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A decision support model for handling customer orders in business chain

NEUROCOMPUTING 2022年第0期482卷 298-309页

作者： Sitek, Pawel Wikarek, Jaroslaw Bocewicz, Grzegorz Nielsen, Izabela Kielce Univ Technol Dept Control & Management Syst Kielce Poland Koszalin Univ Technol Fac Elect & Comp Sci Koszalin Poland Aalborg Univ Dept Mat & Prod Aalborg Denmark

One of the elements of the modern trade and services market is a business chain solution (chain store/retail chain). An example of a business chain is, e.g., a restaurant chain, where each restaurant in the chain has the same decor, organization, menu, and delivery method. Although such solutions have been known for decades, the rapid development of IT technology, the widespread access to the Internet as well as the development of mobile technologies have changed and modernized their formula. Many customers place orders remotely with the option of delivery to their door. This method of ordering and fulfilling orders is becoming more and more popular and ever more common in the recent period due to the pandemic and the resulting restrictions and limitations on the functioning of trade and services. The following key questions arise in relation to customer order processing for chain business managers: How to allocate individual customer orders to selected branches so that the cost of their processing (production and delivery) is the lowest?, How to deliver on time?, etc. To answer these questions, a decision support model has been developed, which combines routing, allocation and planning problems for restaurant/store chains. Two ways to implement the model have been proposed. The first one uses the methods of mathematical modeling and programming, and the other, which is a proprietary approach that integrates the mechanisms of evolution (specialized representations, repair mechanisms, genetic operators, etc.), uses constraint logic programming and dedicated heuristics. In addition, procedures for constraint handling and presolving have been developed. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Decision support Business chain Dedicated genetic algorithm constraint logic programming Mathematical programming Hybrid approach constraint handling procedure

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Hybrid knowledge bases

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 1996年第5期8卷 773-785页

作者： Lu, JJ Nerode, A Subrahmanian, VS CORNELL UNIV ITHACANY 14853 UNIV MARYLAND COLLEGE PKMD 20742

Deductive databases that interact with, and are accessed by, reasoning agents in the real world (such as logic controllers in automated manufacturing, weapons guidance systems, aircraft landing systems, land-vehicle maneuvering systems, and air-traffic control systems) must have the ability to deal with multiple modes of reasoning. Specifically, the types of reasoning we are concerned with include, among others, reasoning about time, reasoning about quantitative relationships that may be expressed in the form of differential equations or optimization problems, and reasoning about numeric modes of uncertainty about the domain which the database seeks to describe. Such databases may need to handle diverse forms of data structures, and frequently they may require use of the assumption-based nonmonotonic representation of knowledge. A hybrid knowledge base is a theoretical framework capturing all the above modes of reasoning. The theory tightly unifies the constraint logic programming Scheme of Jaffar and Lassez [11], the Generalized Annotated logic programming Theory of Kifer and Subrahmanian [16], and the Stable Model semantics of Gelfond and Lifschitz [6]. New techniques are introduced which extend both the work on Annotated logic programming and the Stable Model semantics. (Proofs are omitted from the paper to ensure readability. Complete details of all results may be found in [23].)

关键词： annotated logic constraint logic programming heterogeneous system mediator stable model

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logic-based representation and reasoning about knowledge of constrained resources

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KNOWLEDGE-BASED SYSTEMS 1997年第2期10卷 71-80页

作者： Ryu, YU Department of Decision Sciences The University of Texas at Dallas P.O. Box 830688 M/S JO 4.4 Richardson Texas 75083-0688 USA

It appears that classical logic is not suitable for the representation and reasoning about knowledge of disposable resources. The major difference between reasoning about disposable resources and classical logic is that once a disposable resource is used to produce something, it is not available any more;but a formula of classical logic can be repeatedly used in deduction. Inspired by linear logic, or logic of resources, we propose a language for knowledge-based systems of resources, which can process state space models of systems represented by Petri nets or their subclasses such as marked graphs and state machines. It can serve as a modeling tool for various engineering and social science problems of resource allocations.

