# Heuristic Method for Decision-Making in Common Scheduling Problems
## 5 Characteristic of the Algorithm Class That Generates the Final Parts of the Trajectory
### Decision Technique  
Special attention will be paid here to the methods based on the ALMM methodology. One of the ways is to generate all the decisions from the set of possible decisions \(U_{p}(s)\) that can be taken in a given state. These decisions are then evaluated and one of them is determined by local decision-making procedures. The literature presents a heuristic method of discrete optimization problems using local optimization, but in these methods local optimization was only based on minimization (maximization) of the local increase of quality criterion, whereas ALMM allows one to create sophisticated local optimization criteria, which takes into account much more information than just about the increase of the criterion. An example is a specially designed local optimization task, to determine the distance between a given state and a particular set of states (the states belonging to the set of non-admissible states \(S_{N}\), as well as unfavorable states or distinguished favorable states), uses the term semimetrics (which differs from metrics in that it does not have to fulfill the condition \(\psi(a,b)=0\Leftrightarrow a=b\)). The idea of using a local criterion relating to additional limitation and semimetrics were first proposed by [PERSON] in [27] and developed in [26; 29; 32; 34]. Then the decision with the smallest value of the local criterion is chosen. This local optimization criterion consists of three parts. The first part concerns the value of the global index of quality for the generated trajectory. It is a sum of the increase of the quality index resulting from the realization of the decision under consideration and the value related to the estimation of the quality index for the final trajectory section, which follows the possible realization of the decision under consideration. This part of the criterion is suitable for problems, for which the quality criterion is additively separable and monotonically ascending along the trajectory [27]. The components related to additional limitations or requirements are the second part of the criterion. The third part includes components responsible for the preference for certain types of decisions resulting from problem analysis. It should be emphasized that during the design of the criterion, the components of the second and third parts will also be closely related to the objective of optimization. Other components will be when the goal is to minimize project time (cost) or minimize the number of delayed tasks. Moreover, the coefficient (weight) is associated with each component. The higher the value of the coefficient, the greater the importance of the component. The knowledge gathered during constructing a trajectory is used to change these coefficients. Another way to determine the decision in a given process state is using specially constructed rules. In this case, only one or a few of the decisions belonging to the set of possible decisions \(U_{p}(s)\) are determined. The rules for choosing decisions must be designed in an appropriate manner to ensure both the admissibility of such decisions and their quality. One method is the ALMM-based method of substitute tasks, proposed by [PERSON] [35]. In each state of the process a decision is made on the basis of a specially constructed optimization task, named a substitution task. This task is a certain substitution multistage process with substitution criterion. Substitution tasks are created to facilitate decision-making at a given state by substituting a global optimization task with a simpler local task. To construct the substitution task, the concept of so-called intermediate goals is used. These goals determine a certain set of states the process should reach as soon as possible. This means that they are simultaneously used to define the set of final states of the substitution process. Moreover, the coefficient (weight) is associated with each intermediate goal. The higher the value of the coefficient, the greater the importance of the component.