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.     

Cyclic and non-cyclic crew rostering problems in public bus transit

The crew rostering problem arises in public transport bus companies, and addresses the task of assigning a given set of anonymous duties and some other activities, such as standbys and days off, to drivers or groups of drivers, without violating any complex labor union rules. In addition, the preferences of drivers are considered during the assignment. The plan generated for each driver/group of drivers is called a roster. Optimal rosters are characterized by maximum satisfaction of drivers and minimal operational costs. To generate a personalized roster for each driver/group of drivers, the problem is formulated as a multi-commodity network flow problem in this paper. In each network layer, a roster is generated for each driver or driver group. The network model is very flexible and can accommodate a variety of constraints. In addition, with a minor modification, the network can formulate the cyclic and non-cyclic crew rostering problems. To the best of our knowledge, this is the first publication which solves both problems with one model. The main goal of this paper is to develop a mixed-integer mathematical optimization network model for both problems with sequential and integrated approaches and to solve this model using commercial solvers. Both problems are usually solved with the sequential approach. Therefore, another contribution of this paper is comparing the sequential approach with the integrated one. Our experiments on real-world instances show that the integrated approach outperforms the sequential one in terms of solution quality.     

Multi-objective analysis of an integrated supply chain scheduling problem

We study the problem of minimising the total weighted tardiness and total distribution costs in an integrated production and distribution environment. Orders are received by a manufacturer, processed on a single production line, and delivered to customers by capacitated vehicles. Each order (job) is associated with a customer, weight (priority), processing time, due time, and size (volume or storage space required in the transportation unit). A mathematical model is presented in which a number of weighted linear combinations of the objectives are used to aggregate both objectives into a single objective. Because even the single objective problem is NP-hard, different heuristics based on a genetic algorithm (GA) are developed to further approximate a Pareto-optimal set of solutions for our multi-objective problem.     

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.     

A comparison of stochastic programming and bi-objective optimisation approaches to robust airline crew scheduling

A prominent problem in airline crew scheduling is the pairings or Tour-of-Duty planning problem. The objective is to determine a set of pairings (or Tours-of-Duty) for a crew group to minimise the planned cost of operating a schedule of flights. However, due to unforeseen events the performance in operation can differ considerably from planning, sometimes causing significant additional recovery costs. In recent years there has been a growing interest in robust crew scheduling. Here, the aim is to find solutions that are “cheap” in terms of planned cost as well as being robust, meaning that they are less likely to be disrupted in case of delays. Taking the stochastic nature of delays into account, Yen and Birge (Transp Sci 40:3–14, 2006) formulate the problem as a two-stage stochastic integer programme and develop an algorithm to solve this problem. Based on the contradictory nature of the goals, Ehrgott and Ryan (J Multi-Criteria Decis Anal 11:139–150, 2002) formulate a bi-objective set partitioning model and employ elastic constraint scalarisation to enable the solution by set partitioning algorithms commercially used in crew scheduling software. In this study, we compare the two solution approaches. We improve the algorithm of Yen and Birge (Transp Sci 40:3–14, 2006) and implement both methods with a commercial crew scheduling software. The results of both methods are compared with respect to characteristics of robust solutions, such as the number of aircraft changes for crew. We also conduct experiments to simulate the performance of the obtained solutions. All experiments are performed using actual schedule data from Air New Zealand.     

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.     

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.     

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.     

The home health care problem with working regulations

Due to the geographically dispersed locations of their clients, home health care providers have to perform a complex routing and scheduling task. Besides the well-researched routing problem, the adherence to legal and organizational working regulations is a basis for application in practice. These requirements are already widely incorporated in the nurse rostering problem for stationary institutions, but also have to be considered while generating routes for home care providers. We introduce new and adapted working regulations to the home health care problem. The mixed-integer formulation is adaptable to the requirements of different providers. Our numerical results show that an exact solution approach is noncompetitive with respect to computing time in most cases. We therefore propose a heuristic approach based on an adaptive large neighborhood search to cope with the complexity of the problem. The numerical results are computed on generated but realistic instances as well as on data sets provided in previous publications. The results show that the heuristic achieves good results in comparison to the mixed-integer program in only a portion of the computation time. Additional to a numerical analysis, we investigate the influence of the working regulations on the solutions which indicates the importance of modeling working regulations. If the regulations are neglected, a high number of violations are caused.

