Non-dominated ranked genetic algorithm for a multi-objective mixed-model assembly line sequencing problem

The increasing market demand for product variety forces manufacturers to design mixed-model assembly lines (MMAL) on which a variety of product models similar to product characteristics are assembled. This paper presents a method combining the new ranked based roulette wheel selection algorithm with Pareto-based population ranking algorithm, named non-dominated ranking genetic algorithm (NRGA) to a just-in-time (JIT) sequencing problem when two objectives are considered simultaneously. The two objectives are minimisation the number of setups and variation of production rates. This type of problem is NP-hard. Various operators and parameters of the proposed algorithm are reviewed to calibrate the algorithm by means of the Taguchi method. The solutions obtained via NRGA are compared against solutions obtained via total enumeration (TE) scheme in small problems and also against four other search heuristics in small, medium and large problems. Experimental results show that the proposed algorithm is competitive with these other algorithms in terms of quality and diversity of solutions.     

A simulated annealing approach to mixed-model sequencing with multiple objectives on a just-in-time line

This paper presents a Simulated Annealing based heuristic that simultaneously considers both setups and the stability of parts usage rates when sequencing jobs for production in a just-in-time environment. Varying the emphasis of these two conflicting objectives is explored. Several test problems are solved via the Simulated Annealing heuristic, and their objective function values are compared to solutions obtained via a Tabu Search approach from the literature. Comparison shows that the Simulated Annealing approach provides superior results to the Tabu Search approach. It is also found that the Simulated Annealing approach provides near-optimal solutions for smaller problems.     

JIT mixed-model sequencing with batching and setup considerations via search heuristics

This research addresses the problem of sequencing items for production when it is desired that the production sequences result in minimal usage rates–surrogate measures for flexibility in a JIT environment. While seeking sequences with minimal usage rates, the number of required setups for the sequences is also considered, along with feasible batch-sizing combinations. The general intent is to find minimum usage-rate sequences for each associated number of setups and total batches. This multiple objective problem is addressed via a three-dimensional efficient frontier. Because the combinatorial nature of sequencing problems typically provides an intractable search space for problems of ‘real world’ size, the search heuristics of simulated annealing and genetic algorithms are presented and used to find solutions for several problem sets from the literature. Experimentation shows that the simulated annealing approach outperforms the genetic algorithm approach in both objective function and CPU performance.     

A GRASP algorithm for flexible job-shop scheduling problem with limited resource constraints

A greedy randomised adaptive search procedure (GRASP) is an iterative multi-start metaheuristic for difficult combinatorial optimisation. The GRASP iteration consists of two phases: a construction phase, in which a feasible solution is found and a local search phase, in which a local optimum in the neighbourhood of the constructed solution is sought. In this paper, a GRASP algorithm is presented to solve the flexible job-shop scheduling problem (FJSSP) with limited resource constraints. The main constraint of this scheduling problem is that each operation of a job must follow an appointed process order and each operation must be processed on an appointed machine. These constraints are used to balance between the resource limitation and machine flexibility. The model objectives are the minimisation of makespan, maximum workload and total workload. Representative benchmark problems are solved in order to test the effectiveness and efficiency of the GRASP algorithm. The computational result shows that the proposed algorithm produced better results than other authors’ algorithms.     

Integrating optimisation and simulation approaches for daily scheduling of assembly and test operations

The purpose of this paper is to show how the results of an optimisation model that can be integrated with the decisions made within a simulation model to schedule back-end operations in a semiconductor assembly and test facility. The problem is defined by a set of resources that includes machines and tooling, process plans for each product and the following four hierarchical objectives: minimise the weighted sum of key device shortages, maximise weighted throughput, minimise the number of machines used and minimise the makespan for a given set of lots in queue. A mixed integer programming model is purposed and first solved with a greedy randomised adaptive search procedure (GRASP). The results associated with the prescribed facility configuration are then fed to the simulation model written in AutoSched AP. However, due to the inadequacy of the options built into AutoSched, three new rules were created: the first two are designed to capture the machine set-up profiles provided by the GRASP and the third to prioritise the processing of hot lots containing key devices. The computational analysis showed that incorporating the set-up from the GRASP in dynamic operations of the simulation greatly improved its performance with respect to the four objectives.     

