multi-objective flow shop scheduling problem. We apply a bivariate probabilistic model to generate block which have the better diversity. We employ the non-dominated sorting technique to filter the solutions. To check the performance of proposed approach, we test it on the benchmark problems available in OR-library and then we compare it with non-dominated sorting genetic algorithm-II (NSGA-II). Computational results show that pareto optimal BBEDA provides better result and better convergence than NSGA-II.     

Project management for uncertainty with multiple objectives optimisation of time,cost and reliability

This research adopts an approach that uses computer simulation and statistical analysis of uncertain activity time, activity cost, due date and project budget to address quality and the learning process with regard to project scheduling. Since the learning process affects the scheduling problem, a Cobb–Douglas multiplicative power model is used to represent the relationship between the dependent variable, which is the standard deviation of activity time, and the independent variables, which are the cumulative trials and the mean of activity time. The mean value and standard deviation are used to randomly generate activity times for project scheduling analysis. Response surface methodology (RSM) is used in order to develop a rationale of the time-cost trade-off problem. The solutions found with RSM are optimised only for a single objective, such as project completion time, total project cost, completion time probability and total cost probability. Thus, multiple objectives for further optimisation become necessary and a limited project budget, restricted completion time, allowable total cost probability and acceptable completion time probability have to be considered at the same time as the learning effect. With response functions from RSM, compromise programming is adopted in order to formulate the proposed project scheduling problem for multi-objective optimisation.     

A new heuristic for the flowshop scheduling problem to minimize makespan and maximum tardiness

This paper presents a new heuristic for solving the flowshop scheduling problem that aims to minimize makespan and maximize tardiness. The algorithm is able to take into account the aforementioned performance measures, finding a set of non-dominated solutions representing the Pareto front. This method is based on the integration of two different techniques: a multi-criteria decision-making method and a constructive heuristic procedure developed for makespan minimization in flowshop scheduling problems. In particular, the technique for order preference by similarity of ideal solution (TOPSIS) algorithm is integrated with the Nawaz–Enscore–Ham (NEH) heuristic to generate a set of potential scheduling solutions. To assess the proposed heuristic's performance, comparison with the best performing multi-objective genetic local search (MOGLS) algorithm proposed in literature is carried out. The test is executed on a large number of random problems characterized by different numbers of machines and jobs. The results show that the new heuristic frequently exceeds the MOGLS results in terms of both non-dominated solutions, set quality and computational time. In particular, the improvement becomes more and more significant as the number of jobs in the problem increases.     

Multi-stage lot sizing in a serial production system

This paper summarizes the development and implementation of a large-scale, multi-objective, lot-sizing model for scheduling tablet pharmaceuticals in a serial production system. The model places multiple resource capacity constraints on production at various stages of the manufacturing process and explicitly considers resource set-up times to ensure the generation of a feasible schedule. The multi-period model uniquely allows for variable lot sizes by stage and by period, subject to integrality restrictions arising from the technological nature of the multi-stage process. An integer goal programming approach is used for determining non-dominated solutions to the multi-item problem. The implementation and utilization of the model by an international manufacturer of pharmaceuticals is described, and model results are presented and discussed.     

An efficient multi-objective optimization approach based on the micro genetic algorithm and its application

In this paper, an efficient multi-objective optimization approach based on the micro genetic algorithm is suggested to solving the multi-objective optimization problems. An external elite archive is used to store Pareto-optimal solutions found in the evolutionary process. A non-dominated sorting is employed to classify the combinational population of the evolutionary population and the external elite population into several different non-dominated levels. Once the evolutionary population converges, an exploratory operator will be performed to explore more non-dominated solutions, and a restart strategy will be subsequently adopted. Simulation results for several difficult test functions indicate that the present method has higher efficiency and better convergence near the globally Pareto-optimal set for all test functions, and a better spread of solutions for some test functions compared to NSGAII. Eventually, this approach is applied to the structural optimization of a composite laminated plate for maximum stiffness in thickness direction and minimum mass.     

