A genetic algorithm for the proportionate multiprocessor open shop

The multiprocessor open shop (MPOS) scheduling problem is NP-complete, a category of hard combinatorial optimization problems that have not received much attention in the literature. In this work, a special MPOS—a proportionate one—is introduced for the first time. Two original mixed integer programming formulations for the proportionate MPOS are developed and their complexity is discussed. Due to the complexity of the MPOS, this paper develops a compu-search methodology (a genetic algorithm (GA)) to schedule the shop with the objective of minimizing the makespan. In this novel GA, a clever chromosome representation of a schedule is developed that succinctly encodes a schedule of jobs across multiple stages. The innovative design of this chromosome enables any permutation of its genes to yield a feasible solution. This simple representation of an otherwise very complex schedule enables the genetic operators of crossover and mutation to easily manipulate a schedule as the algorithm iteratively searches for better schedules. A testbed of difficult instances of the problem are created to evaluate the performance of the GA. The solution for each instance is compared with a derived lower bound. Computational results reveal that the algorithm performs extremely well, demonstrating its potential to efficiently schedule MPOS problems. More importantly, successful experiments on large-scale problem instances suggest the readiness of the GA for industrial use.     

Ant colony optimization algorithm for the Euclidean location-allocation problem with unknown number of facilities

This paper addresses the Euclidean location-allocation problem with an unknown number of facilities, and an objective of minimizing the fixed and transportation costs. This is a NP-hard problem and in this paper, a three-stage ant colony optimization (ACO) algorithm is introduced and its performance is evaluated by comparing its solutions to the solutions of genetic algorithms (GA). The results show that ACO outperformed GA and reached better solutions in a faster computational time. Furthermore, ACO was tested on the relaxed version of the problem where the number of facilities is known, and compared to existing methods in the literature. The results again confirmed the superiority of the proposed algorithm.     

Two-machine flow shop scheduling integrated with preventive maintenance planning

This paper investigates an integrated optimisation problem of production scheduling and preventive maintenance (PM) in a two-machine flow shop with time to failure of each machine subject to a Weibull probability distribution. The objective is to find the optimal job sequence and the optimal PM decisions before each job such that the expected makespan is minimised. To investigate the value of integrated scheduling solution, computational experiments on small-scale problems with different configurations are conducted with total enumeration method, and the results are compared with those of scheduling without maintenance but with machine degradation, and individual job scheduling combined with independent PM planning. Then, for large-scale problems, four genetic algorithm (GA) based heuristics are proposed. The numerical results with several large problem sizes and different configurations indicate the potential benefits of integrated scheduling solution and the results also show that proposed GA-based heuristics are efficient for the integrated problem.     

A combined genetic algorithms-shooting method approach to solving optimal control problems

In this paper, an alternative method for solving optimal control problems is presented. By applying calculus of variations, the optimal control problem can be reduced to solving a two-point boundary value problem. Here, the solution is generated with a combination of two methods genetic algorithms (GA) and the shooting method. An estimate of the optimal solution is first obtained using GA. This solution is in turn used as the initial guess for the shooting method. This combined method is applied to an optimal missile guidance problem. The performances of the combined method and GA are evaluated by simulation and compared. The results clearly show that the proposed combined method is able to locate the optimal solution more efficiently than GA. The results also show that the combined method never fails to correctly determine the optimal solution. Therefore, it proves to be more robust than the shooting method whose convergence is not always guaranteed.     

An evolutionary method for efficient computation of mutual capacitance for VLSI circuits based on the method of images

The problem of computing the capacitance coupling in Very Large Scale Integrated (VLSI) circuits is studied in this work. The proposed method is an approximate extended version of the method of images. The initial problem is formulated here as an optimization problem for the solution of which a genetic algorithm (GA) is employed. The proposed method is fast, general, does not rely on fitting techniques and is applicable to an arbitrary 2D or 3D geometry configuration of conductors. Extensive simulation results are presented for several practical case studies. Comparative results are given with other methods from literature and a commercial tool employing the Finite Element Method (FEM). The results show that the capacitance value computed by our method is in close agreement to the value obtained by the other methods from literature and also by the commercial tool with the average difference ranging between 2% and 5% while demonstrating better scalability as the problem complexity rises.     

A simple and effective genetic algorithm for the two-stage capacitated facility location problem

This paper presents a simple and effective Genetic Algorithm (GA) for the two-stage capacitated facility location problem (TSCFLP). The TSCFLP is a typical location problem which arises in freight transportation. In this problem, a single product must be transported from a set of plants to meet customers demands, passing out by intermediate depots. The objective is to minimize the operation costs of the underlying two-stage transportation system thereby satisfying demand and capacity constraints of its agents. For this purpose, a GA is proposed and computational results are reported comparing the heuristic results with those obtained by two state-of-the-art Lagrangian heuristics proposed in the literature for the problem.     