Optimal feeding profile in fed-batch bioreactors using a genetic algorithm

An optimal feeding profile for a fed-batch process was designed based on an evolutionary algorithm. Usually the presence of multiple objectives in a problem leads to a set of optimal solutions, commonly known as Pareto-optimal solutions. Evolutionary algorithms are well suited for deriving multi-objective optimisation since they evolve a set of non-dominated solutions distributed along the Pareto front. Several evolutionary multi-objective optimisation algorithms have been developed, among which the Non-dominated Sorting Genetic Algorithm NSGA-II is recognised to be very effective in overcoming a variety of problems. To demonstrate the applicability of this technique, an optimal control problem from the literature was solved using several methods considering the single-objective dynamic optimisation problem.     

Optimizing production smoothing decisions via batch selection for mixed-model just-in-time manufacturing systems with arbitrary setup and processing times

This paper is concerned with the production smoothing problem that arises in the context of just-in-time manufacturing systems. The production smoothing problem can be solved by employing a two-phase solution methodology, where optimal batch sizes for the products and a sequence for these batches are specified in the first and second phases, respectively. In this paper, we focus on the problem of selecting optimal batch sizes for the products. We propose a dynamic programming (DP) algorithm for the exact solution of the problem. Our computational experiments demonstrate that the DP approach requires significant computational effort, rendering its use in a real environment impractical. We develop three meta-heuristics for the near-optimal solution of the problem, namely strategic oscillation, scatter search and path relinking. The efficiency and efficacy of the methods are tested via a computational study. The computational results show that the meta-heuristic methods considered in this paper provide near-optimal solutions for the problem within several minutes. In particular, the path relinking method can be used for the planning of mixed-model manufacturing systems in real time with its negligible computational requirement and high solution quality.     

Minimising utility work and utility worker transfers for a mixed-model assembly line

Mixed-model assembly lines (MMALs) are types of production lines that are able to respond to diversified costumers’ demand for a variety of models without holding large inventories. The effective utilisation of a mixed-model assembly line requires the determination of the assembly sequence for different models. In this paper, two objectives are considered in a sequential manner, namely minimising: (i) total utility work, which means work from an additional worker to assist an operator for completion of an assembly task; and (ii) utility worker transfer which states the move of a utility worker to a different segment of the assembly line. First, due to the NP-hard nature of the problem, three heuristic methods are proposed with the aim of minimising total utility work. Then, the solutions which are obtained from the heuristics are improved in terms of the total number of utility worker transfers via a local search based method. Furthermore, the solution approach was applied in a real life mixed model tractor assembly line. Results validated the effectiveness of sequencing approach in terms of solution quality.     

Simultaneous balancing and sequencing of mixed-model parallel two-sided assembly lines

Growing interests from customers in customised products and increasing competitions among peers necessitate companies to configure their manufacturing systems more effectively than ever before. We propose a new assembly line system configuration for companies that need intelligent solutions to satisfy customised demands on time with existing resources. A mixed-model parallel two-sided assembly line system is introduced based on the parallel two-sided assembly line system previously proposed in the literature. The mixed-model parallel two-sided assembly line balancing problem is illustrated with examples from the perspective of simultaneous balancing and sequencing. An agent-based ant colony optimisation algorithm is proposed to solve the problem. This algorithm is the first attempt in the literature to solve an assembly line balancing problem with an agent-based ant colony optimisation approach. The algorithm is illustrated with an example and its operational procedures and principles are explained and discussed.     

An MILP model and clustering heuristics for LED assembly optimisation on high-speed hybrid pick-and-place machines

This paper deals with a scheduling optimisation problem arising in printed circuit board (PCB) assembly. In one class of PCB assembly, light-emitting diodes are to be assembled into the placement locations on PCBs by a machine with multiple pick-and-place heads. The scheduling optimisation problem is to determine the assembly sequence of placement locations and the assignment of pick-and-place heads for locations so as to minimise the assembly time. We formulate it as a mixed integer linear programming model. To solve the problem efficiently, we classify the PCBs into two types. For the first type of PCBs, on which the locations are linearly arranged, a constructive heuristic is proposed based on the analysis of the best next location after a location is assembled. For the second type of PCBs, on which the locations are circularly arranged, a heuristic based on clustering strategy and path relinking method is proposed. Computational experiments show that the solutions obtained by the two heuristics make 2.32 and 6.82% improvements averagely for the PCBs with linearly and circularly arranged locations, respectively, as compared to the solutions used in real production, and they are also better than those obtained by a hybrid genetic algorithm.     