     

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.     

Tramp ship routing and scheduling with voyage separation requirements

In this paper we explore tramp ship routing and scheduling. Tramp ships operate much like taxies following the available demand. Tramp operators can determine some of their demand in advance by entering into long-term contracts and then try to maximise profits from optional voyages found in the spot market. Routing and scheduling a tramp fleet to best utilise fleet capacity according to current demand is therefore an ongoing and complicated problem. Here we add further complexity to the routing and scheduling problem by incorporating voyage separation requirements that enforce a minimum time spread between some voyages. The incorporation of these separation requirements helps balance the conflicting objectives of maximising profit for the tramp operator and minimising inventory costs for the charterer, since these costs increase if similar voyages are not performed with some separation in time. We have developed a new and exact branch-and-price procedure for this problem. We use a dynamic programming algorithm to generate columns and describe a time window branching scheme used to enforce the voyage separation requirements which we relax in the master problem. Computational results show that our algorithm in general finds optimal solutions very quickly and performs much faster compared to an earlier a priori path generation method. Finally, we compare our method to an earlier adaptive large neighbourhood search heuristic and find that on similar-sized instances our approach generally uses less time to find the optimal solution than the adaptive large neighbourhood search method uses to find a heuristic solution.

     

A joint pricing,lot-sizing,and supplier selection model

In this paper, we integrate the three strategies that are important to most firms, namely pricing, lot-sizing and supplier selection. Combining the three objectives of total profit, inconsistency, and deficiency with a set of constraints, we formulate this integrated problem as a multi-objective nonlinear programming model, proposing a genetic algorithm (NSGA-II) that provides decision-makers with a number of Pareto-optimal solutions, one of which can be selected on the basis of the higher-level information. We analyse the trade-off between the different Pareto-optimal solutions and discuss the results of that analysis. We then evaluate the performance of NSGA-II compared with SPEA2 in solving the model, which shows NSGA-II performs better. Finally, concluding remarks and suggestions for future research are provided.     

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.     

Pareto layer: Its formulation and search by way of evolutionary multi-objective optimization

This article examines multi-objective problems where a solution (product) is related to a cluster of performance vectors within a multi-objective space. Here the origin of such a cluster is not uncertainty, as is typical, but rather the range of performances attainable by the product. It is shown that, in such cases, comparison of a solution to other solutions should be based on its best performance vectors, which are extracted from the cluster. The result of solving the introduced problem is a set of Pareto optimal solutions and their representation in the objective space, which is referred to here as the Pareto layer. The authors claim that the introduced Pareto layer is a previously unattended novel representation. In order to search for these optimal solutions, an evolutionary multi-objective algorithm is suggested. The article also treats the selection of a solution from the obtained optimal set.     

A hybrid evolutionary graph-based multi-objective algorithm for layout optimization of truss structures

In this paper a new graph-based evolutionary algorithm, gM-PAES, is proposed in order to solve the complex problem of truss layout multi-objective optimization. In this algorithm a graph-based genotype is employed as a modified version of Memetic Pareto Archive Evolution Strategy (M-PAES), a well-known hybrid multi-objective optimization algorithm, and consequently, new graph-based crossover and mutation operators perform as the solution generation tools in this algorithm. The genetic operators are designed in a way that helps the multi-objective optimizer to cover all parts of the true Pareto front in this specific problem. In the optimization process of the proposed algorithm, the local search part of gM-PAES is controlled adaptively in order to reduce the required computational effort and enhance its performance. In the last part of the paper, four numeric examples are presented to demonstrate the performance of the proposed algorithm. Results show that the proposed algorithm has great ability in producing a set of solutions which cover all parts of the true Pareto front.     

