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The genetic algorithm is an operational research method that may be used to solve scheduling problems in production planning.
To be competitive, corporations must minimize inefficiencies and maximize productivity. In manufacturing, productivity is inherently linked to how well the firm can optimize the available resources, reduce waste and increase efficiency. Finding the best way to maximize efficiency in a manufacturing process can be extremely complex. Even on simple projects, there are multiple inputs, multiple steps, many constraints and limited resources. In general a resource constrained scheduling problem consists of:
A typical factory floor setting is a good example of this, where it is necessary to schedule which jobs need to be completed on which machines, by which employees, in what order and at what time.
In very complex problems such as scheduling there is no known way to get to a final answer, so we resort to searching for it trying to find a "good" answer. Scheduling problems most often use heuristic algorithms to search for the optimal solution. Heuristic search methods suffer as the inputs become more complex and varied. This type of problem is known in computer science as an NP-Hard problem. This means that there are no known algorithms for finding an optimal solution in polynomial time.
Genetic algorithms are well suited to solving production scheduling problems, because unlike heuristic methods genetic algorithms operate on a population of solutions rather than a single solution. In production scheduling this population of solutions consists of many answers that may have different sometimes conflicting objectives. For example, in one solution we may be optimizing a production process to be completed in a minimal amount of time. In another solution we may be optimizing for a minimal amount of defects. By cranking up the speed at which we produce we may run into an increase in defects in our final product.
As we increase the number of objectives we are trying to achieve we also increase the number of constraints on the problem and similarly increase the complexity. Genetic algorithms are ideal for these types of problems where the search space is large and the number of feasible solutions is small.
To apply a genetic algorithm to a scheduling problem we must first represent it as a genome. One way to represent a scheduling genome is to define a sequence of tasks and the start times of those tasks relative to one another. Each task and its corresponding start time represents a gene.
A specific sequence of tasks and start times (genes) represents one genome in our population. To make sure that our genome is a feasible solution we must take care that it obeys our precedence constraints. We generate an initial population using random start times within the precedence constraints. With genetic algorithms we then take this initial population and cross it, combining genomes along with a small amount of randomness (mutation). The offspring of this combination is selected based on a fitness function that includes one or many of our constraints, such as minimizing time and minimizing defects. We let this process continue either for a pre-allotted time or until we find a solution that fits our minimum criteria. Overall each successive generation will have a greater average fitness, i.e. taking less time with higher quality than the preceding generations. In scheduling problems, as with other genetic algorithm solutions, we must make sure that we do not select offspring that are infeasible, such as offspring that violate our precedence constraint. We of course may have to add further fitness values such as minimizing costs; however, each constraint added greatly increases the search space and lowers the number of solutions that are good matches.
In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems by relying on biologically inspired operators such as mutation, crossover and selection. Some examples of GA applications include optimizing decision trees for better performance, solving sudoku puzzles, hyperparameter optimization, causal inference, etc.
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming.
Mathematical optimization or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. For large numbers of local optima, SA can find the global optima. It is often used when the search space is discrete. For problems where finding an approximate global optimum is more important than finding a precise local optimum in a fixed amount of time, simulated annealing may be preferable to exact algorithms such as gradient descent or branch and bound.
In computational intelligence (CI), an evolutionary algorithm (EA) is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses mechanisms inspired by biological evolution, such as reproduction, mutation, recombination, and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions. Evolution of the population then takes place after the repeated application of the above operators.
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints are linear.
A fitness function is a particular type of objective function that is used to summarise, as a single figure of merit, how close a given design solution is to achieving the set aims. Fitness functions are used in evolutionary algorithms (EA), such as genetic programming and genetic algorithms to guide simulations towards optimal design solutions.
Branch and bound is a method for solving optimization problems by breaking them down into smaller sub-problems and using a bounding function to eliminate sub-problems that cannot contain the optimal solution. It is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root. The algorithm explores branches of this tree, which represent subsets of the solution set. Before enumerating the candidate solutions of a branch, the branch is checked against upper and lower estimated bounds on the optimal solution, and is discarded if it cannot produce a better solution than the best one found so far by the algorithm.
In genetic algorithms and evolutionary computation, crossover, also called recombination, is a genetic operator used to combine the genetic information of two parents to generate new offspring. It is one way to stochastically generate new solutions from an existing population, and is analogous to the crossover that happens during sexual reproduction in biology. Solutions can also be generated by cloning an existing solution, which is analogous to asexual reproduction. Newly generated solutions are typically mutated before being added to the population.