关键词： constrained resource programming constraint logic programming logic-based knowledge representation Petri nets

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Proof Automation in the Theory of Finite Sets and Finite Set Relation Algebra

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COMPUTER JOURNAL 2022年第7期65卷 1891-1903页

作者： Cristia, Maximiliano Katz, Ricardo D. Rossi, Gianfranco Univ Nacl Rosario Pellegrini 250 RA-2000 Rosario Argentina CIFASIS Pellegrini 250 RA-2000 Rosario Argentina CIFASIS CONICET Bv 27 Febrero 210 Bis RA-2000 Rosario Argentina Univ Parma Parco Area Sci 53-A I-43100 Parma Italy

{log} ('setlog') is a satisfiability solver for formulas of the theory of finite sets and finite set relation algebra (FS&RA). As such, it can be used as an automated theorem prover for this theory. {log} is able to automatically prove a number of FS&RA theorems, but not all of them. Nevertheless, we have observed that many theorems that {log} cannot automatically prove can be divided into a few subgoals automatically dischargeable by {log}. The purpose of this work is to present a prototype interactive theorem prover (ITP), called {log}-ITP, providing evidence that a proper integration of {log} into world-class ITP's can deliver a great deal of proof automation concerning FS&RA. An empirical evaluation based on 210 theorems from the TPTP and Coq's SSReflect libraries shows a noticeable reduction in the size and complexity of the proofs with respect to Coq.

关键词： {log} set theory automated proofs constraint logic programming

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A hybrid approach of linear programming and logic modeling for the market core of sealed bid auctions

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Annals of Operations Research 1997年第75期75卷 209-209页

作者： Lee, H. G. Lee, R. M. Dept. of Business Administration School of Business and Economics Yonsei University Seoul 120-749 South Korea Erasmus Univ. Res. Inst. Decis. I. Erasmus University Rotterdam 3000 DR Rotterdam P.O. Box 1738 Netherlands

This paper presents a hybrid approach for sealed bid auction that integrates linear programming and logic modeling techniques. A linear programming model for the sealed bid auction considers only prices for transaction arrangements and yields multiple market cores when goods from sellers are equally attractive to many buyers. The hybrid approach takes into account ordinal preferences of traders as well to find the best market core. On the one hand, the hybrid approach uses a linear programming model to maximize total surplus of market participants based on the bid and ask prices. On the other hand, it employs a logical inferencing approach to satisfy traders' ordinal preferences that are not included in a single combination of bid and ask prices. A constraint logic programming scheme, which combines a mathematical program with a logical inferencing technique in an integrated formalism, is introduced to implement the hybrid approach. The hybrid approach is validated through market simulations, where a set of computer-generated trading data is applied to both the hybrid approach and the linear programming model for their market performance comparison.

关键词： constraint logic programming Hybrid approach of MS and AI Sealed bid auction

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META-LEVEL INTERPRETATION OF constraint LANGUAGES A CASE-STUDY - logicAL PRIMITIVES

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NEW GENERATION COMPUTING 1992年第4期10卷 361-384页

作者： HICKEY, TJ COHEN, J DESCHAMPS, V BRANDEIS UNIV MICHTOM SCH COMP SCIWALTHAMMA 02254

This paper provides a detailed presentation of a Prolog-written meta-level interpreter for a constraint logic programming (CLP) language for expressing equalities and disequalities of finite trees, as well as non-negative integers (arities). The logical interpretation of the Prolog primitive functor (whose arguments are trees and arity) is used to illustrate the interactions among constraints pertaining to multiple domains. The paper's objective is to provide insights about CLP language design and to present a modularized, incrementally-expandable meta-processor for this class of languages.

关键词： constraint logic programming META-LEVEL INTERPRETATION PROLOGS FUNCTOR PRIMITIVE DISEQUALITIES EXPLICIT UNIFICATION

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Introduction of a new class of variables to discrete and integer programming problems

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ANNALS OF OPERATIONS RESEARCH 1999年 86卷 39-51页

作者： Hajian, MT Rodosek, R Richards, B Univ London Imperial Coll Sci Technol & Med William Penny Lab London SW7 2AZ England

In formulating a combinatorial optimisation problem (COP) using Discrete or Integer programming (IP) modelling techniques, the modeller is restricted to use only certain predefined discrete variables and sets which are linked by sets of linear equality and inequality constraints. Definition of many COPs includes restrictions in which the use of disequality (DI) constraints in their mathematical representation is inevitable. To represent this type of constraint a number of binary variables and extra constraints are usually introduced, which lead to an increase in the size of the model in terms of variables and constraints. In this paper, we introduce a new class of discrete variables which enables the modeller to represent DI constraints more efficiently in the mathematical formulation of a combinatorial optimisation problem. We have also introduced a new branching scheme to the conventional simplex based Branch and Bound (B & B) algorithm in order to deal with this type of variables. To study the effect of these variables, we modelled and solved a set of five classic problems, first using conventional MP variables and second, exploiting the new proposed variables, and compared the results. The empirical results show a promising improvement on the performance of the B & B algorithm. The contribution of this paper is (1) the introduction of a new class of discrete variables which can help to build smaller models, and (2) new branching schemes on these variables that can improve the B & B performance.