Solving lot-sizing problem with quantity discount and transportation cost

Owing to today's increasingly competitive market and ever-changing manufacturing environment, the inventory problem is becoming more complicated to solve. The incorporation of heuristics methods has become a new trend to tackle the complex problem in the past decade. This article considers a lot-sizing problem, and the objective is to minimise total costs, where the costs include ordering, holding, purchase and transportation costs, under the requirement that no inventory shortage is allowed in the system. We first formulate the lot-sizing problem as a mixed integer programming (MIP) model. Next, an efficient genetic algorithm (GA) model is constructed for solving large-scale lot-sizing problems. An illustrative example with two cases in a touch panel manufacturer is used to illustrate the practicality of these models, and a sensitivity analysis is applied to understand the impact of the changes in parameters to the outcomes. The results demonstrate that both the MIP model and the GA model are effective and relatively accurate tools for determining the replenishment for touch panel manufacturing for multi-periods with quantity discount and batch transportation. The contributions of this article are to construct an MIP model to obtain an optimal solution when the problem is not too complicated itself and to present a GA model to find a near-optimal solution efficiently when the problem is complicated.     

Hybrid real coded genetic algorithm solution to economic dispatch problem

This paper presents a new, two-phase hybrid real coded genetic algorithm (GA) based technique to solve economic dispatch (ED) problem with multiple fuel options. The proposed hybrid scheme is developed in such a way that a simple real coded GA is acting as a base level search, which makes a quick decision to direct the search towards the optimal region, and local optimization by direct search and systematic reduction in size of the search region method is next employed to do the fine tuning. Constraint satisfaction technique has been employed to improve the solution quality and reduce the computational expenses. In order to validate the effectiveness of the proposed hybrid real coded genetic algorithm, the result of 10-generation unit ED problem with multiple fuel options is considered. The result shows that the proposed hybrid algorithm not only improves the solution accuracy and reliability but also makes the algorithm more efficient in terms of number of function evaluations and computation time. The simulation study clearly demonstrates that the proposed hybrid real coded genetic algorithm is practical and valid for real-time applications.     

A COMPARATIVE STUDY ON PARTICLE SWARM OPTIMIZATION AND GENETIC ALGORITHMS FOR TRAVELING SALESMAN PROBLEMS

This article deals with a performance evaluation of particle swarm optimization (PSO) and genetic algorithms (GA) for traveling salesman problem (TSP). This problem is known to be NP-hard, and consists of the solution containing N! permutations. The objective of the study is to compare the ability to solve the large-scale and other benchmark problems for both algorithms. All simulation has been performed using a software program developed in the Delphi environment. As yet, overall results show that genetic algorithms generally can find better solutions compared to the PSO algorithm, but in terms of average generation it is not good enough.     

A Genetic Algorithm Based on Relaxation Induced Neighborhood Search in a Local Branching Framework for Capacitated Multicommodity Network Design

The fixed-charge Capacitated Multicommodity Network Design (CMND) is a well-known problem of both practical and theoretical significance. This article proposes the Genetic Algorithm (GA) cooperative Relaxation Induced Neighborhood Search (RINS) in a Local Branching (LB) framework for CMND problem. GA algorithm is started by initial population which is made by two parents obtain from hybrid LB and RINS algorithms. The basic idea of the proposed solution method is to use the GA algorithm to explore the search space and the hybrid LB and RINS methods to move from current solution to neighbor solution. Adapting the metaheuristic algorithm with RINS method to fit within an LB framework represents an interesting challenge. To evaluate the proposed algorithm, the standard problems with different sizes are used. The parameters of the algorithm are tuned by design of experiments. In order to prove the efficiency and effectiveness of the proposed algorithm, the results are compared with the best results available in the literature. The statistical analysis shows high performance of the proposed algorithm.     