Simultaneous solving of balancing and sequencing problems in mixed-model assembly line systems

Recently, the mixed-model assembly line (MMAL) has been widely studied by many researchers. In fact, there are two basic problems, namely balancing and sequencing problems, which have been investigated in a lot of studies separately, but few researchers have solved both problems simultaneously. Regarding this, the best results in minimising total utility work have been gained by developing a co-evolutionary genetic algorithm (Co-GA) so far. This paper provides a mixed-integer linear programming (MILP) model to jointly solve the problems. Because of NP-hardness, an evolution strategies (ES) algorithm is presented and evaluated by the same test problems in the literature. Two main hypotheses, namely simultaneous search and feasible search, are tested in the proposed algorithm to improve the quality of solutions. To calibrate the algorithm, a Taguchi design of experiments is employed. The proposed ES is compared with the modified version of Co-GA and the MILP model results. According to numerical experiments and statistical proving, the proposed ES outperformed the modified Co-GA from two points of view: the objective function and the computational time. Additionally, the meta-heuristic algorithms are examined in terms of other well-known criteria in MMAL. Finally, the contribution of each hypothesis in accounting for this superiority is analysed.     

An evolutionary algorithm to generate alternatives (EAGA) for engineering optimization problems

Typically for a real optimization problem, the optimal solution to a mathematical model of that real problem may not always be the ‘best’ solution when considering unmodeled or unquantified objectives during decision-making. Formal approaches to explore efficiently for good but maximally different alternative solutions have been established in the operations research literature, and have been shown to be valuable in identifying solutions that perform expectedly well with respect to modeled and unmodeled objectives. While the use of evolutionary algorithms (EAs) to solve real engineering optimization problems is becoming increasingly common, systematic alternatives-generation capabilities are not fully extended for EAs. This paper presents a new EA-based approach to generate alternatives (EAGA), and illustrates its applicability via two test problems. A realistic airline route network design problem was also solved and analyzed successfully using EAGA. The EAGA promises to be a flexible procedure for exploring alternative solutions that could assist when making decisions for real engineering optimization problems riddled with unmodeled or unquantified issues.     

Discrete electromagnetism-like mechanism algorithm for assembly sequences planning

Assembly sequence planning (ASP) plays an important role in digital manufacturing. It is a combinatorial optimisation problem with strong constraints aiming to work out a specific sequence to assemble together all components of a product. The connector-based ASP, which uses the connector to simplify the complex assembly problem, is one of the most important and hardest types. In order to solve this problem effectively, a discrete electromagnetism-like mechanism (DEM) algorithm is proposed. A charge formula and a force formula are redefined in DEM algorithm. An adjacency list is applied to handle the precedence relationship and prevent infeasible solutions. Two movements based on path relinking are employed. Moreover, with two different guided mutations, the population diversity can be guaranteed. Five examples are used to test and evaluate the performance of DEM. The comparisons among the proposed DEM, traditional genetic algorithms (GAs), guided GAs, memetic algorithms and artificial immune systems show that DEM outperforms among these algorithms in terms of running time, computation accuracy, convergence speed and parameter robustness.     

Soft constraint handling for a real-world multiobjective energy distribution problem

Real-world optimisation problems usually involve some conflicting objectives and a number of constraints. In such cases, finding a feasible, Pareto-optimal solution poses a demanding challenge. In reality, constraints bear different importance levels to these conflicting objectives. If some constraints are relaxed within an acceptable degree, quality infeasible solutions could be found on the boundary from the infeasible side of the searching region. This paper formulates an energy distribution problem arising from a real-world iron and steel production as a multiobjective optimisation problem. During the course of the optimisation search, this paper attempts to handle certain constraints in a soft manner to find solutions with good balance among objective and constraints violation. Based on the analysis of constraints from the real-world perspective, different tolerance values are defined. The proposed constraint violation degree-based soft handling approach is incorporated into the advanced version of non-dominated sorting genetic algorithm framework, as a case study, to examine the efficiency of the proposed soft constraint handling approach for a real-world energy distribution problem. The proposed approach is also implemented in different ways of constraint handling and tested on some benchmark functions to further demonstrate the performance of soft constraint handling for multiobjective optimisation problems.     

An improved approach for determination of index positions on CNC magazines with cutting tool duplications by integrating shortest path algorithm

Optimisation of automatic tool changer (ATC) indexing problem, where cutting tools are allocated to the stations on a turret magazine of a CNC machine, is one of the challenging problems in machining. The aim of the problem is to minimise the total indexing time of ATC. This problem becomes even more challenging if duplication of cutting tools is allowed and a bidirectional ATC is used. The problem has a unique feature which has not been stressed yet by other researchers, that is, although ATC indexing (master problem) is the main optimisation problem, objective function evaluation of this problem is a standalone optimisation problem (sub problem) indeed. Although an approximation algorithm does not guarantee optimality for the master problem, the subproblem must be solved optimally; otherwise, deficiencies arising from ill-defined objective function might be encountered. Considering this interesting future, a novel methodology, which employs a shortest path algorithm, is developed. Thus, the subproblem of this complicated problem can be optimally solved. Moreover, two metaheuristics, based on threshold accepting and descent first improvement greedy methodologies, are proposed for generating efficient solutions. Finally, several benchmarking instances are generated and solved to test the proposed algorithms.     