A graph partitioning strategy for solving large-scale crew scheduling problems

Railway crew scheduling deals with generating driver duties for a given train timetable such that all work regulations are met and the resulting schedule has minimal cost. Typical problem instances in the freight railway industry require the generation of duties for thousands of drivers operating tens of thousands of trains per week. Due to short runtime requirements, common solution approaches decompose the optimization problem into smaller subproblems that are solved separately. Several studies have shown that the way of decomposing the problem significantly affects the solution quality. An overall best decomposition strategy for a freight railway crew scheduling problem, though, is not known. In this paper, we present general considerations on when to assign two scheduled train movements to separate subproblems (and when to rather assign them to the same subproblem) and deduct a graph partitioning based decomposition algorithm with several variations. Using a set of real-world problem instances from a major European railway freight carrier, we evaluate our strategy and benchmark the performance of the decomposition algorithm both against a common non-decomposition algorithm and a lower bound on the optimal solution schedule. The test runs show that our decomposition algorithm is capable of producing high-quality solution schedules while significantly cutting runtimes compared to the non-decomposition solution algorithm. We are following a ”greenfield” approach, where no information on previous schedules is needed. Hence, our approach is applicable to any railway crew scheduling setting, including network enlargement, integration of new customers, etc.     

Sequential interactive evolution for finding high-quality topologies

Finding a diverse set of high-quality (HQ) topologies for a single-objective optimization problem using an evolutionary computation algorithm can be difficult without a reliable measure that adequately describes the dissimilarity between competing topologies. In this article, a new approach for enhancing diversity among HQ topologies for engineering design applications is proposed. The technique initially selects one HQ solution and then searches for alternative HQ solutions by performing an optimization of the original objective and its dissimilarity with respect to the previously found solution. The proposed multi-objective optimization approach interactively amalgamates user articulated preferences with an evolutionary search so as sequentially to produce a set of diverse HQ solutions to a single-objective problem. For enhancing diversity, a new measure is suggested and an approach to reducing its computational time is studied and implemented. To illustrate the technique, a series of studies involving different topologies represented as bitmaps is presented.     

A hybrid Pareto-based local search algorithm for multi-objective flexible job shop scheduling problems

This paper presents a hybrid Pareto-based local search (PLS) algorithm for solving the multi-objective flexible job shop scheduling problem. Three minimisation objectives are considered simultaneously, i.e. the maximum completion time (makespan), the total workload of all machines, and the workload of the critical machine. In this study, several well-designed neighbouring approaches are proposed, which consider the problem characteristics and thus can hold fast convergence ability while keep the population with a certain level of quality and diversity. Moreover, a variable neighbourhood search (VNS) based self-adaptive strategy is embedded in the hybrid algorithm to utilise the neighbouring approaches efficiently. Then, an external Pareto archive is developed to record the non-dominated solutions found so far. In addition, a speed-up method is devised to update the Pareto archive set. Experimental results on several well-known benchmarks show the efficiency of the proposed hybrid algorithm. It is concluded that the PLS algorithm is superior to the very recent algorithms, in term of both search quality and computational efficiency.     

An efficient hybrid artificial bee colony algorithm for disassembly line balancing problem with sequence-dependent part removal times

This study deals with a sequence-dependent disassembly line balancing problem by considering the interactions among disassembly tasks, and a multi-objective mathematical model is established. Subsequently, a novel hybrid artificial bee colony algorithm is proposed to solve the problem. A new rule is used to initialize a bee colony population with certain diversity, and a dynamic neighbourhood search method is introduced to guide the employed/onlooker bees to promising regions. To rapidly leave the local optima, a global learning strategy is employed to explore higher quality solutions. In addition, a multi-stage evaluation method is designed for onlookers to effectively select employed bees to follow. The performance of the proposed algorithm is tested on a set of benchmark instances and two case scenarios, and the results are compared with several other metaheuristics in terms of solution quality and computation time. The comparisons demonstrate that the proposed algorithm exhibits superior performance.