Math modeling and GA approach to simultaneously make overtime decisions,load cells and sequence products

The problem studied in this paper was inspired from an actual textile company. The problem is more complex than usual scheduling problems in that we need to decide additional capacity requirements at the same time we make scheduling decisions. It is assumed that tardy jobs are lost sales and since this is not desirable, we allow overtime to minimize the number of tardy jobs. However, overtime brings additional costs to a company. Therefore, the overall objective is to maximize profits. We propose both a Mathematical Model and a Genetic Algorithm (GA) approach to solve this problem. We experimented with 20-job, 30-job, 40-job, 50-job, 60-job, 70-job, 80-job and 90-job problems in the paper. Math model was fast in solving 20-job and 30-job problems. GA found optimal solutions with a high frequency in these job categories as well. GA found near optimal solutions for large problems that Math Model could find optimal solution. GA includes some newly proposed mutation operators, dynamic and twin. The proposed twin mutation strategy produced the best results in all problem sizes. Finally, OPL software was run with 2-min restriction for large problems where optimal solutions could not be found due to memory restrictions. In this case, “Best-so-far” results obtained from OPL runs outperformed corresponding GA results in all instances. The paper concludes that math model is the preferred solution approach for the problem on hand.     

Generalized quadratic multiple knapsack problem and two solution approaches

The Quadratic Knapsack Problem (QKP) is one of the well-known combinatorial optimization problems. If more than one knapsack exists, then the problem is called a Quadratic Multiple Knapsack Problem (QMKP). Recently, knapsack problems with setups have been considered in the literature. In these studies, when an item is assigned to a knapsack, its setup cost for the class also has to be accounted for in the knapsack. In this study, the QMKP with setups is generalized taking into account the setup constraint, assignment conditions and the knapsack preferences of the items. The developed model is called Generalized Quadratic Multiple Knapsack Problem (G-QMKP). Since the G-QMKP is an NP-hard problem, two different meta-heuristic solution approaches are offered for solving the G-QMKP. The first is a genetic algorithm (GA), and the second is a hybrid solution approach which combines a feasible value based modified subgradient (F-MSG) algorithm and GA. The performances of the proposed solution approaches are shown by using randomly generated test instances. In addition, a case study is realized in a plastic injection molding manufacturing company. It is shown that the proposed hybrid solution approach can be successfully used for assigning jobs to machines in production with plastic injection, and good solutions can be obtained in a reasonable time for a large scale real-life problem.     

A genetic algorithm approach to the multiple machine tool selection problem

A number of earlier researches have emphasized the on-the-job scheduling problems that occur with a single flexible machine. Two solutions to the problem have generally been considered; namely minimization of tool switches and minimization of tool switching instances. Methods used to solve the problems have included KTNS heuristic, dual-based relaxation heuristic, and non-LP-based branch-and-bound methods. However, scant literature has considered the case of job scheduling on multiple parallel machines which invokes another problem involving machine assignment. This paper addresses the problem of job scheduling and machine assignment on a flexible machining workstation (FMW) equipped with multiple parallel machines in a tool-sharing environment. Under these circumstances, the authors have attempted to model the problem with the objective of simultaneously minimizing both the number of tool switches and the number of tool switching instances. Furthermore, a set of realistic constraints has been included in the investigation. A novel genetic algorithm (GA) heuristic has been developed to solve the problem, and performance results show that GA is an appropriate solution.     

Applied Genetic Algorithm for Solving Rich VRP

In this article, we present a study of the effectiveness of a genetic algorithm (GA) to solve a combinatorial problem, that is, a vehicle routing problem (VRP). We propose a new selection method, called “rank and select,” based on selection rate, and we compare it with roulette wheel selection. In this article, we use two types of crossover method and two types of mutation method. These are applied for comparing the best fitness at the end of a generation. The problem solved in this study is how to generate feasible route combinations for a rich VRP and meet all the requirements with an optimum solution. Initial test results show that the route produced by the GA was effectively used for solving rich VRP and especially for a large number of customers, depots, and vehicles. Fuel consumption by proposed routes was lower by about 20.38% compared to that of an existing route.     

Minimizing the bicriteria of makespan and maximum tardiness with an upper bound on maximum tardiness

This paper studies the flowshop scheduling problem with a complex bicriteria objective function. A weighted sum of makespan and maximum tardiness subject to a maximum tardiness threshold value is to be optimized. This problem, with interesting potential applications in practice, has been sparsely studied in the literature. We propose global and local dominance relationships for the three-machine problem and a fast and effective genetic algorithm (GA) for the more general m$m$-machine case. The proposed GA incorporates a novel three-phase fitness assignment mechanism specially targeted at dealing with populations in which both feasible as well as infeasible solutions might coexist. Comprehensive computational and statistical experiments show that the proposed GA outperforms the two most effective existing heuristics by a considerable margin in all scenarios. Furthermore, the proposed GA is also faster and able to find more feasible solutions. It should be noted that when the weight assigned to maximum tardiness is zero, then the problem is reduced to minimizing makespan subject to a maximum tardiness threshold value. Heuristics for both problems have been provided in the literature recently but they have not been compared. Another contribution of this paper is to compare these recent heuristics with each other.     