混合工作日历下批量生产柔性作业车间多目标调度方法

提出了一种混合工作日历下批量生产柔性作业车间多目标调度方法。考虑设备的混合工作日历约束,构建了以生产周期最短、制造成本最低为优化目标的批量生产柔性作业车间多目标调度模型。设计了一种带精英策略的非支配排序遗传算法(NSGA II)求解该模型。算法中,采用“基于工序和设备的分段编码”方式分别对工序和设备进行编码;采用“基于工序和设备的分段交叉和变异方式”进行交叉和变异操作,采用“遗传算子改进策略”保证交叉、变异后子代个体的可行性;解码操作采用“基于平顺移动的原理”和“基于工作日历的时间推算技术”推算工序的调整开始、调整结束、加工开始和加工结束时刻。最后,通过案例分析验证了所提方法的有效性。     

一种基于近似模型管理的多目标优化方法

针对实际工程优化问题,为了提高效率和减少近似模型带来的误差,提出一种基于模型管理的多目标优化方法。利用加强径向基插值函数在整个寻优区域内构造目标和约束的近似模型,结合微型多目标遗传算法寻找当前非支配解。通过模型管理方法更新近似模型,并控制由于近似模型带来的误差和更新次数,最后将误差控制在一定范围内的多个非支配解当作实际问题的解。在测试函数中验证了此方法的效率及非支配解的精度和分布的均匀性。最后成功应用于车身薄壁构件的耐撞性优化中,表明了可用于求解复杂的工程优化问题。     

A multi-phase covering Pareto-optimal front method to multi-objective parallel machine scheduling

This paper considers the problem of parallel machine scheduling with sequence-dependent setup times to minimise both makespan and total earliness/tardiness in the due window. To tackle the problem considered, a multi-phase algorithm is proposed. The goal of the initial phase is to obtain a good approximation of the Pareto-front. In the second phase, to improve the Pareto-front, non-dominated solutions are unified to constitute a big population. In this phase, based on the local search in the Pareto space concept, three multi-objective hybrid metaheuristics are proposed. Covering the whole set of Pareto-optimal solutions is a desired task of multi-objective optimisation methods. So in the third phase, a new method using an e-constraint hybrid metaheuristic is proposed to cover the gaps between the non-dominated solutions and improve the Pareto-front. Appropriate combinations of multi-objective methods in various phases are considered to improve the total performance. The multi-phase algorithm iterates over a genetic algorithm in the first phase and three hybrid metaheuristics in the second and third phases. Experiments on the test problems with different structures show that the multi-phase method is a better tool to approximate the efficient set than the global archive sub-population genetic algorithm presented previously.     

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.     

Optimal configuration selection for reconfigurable manufacturing system using NSGA II and TOPSIS

Reconfigurable Manufacturing Systems provide the functionality and capacity needed, when needed. The Reconfigurable Machine Tool (RMT) plays a pivotal role in the fulfilment of this objective through their modular structure consisting of basic and auxiliary modules along with the open architecture software. In the present work, a novel approach based on the module interactions and machine capability is proposed to measure the machine reconfigurability and operational capability of an RMT. The developed performance measures along with cost are considered as the multiple objectives for the optimal machine assignment for a single part flow line allowing paralleling of similar machines. The multi-objective optimisation problem in hand is targeted in two phases. In the first phase, non-dominated sorting genetic algorithm II is applied to obtain the non-dominated solutions. In the subsequent stage, a multiple attribute decision-making approach is employed to rank the pareto frontiers. The proposed solutions are ranked based on Shannon entropy weight and Technique for Order Preference by Similarity to Ideal Solution method. The study reveals that the developed performance measures along with the hybrid approach have a great potential in handling the RMS optimisation and cost–benefit issues.     

A multi-point simulated annealing heuristic for solving multiple objective unrelated parallel machine scheduling problems

This study considers the problem of job scheduling on unrelated parallel machines. A multi-objective multi-point simulated annealing (MOMSA) algorithm was proposed for solving this problem by simultaneously minimising makespan, total weighted completion time and total weighted tardiness. To assess the performance of the proposed heuristic and compare it with that of several benchmark heuristics, the obtained sets of non-dominated solutions were assessed using four multi-objective performance indicators. The computational results demonstrated that the proposed heuristic markedly outperformed the benchmark heuristics in terms of the four performance indicators. The proposed MOMSA algorithm can provide a new benchmark for future research related to the unrelated parallel machine scheduling problem addressed in this study.     

A particle swarm optimizer for constrained multi-objective engineering design problems

This article presents a particle swarm optimizer (PSO) capable of handling constrained multi-objective optimization problems. The latter occur frequently in engineering design, especially when cost and performance are simultaneously optimized. The proposed algorithm combines the swarm intelligence fundamentals with elements from bio-inspired algorithms. A distinctive feature of the algorithm is the utilization of an arithmetic recombination operator, which allows interaction between non-dominated particles. Furthermore, there is no utilization of an external archive to store optimal solutions. The PSO algorithm is applied to multi-objective optimization benchmark problems and also to constrained multi-objective engineering design problems. The algorithmic effectiveness is demonstrated through comparisons of the PSO results with those obtained from other evolutionary optimization algorithms. The proposed particle swarm optimizer was able to perform in a very satisfactory manner in problems with multiple constraints and/or high dimensionality. Promising results were also obtained for a multi-objective engineering design problem with mixed variables.     