关键词： mathematical modelling discrete programming constraint logic programming dis-equality constraints branch and bound

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CONSTRAINED RELATIVE LEAST GENERAL GENERALIZATION FOR INDUCING constraint logic PROGRAMS

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NEW GENERATION COMPUTING 1995年第3-4期13卷 335-368页

作者： MIZOGUCHI, F OHWADA, H Science University of Tokyo Chiba Japan

Relative least general generalization, proposed by Plotkin, is widely used for generalizing first-order clauses in Inductive logic programming, and this paper describes an extension of Plotkin's work to allow various computation domains: Herbrand Universe, sets, numerical data, etc. The theta-subsumption in Plotkin's framework is replaced by a more general constraint-based subsumption. Since this replacement is analogous to that of unification by constraint solving in constraint logic programming, the resultant method can be viewed as a constraint logic programming version of relative least general generalization. constraint-based subsumption, however, leads to a search on an intractably large hypothesis space. We therefore provide meta-level constraints that are used as semantic bias on the hypothesis language. The constraints functional dependency and monotonicity are introduced by analyzing clausal relationships. Finally, the advantage of the proposed method is demonstrated through a simple layout problem, where geometric constraints used in space planning tasks are produced automatically.

关键词： INDUCTIVE logic programming constraint logic programming constraint ACQUISITION RELATIVE LEAST GENERAL GENERALIZATION

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Mixed global constraints and inference in hybrid CLP-IP solvers

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ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE 2002年第4期34卷 271-290页

作者： Ottosson, G Thorsteinsson, ES Hooker, JN Uppsala Univ Dept Comp Sci S-75105 Uppsala Sweden Carnegie Mellon Univ Grad Sch Ind Adm Pittsburgh PA 15213 USA

The complementing strengths of constraint (logic) programming (CLP) and Mixed Integer programming (IP) have recently received significant attention. Although various optimization and constraint programming packages at a first glance seem to support mixed models, the modeling and solution techniques encapsulated are still rudimentary. Apart from exchanging bounds for variables and objective, little is known of what constitutes a good hybrid model and how a hybrid solver can utilize the complementary strengths of inference and relaxations. This paper adds to the field by identifying constraints as the essential link between CLP and IP and introduces an algorithm for bidirectional inference through these constraints. Together with new search strategies for hybrid solvers and cut-generating mixed global constraints, solution speed is improved over both traditional IP codes and newer mixed solvers.

关键词： mixed integer programming constraint logic programming integration mixed global contraints dynamic linear relaxations inference

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GENERATION OF DESIGN VERIFICATION TESTS FROM BEHAVIORAL VHDL PROGRAMS USING PATH ENUMERATION AND constraint programming

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IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS 1995年第2期3卷 201-214页

作者： VEMURI, R KALYANARAMAN, R INTEL CORP CHANDLERAZ 85226

A method for generation of design verification tests from behavior-level VHDL programs is presented. The method generates stimuli to execute desired control-how paths in the given VHDL program. This method is based on path enumeration, constraint generation and constraint solving techniques that have been traditionally used for software testing. Behavioral VHDL programs contain multiple communicating processes, signal assignment statements, and wait statements which are not found in traditional software programming languages. Our model of constraint generation is specifically developed for VHDL programs with such constructs. Control-flow paths for which design verification tests are desired are specified through certain annotations attached to the control statements in the VHDL programs. These annotations are used to enumerate the desired paths. Each enumerated path is translated into a set of mathematical constraints corresponding to the statements in the path. Methods for generating constraint variables corresponding to various types of carriers in VHDL and for mapping various VHDL statements into mathematical relationships among these constraint variables are developed. These methods treat spatial and temporal incarnations of VHDL carriers as unique constraint variables thereby preserving the semantics of the behavioral VHDL programs. constraints are generated in the constraint programming language CLP(R) and are solved using the CLP(R) system. A solution to the set of constraints so generated yields a design verification test sequence which can be applied for executing the corresponding control path when the design is simulated. If no solution exists, then it implies that the corresponding path can never be executed. Experimental studies pertaining to the quality of path coverage and fault coverage of the verification tests are presented.

关键词： DESIGN VERIFICATION TESTING FUNCTIONAL TESTING BEHAVIOR-LEVEL TEST GENERATION VHDL (VHSIC HARDWARE DESCRIPTION LANGUAGE) PATH ANALYSIS constraint SATISFACTION constraint logic programming SYMBOLIC EXECUTION

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