A new encoding scheme-based hybrid algorithm for minimising two-machine flow-shop group scheduling problem

This article investigates the two-machine flow-shop group scheduling problem (GSP) with sequence-dependent setup and removal times, and job transportation times between machines. The objective is to minimise the total completion time. As known, this problem is an NP-hard problem and generalises the typical two-machine GSPs. In this article, a new encoding scheme based on permutation representation is proposed to transform a random job permutation to a feasible permutation for GSPs. The proposed encoding scheme simultaneously determines both the sequence of jobs in each group and the sequence of groups. By reasonably combining particle swarm optimisation (PSO) and genetic algorithm (GA), we develop a fast and easily implemented hybrid algorithm (HA) for solving the considered problems. The effectiveness and efficiency of the proposed HA are demonstrated and compared with those of standard PSO and GA by numerical results of various tested instances with group numbers up to 20. In addition, three different lower bounds are developed to evaluate the solution quality of the HA. Limited numerical results indicate that the proposed HA is a viable and effective approach for the studied two-machine flow-shop group scheduling problem.     

An innovative framework for designing genetic algorithm structures

Genetic Algorithms are popular optimization algorithms, often used to solve complex large scale optimization problems in many fields. Like other meta-heuristic algorithms, Genetic Algorithms can only provide a probabilistic guarantee of the global optimal solution. Having a Genetic Algorithm (GA) capable of finding the global optimal solution with high success probability is always desirable. In this article, an innovative framework for designing an effective GA structure that can enhance the GA's success probability of finding the global optimal solution is proposed. The GA designed with the proposed framework has three innovations. First, the GA is capable of restarting its search process, based on adaptive condition, to jump out of local optima, if being trapped, to enhance the GA's exploration. Second, the GA has a local solution generation module which is integrated in the GA loop to enhance the GA's exploitation. Third, a systematic method based on Taguchi Experimental Design is proposed to tune the GA parameter set to balance the exploration and exploitation to enhance the GA capability of finding the global optimal solution. Effectiveness of the proposed framework is validated in 20 large-scale case study problems in which the GA designed by the proposed framework always outperforms five other algorithms available in the global optimization literature.     

Simultaneous scheduling of football games and referees using Turkish league data

Assignment decisions of referees to football (soccer) games are highly debated in sports media. Referee assignments are typically done on a weekly basis as the league progresses. However, this practice ignores important workload constraints on referees. Moreover, referees' skill levels should also be considered in determining their assignments. In this article, we first give a mixed integer linear program formulation for the problem of simultaneously generating a game schedule and assigning main referees to games by incorporating specific rules in the Turkish league. We also approach this problem using a genetic algorithm (GA) because of the computational difficulties in solving the problem. In the GA solution pool, we suggest using templates for referee assignments that follow several referee‐related workload constraints. We explain how these templates can be obtained by solving a mixed integer linear model prior to running the GA. The usage of these templates for referee assignments is conceptually similar to using a basic match schedule for game scheduling such as the one used in the Turkish Football League. We use the Turkish Football League fixtures for 2010–2013 as a case study. Experiments with the GA using real‐world data show a rather modest performance in terms of computation time and objective function value. Our numerical results indicate that the problem is extremely hard to solve.     

基于浮点数编码遗传算法的PI参数优化算法

本文介绍了基于浮点数编码遗传算法寻优的PID参数优化方法,采用误差绝对值时间平方积分性能指标作为参数选择的目标函数,利用遗传算法的全局搜索能力,实现对全局最优解的寻优,以降低PID参数整定的难度,达到总体提高系统性能的目的.仿真结果表明,通过浮点数编码遗传算法进行PI参数优化可使系统具有很好的动态品质和稳态特性.     

A GA methodology for the scheduling of yarn-dyed textile production

This paper presents a scheduling approach for yarn-dyed textile manufacturing. The scheduling problem is distinct in having four characteristics: multi-stage production, sequence-dependent setup times, hierarchical product structure, and group-delivery (a group of jobs pertaining to a particular customer order must be delivered together), which are seldom addressed as a whole in literature. The scheduling objective is to minimize the total tardiness of customer orders. The problem is formulated as a mixed integer programming (MIP) model, which is computationally extensive. To reduce the problem complexity, we decomposed the scheduling problem into a sequence of sub-problems. Each sub-problem is solved by a genetic algorithm (GA), and an iteration of solving the whole sequence of sub-problems is repeated until a satisfactory solution has been obtained. Numerical experiment results indicated that the proposed approach significantly outperforms the EDD (earliest due date) scheduling method—currently used in the yarn-dyed textile industry.