Algebraic-logical Meta-model Research Articles

Knowledge Base component of Intelligent ALMM System based on the ontology approach

This paper presents the implementation of a knowledge base supporting an intelligent system to solve problems of optimization especially problems of discrete production processes optimization called Intelligent Algebraic-Logical Meta-Model (ALMM) Solver. Using a unified description of selected optimization problems, an ontological knowledge base was designed, which allows for selective selection of Intelligent ALMM Solver components necessary to solve and model problems. Using the definitions of the properties of optimization problems, scalable components describing exemplary optimization jobs were selected. Ontology for this area was developed, with particular emphasis on the requirements of the ALMM Solver. Using the possibility of interactive communication with the ALMM ontology in the form of SQL queries in the experimental part of the work, exemplary queries for the designed Knowledge Base (KB) module were presented, and the response generated by the system is a scenario of intelligent selection of a set of components modeling and solving a given problem. Such an innovative approach allows for dynamic construction of algorithms solving problems of discrete optimization. The use of knowledge about the properties of the considered processes and ALMM technology universalizes the proposed KB system making it an intelligent and efficient tool for solving discrete optimization jobs. The key advantage of the proposed ontological approach is the ability to flexibly expand it and extend its use to other classes of problems which have already been described in the ALMM technology.

Formal scheduling method for zero-defect manufacturing

A defect prevention is a part of manufacturing company practice. Paper proposes a formal approach for solving scheduling problems with unexpected events as extension of general frameworks for Zero-Defect Manufacturing (ZDM) strategy. ZDM aims to improve the process efficiency and the product quality while eliminating defects and minimizing process errors. However, most of ZDM applications focus on using the technological achievements of Industry 4.0 to detect and predict defects, forgetting to optimize the schedule on the production line. We propose formal method to create predictive-reactive schedule for problems with defect detection and repair. Our proposal is based on the formal Algebraic-Logical Meta-Model (ALMM). In particular, it uses the model switching method and combines defect detection, heuristics construction and decision support containing predictions of disturbances in the production process and enabling their prevention. Production defects are detected and repaired, and consequently, production delivers components without defects, and in the shortest possible time. Moreover, the collection and analysis of data related to the occurrence of disturbances in the production process helps the management board in making decisions based on analysis gathered and stored data. Thus, the proposed method includes strategies such as detection, repair, prediction and prevention for defect-free production. We illustrate the proposed method on the example of a flow-shop system with different types of product defect problem.

Dynamic Vehicle Routing Problem—Predictive and Unexpected Customer Availability

The Dynamic Vehicle Routing Problem (DVRP) is one of the most important problems in the area of enterprise logistics. DVRP problems involve these dynamics: the appearance of customers, travel times, service times, or vehicle availability. One of the most often considered aspects of the DVRP is the availability of customers, in which a part or all of the customers are revealed dynamically during the design or execution of the routes. A classification of the DVRP problem due to various elements causing dynamism is proposed. The aim of the paper is to distinguish dynamic VRP, which takes into account the dynamic appearance of customers to serve during the design or execution of the routes. In particular, the difference between the predictive and unexpected aspects of the customer’s availability is considered. Above all, the variant of customer’s availability which is predicted according to an appropriate general rule is modeled using the algebraic-logical meta-model (ALMM). It is a methodology which enables making collective decisions in successive process stages, not separately for individual vehicles. The algebraic-logical model of the dynamic vehicle routing problem with predicted consumer availability is proposed. The paper shows the possibilities of applying the ALMM approach to dynamic problems both with predicted and unexpected customer availability.

Collective decision making in dynamic vehicle routing problem

The paper presents a collective decision making in dynamic vehicle routing problem. In contrast to the static problem, a part or all of the customers’ companies are revealed dynamically during the design or execution of the routes. The problem is modelled using the algebraic-logical meta-model (ALMM) methodology, which enables making collective decisions in successive process stages, not separately for individual vehicles. ALMM is considered to be the rule according to which the availability of companies is determined. The steps and schematics of the general algorithm that take into account the dynamic appearance of new companies are shown. The proposed approach belongs to trajectory-based metaheuristics methods.

Heuristic Method for Decision-Making in Common Scheduling Problems

The aim of the paper is to present a heuristic method for decision-making regarding an NP-hard scheduling problem with limitations related to tasks and the resources dependent on the current state of the process. The presented approach is based on the algebraic-logical meta-model (ALMM), which enables making collective decisions in successive process stages, not separately for individual objects or executors. Moreover, taking into account the limitations of the problem, it involves constructing only an acceptable solution and significantly reduces the amount of calculations. A general algorithm based on the presented method is composed of the following elements: preliminary analysis of the problem, techniques for the choice of decision at a given state, the pruning non-perspective trajectory, selection technique of the initial state for the trajectory final part, and the trajectory generation parameters modification. The paper includes applications of the presented approach to scheduling problems on unrelated parallel machines with a deadline and machine setup time dependent on the process state, where the relationship between tasks is defined by the graph. The article also presents the results of computational experiments.

Component Library of Problem Models for ALMM Solver

ABSTRACTThe article presents the software tool named Algebraic-Logical Meta-Model of Multistage Decision Processes (ALMM) Solver to solve combinatorial and discrete optimization problems including non-deterministic polynomial-time hard ones. The solver utilizes the modelling paradigm named ALMM and its theory, both developed by Dudek-Dyduch E. ALMM enables a unified approach to creating discrete optimization problem models and representing knowledge about the problems as well as the solving methods for them. The models have a component structure and are stored in a module named Problem Model Library (PML). A new, extended modular structure of ALMM Solver is presented together with a basic layout of the PML. The article focuses on application of the component technology to the PML designing and component modelling of different type of limitations. General library source code organization is proposed. Considerations are illustrated by means of a sample class of scheduling problems.

Algebraic-logical meta-model based approach for scheduling manufacturing problem with defects removal

The article deals with a formal approach to solving manufacturing problem with defects removal and presents the application of this approach to flow-shop system with defects. The defects are detected during quality control and thus they are unexpected events. Moreover, a job processing time is not predetermined, and it may contain the unknown time needed to repair. Therefore, stochastic uncertainties are considered, but in addition, we model the process of decision making. The algebraic-logical meta-model methodology constitutes the basis for our approach. A hybrid algorithm for constructing a solution based on the process simulation using special local optimizing task and algebraic-logical models switching when defect detection occurs is presented. In particular, the following elements of the presented approach are shown: disturbances type analyzing, definition of switching states set, definition of subproblems, algebraic-logical meta-models creating for all subproblems, switching types determining, determination of the switching rules, the switching function, and components of special local criterion definition. The article shows results of computer experiments.