Optimization algorithms are important for deep learning. On one hand, training a complex deep learning model can take hours, days, or even weeks. The performance of the optimization algorithm directly affects the model’s training efficiency. On the other hand, understanding the principles of different optimization algorithms and the role of their parameters will enable us to tune the hyper parameters in a targeted manner to improve the performance of deep learning models.

Optimization and Deep Learning

In this section, we will discuss the relationship between optimization and deep learning as well as the challenges of using optimization in deep learning. For a deep learning problem, we will usually define a loss function first. Once we have the loss function, we can use an optimization algorithm in attempt to minimize the loss. In optimization, a loss function is often referred to as the objective function of the optimization problem. By tradition and convention most optimization algorithms are concerned with minimization. If we ever need to maximize an objective there is a simple solution: just flip the sign on the objective.

PSP modelling

In literature, the PSP was initially introduced within the manufacturing industry for job‐shop scheduling, with a main concern of optimal allocation over time of the shop floor's scarce resources. Consequently, the PSP modelling has developed through the development of the basic modelling of the RCPSP.

Several problem notations and models were presented for the RCPSP, as surveyed by Brucker, from which the basic and most widely adopted notation can be summarized as follows: A project is represented by a set of activities V = {1,…,n}, where 1 and n are two dummy activities resembling the project network's start and end nodes. The characteristics defining each activity, that is, V: processing duration di, resource requirements rik (for each resource k) along the activity's processing time, and a set of predecessors Pi logically tied to activity i with finish‐to‐start (FS) logic relations. The availability of each resource k is constrained throughout the project by the available resource units. And finally, the problem's objective is to minimize the time span T of the project's schedule S without violating the resources constraints; where S is represented by a set of activities’ start times S1 to Sn; and T =Sn.

The basic RCPSP model has several short falls with respect to over‐simplifying the characteristics of real‐life scheduling problems. Consequently, several studies in the PSP context were focused on improving the problem's modelling by developing extensions which add missing practical aspects to the basic PSP model.

The design and implementation of a robust scheduling system are essential for the successful use of planning and scheduling practices within projects. A scheduling system involves modelling the problem, selecting a solution approach to be used in a static and/or dynamic analysis for optimizing schedules, and finally the selection of an optimization technique which suits most the characteristics and conditions of the project type under analysis.

This study reviewed the concepts and researches presented for these three factors of building a scheduling system, with a more detailed focus on meta‐heuristic optimization algorithms adopted in the project‐scheduling context.

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