Scheduling is the process of arranging, controlling and optimizing work and workloads in a production process or manufacturing process. Scheduling is used to allocate plant and machinery resources, plan human resources, plan production processes and purchase materials.
In computer programming, genetic representation is a way of presenting solutions/individuals in evolutionary computation methods. The term encompasses both the concrete data structures and data types used to realize the genetic material of the candidate solutions in the form of a genome, and the relationships between search space and problem space. In the simplest case, the search space corresponds to the problem space. The choice of problem representation is tied to the choice of genetic operators, both of which have a decisive effect on the efficiency of the optimization. Genetic representation can encode appearance, behavior, physical qualities of individuals. Difference in genetic representations is one of the major criteria drawing a line between known classes of evolutionary computation.
Single-machine scheduling or single-resource scheduling is an optimization problem in computer science and operations research. We are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on a single machine, in a way that optimizes a certain objective, such as the throughput.
A memetic algorithm (MA) in computer science and operations research, is an extension of the traditional genetic algorithm (GA) or more general evolutionary algorithm (EA). It may provide a sufficiently good solution to an optimization problem. It uses a suitable heuristic or local search technique to improve the quality of solutions generated by the EA and to reduce the likelihood of premature convergence.
The Shifting Bottleneck Heuristic is a procedure intended to minimize the time it takes to do work, or specifically, the makespan in a job shop. The makespan is defined as the amount of time, from start to finish, to complete a set of multi-machine jobs where machine order is pre-set for each job. Assuming that the jobs are actually competing for the same resources (machines) then there will always be one or more resources that act as a 'bottleneck' in the processing. This heuristic, or 'rule of thumb' procedure minimises the effect of the bottleneck. The Shifting Bottleneck Heuristic is intended for job shops with a finite number of jobs and a finite number of machines.
Job-shop scheduling, the job-shop problem (JSP) or job-shop scheduling problem (JSSP) is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. In a general job scheduling problem, we are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on m machines with varying processing power, while trying to minimize the makespan – the total length of the schedule. In the specific variant known as job-shop scheduling, each job consists of a set of operationsO1, O2, ..., On which need to be processed in a specific order. Each operation has a specific machine that it needs to be processed on and only one operation in a job can be processed at a given time. A common relaxation is the flexible job shop, where each operation can be processed on any machine of a given set.
A hyper-heuristic is a heuristic search method that seeks to automate, often by the incorporation of machine learning techniques, the process of selecting, combining, generating or adapting several simpler heuristics to efficiently solve computational search problems. One of the motivations for studying hyper-heuristics is to build systems which can handle classes of problems rather than solving just one problem.
In graph theory and combinatorial optimization, a closure of a directed graph is a set of vertices C, such that no edges leave C. The closure problem is the task of finding the maximum-weight or minimum-weight closure in a vertex-weighted directed graph. It may be solved in polynomial time using a reduction to the maximum flow problem. It may be used to model various application problems of choosing an optimal subset of tasks to perform, with dependencies between pairs of tasks, one example being in open pit mining.
Flow-shop scheduling is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. In a general job-scheduling problem, we are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on m machines with varying processing power, while trying to minimize the makespan – the total length of the schedule. In the specific variant known as flow-shop scheduling, each job contains exactly m operations. The i-th operation of the job must be executed on the i-th machine. No machine can perform more than one operation simultaneously. For each operation of each job, execution time is specified.
HeuristicLab is a software environment for heuristic and evolutionary algorithms, developed by members of the Heuristic and Evolutionary Algorithm Laboratory (HEAL) at the University of Applied Sciences Upper Austria, in Hagenberg im Mühlkreis. HeuristicLab has a strong focus on providing a graphical user interface so that users are not required to have comprehensive programming skills to adjust and extend the algorithms for a particular problem. In HeuristicLab algorithms are represented as operator graphs and changing or rearranging operators can be done by drag-and-drop without actually writing code. The software thereby tries to shift algorithm development capability from the software engineer to the user and practitioner. Developers can still extend the functionality on code level and can use HeuristicLab's plug-in mechanism that allows them to integrate custom algorithms, solution representations or optimization problems.
The nurse scheduling problem (NSP), also called the nurse rostering problem (NRP), is the operations research problem of finding an optimal way to assign nurses to shifts, typically with a set of hard constraints which all valid solutions must follow, and a set of soft constraints which define the relative quality of valid solutions. Solutions to the nurse scheduling problem can be applied to constrained scheduling problems in other fields.