Sequencing mixed-model assembly lines operating with a heterogeneous workforce

We study the problem of sequencing mixed-model assembly lines operating with a heterogeneous workforce. The practical motivation for this study comes from the context of managing assembly lines in sheltered work centres for the disabled. We propose a general framework in which task execution times are both worker and model dependent. Within this framework, the problem is defined and mathematical mixed-integer models and heuristic procedures are proposed. These include a set of fast constructive heuristics, two local search procedures based on approximate measures using either a solution upper bound or the solution of a linear program and a GRASP metaheuristic. Computational tests with instances adapted from commonly used literature databases are used to validate the proposed approaches. These tests give insight on the quality of the different techniques, which prove to be very efficient both in terms of computational effort and solution quality when compared to other strategies such as a random sampling or the solution of the MIP models using a commercial solver.     

Hybrid intelligent water drops algorithm to unrelated parallel machines scheduling problem: a just-in-time approach

Minimising earliness and tardiness penalties as well as maximum completion time (makespan) simultaneously on unrelated parallel machines is tackled in this research. Jobs are sequence-dependent set-up times and due dates are distinct. Since the machines are unrelated, jobs processing time/cost on different machines may vary, i.e. each job could be processed at different processing times with regard to other machines. A mathematical model which minimises the mentioned objective is proposed which is solved optimally via lingo in small-sized cases. An intelligent water drop (IWD) algorithm, as a new swarm-based nature-inspired optimisation one, is also adopted to solve this multi-criteria problem. The IDW algorithm is inspired from natural rivers. A set of good paths among plenty of possible paths could be found via a natural river in its ways from the starting place (source) to the destination which results in eventually finding a very good path to their destination. A comprehensive computational and statistical analysis is conducted to analyse the algorithms’ performances. Experimental results reveal that the proposed hybrid IWD algorithm is a trustable and proficient one in finding very good solutions, since it is already proved that the IWD algorithm has the property of the convergence in value.     

An adaptive genetic algorithm approach for the mixed-model assembly line sequencing problem

A mixed-model assembly line (MMAL) is a type of production line that is capable of producing a variety of different product models simultaneously and continuously. The design and planning of such lines involve several long- and short-term problems. Among these problems, determining the sequence of products to be produced has received considerable attention from researchers. This problem is known as the Mixed-Model Assembly Line Sequencing Problem (MMALSP). This paper proposes an adaptive genetic algorithm approach to solve MMALSP where multiple objectives such as variation in part consumption rates, total utility work and setup costs are considered simultaneously. The proposed approach integrates an adaptive parameter control (APC) mechanism into a multi-objective genetic algorithm in order to improve the exploration and exploitation capabilities of the algorithm. The APC mechanism decides the probability of mutation and the elites that will be preserved for succeeding generations, all based on the feedback obtained during the run of the algorithm. Experimental results show that the proposed adaptive GA-based approach outperforms the non-adaptive algorithm in both solution quantity and quality.     

Operational strategies for seru production system: a bi-objective optimisation model and solution methods

In recent years, the interest in seru production system (SPS) has increased to enhance the flexibility of production systems. Because the worker resource in an SPS is critical for adapting to changes in demand, this study focuses on workforce-related operational strategies rarely considered for SPS. To this end, for the first time in the literature, a bi-objective workforce scheduling problem is addressed by considering the interseru worker transfer in SPS. A novel optimisation model is proposed to achieve two objectives, that of minimising makespan and reducing workload imbalance among workers. Because it is proved that the problem falls within a non-deterministic polynomial-time hardness (NP-hard) class, non-dominated sorting genetic algorithm-II (NSGA-II) is employed to solve large-sized problems. For small-sized problems, the second version of the augmented ε-constrained (AUGMECON2) method is implemented and Pareto-optimal solutions are obtained. A set of evaluation metrics is considered to compare two different operational strategies in terms of the desired objectives. The computational results indicate that allowing worker transfer leads to better results for all metrics. The main contribution of the present study is to provide a novel optimisation model for the addressed problem to compare two operational strategies by considering the heterogeneity inherent of workers.