A Compromise Programming to Task Assignment Problem in Software Development Project

The scheduling process that aims to assign tasks to members is a difficult job in project management. It plays a prerequisite role in determining the project’s quality and sometimes winning the bidding process. This study aims to propose an approach based on multi-objective combinatorial optimization to do this automatically. The generated schedule directs the project to be completed with the shortest critical path, at the minimum cost, while maintaining its quality. There are several real-world business constraints related to human resources, the similarity of the tasks added to the optimization model, and the literature’s traditional rules. To support the decision-maker to evaluate different decision strategies, we use compromise programming to transform multi-objective optimization (MOP) into a single-objective problem. We designed a genetic algorithm scheme to solve the transformed problem. The proposed method allows the incorporation of the model as a navigator for search agents in the optimal solution search process by transferring the objective function to the agents’ fitness function. The optimizer can effectively find compromise solutions even if the user may or may not assign a priority to particular objectives. These are achieved through a combination of non-preference and preference approaches. The experimental results show that the proposed method worked well on the tested dataset.     

A multi-objective optimisation model to integrating flexible process planning and scheduling based on hybrid multi-objective simulated annealing

Process planning and production scheduling play important roles in manufacturing systems. In this paper we present a mixed integer linear programming (MILP) scheduling model, that is to say a slot-based multi-objective multi-product, that readily accounts for sequence-dependent preparation times (transition and set up times or machine changeover time). The proposed scheduling model becomes computationally expensive to solve for long time horizons. The aim is to find a set of high-quality trade-off solutions. This is a combinatorial optimisation problem with substantially large solution space, suggesting that it is highly difficult to find the best solutions with the exact search method. To account for this, the hybrid multi-objective simulated annealing algorithm (MOHSA) is proposed by fully utilising the capability of the exploration search and fast convergence. Two numerical experiments have been performed to demonstrate the effectiveness and robustness of the proposed algorithm.     

Self-adaptive multi-objective harmony search for optimal design of water distribution networks

In multi-objective optimization computing, it is important to assign suitable parameters to each optimization problem to obtain better solutions. In this study, a self-adaptive multi-objective harmony search (SaMOHS) algorithm is developed to apply the parameter-setting-free technique, which is an example of a self-adaptive methodology. The SaMOHS algorithm attempts to remove some of the inconvenience from parameter setting and selects the most adaptive parameters during the iterative solution search process. To verify the proposed algorithm, an optimal least cost water distribution network design problem is applied to three different target networks. The results are compared with other well-known algorithms such as multi-objective harmony search and the non-dominated sorting genetic algorithm-II. The efficiency of the proposed algorithm is quantified by suitable performance indices. The results indicate that SaMOHS can be efficiently applied to the search for Pareto-optimal solutions in a multi-objective solution space.     

Multi-objective scheduling problems: Determination of pruned Pareto sets

There are often multiple competing objectives for industrial scheduling and production planning problems. Two practical methods are presented to efficiently identify promising solutions from among a Pareto optimal set for multi-objective scheduling problems. Generally, multi-objective optimization problems can be solved by combining the objectives into a single objective using equivalent cost conversions, utility theory, etc., or by determination of a Pareto optimal set. Pareto optimal sets or representative subsets can be found by using a multi-objective genetic algorithm or by other means. Then, in practice, the decision maker ultimately has to select one solution from this set for system implementation. However, the Pareto optimal set is often large and cumbersome, making the post-Pareto analysis phase potentially difficult, especially as the number of objectives increase. Our research involves the post Pareto analysis phase, and two methods are presented to filter the Pareto optimal set to determine a subset of promising or desirable solutions. The first method is pruning using non-numerical objective function ranking preferences. The second approach involves pruning by using data clustering. The k-means algorithm is used to find clusters of similar solutions in the Pareto optimal set. The clustered data allows the decision maker to have just k general solutions from which to choose. These methods are general, and they are demonstrated using two multi-objective problems involving the scheduling of the bottleneck operation of a printed wiring board manufacturing line and a more general scheduling problem.