Papers by Angelo Monfroglio
Rivista di Informatica archive, Sep 1, 1989
Rivista di Informatica archive, Dec 1, 1986
International Journal of Intelligent Systems, Dec 7, 1998
ABSTRACT Hybrid genetic algorithms are presented that use optimization heuristics and genetic tec... more ABSTRACT Hybrid genetic algorithms are presented that use optimization heuristics and genetic techniques to outperform all existing programs for the timetabling problem. The timetabling problem is very hard (NP-complete) and a general polynomial time deterministic algorithm is not known. An artificial intelligence approach, in a logic programming environment, may be useful for such a problem. The decomposition and classification of constraints and the constraint ordering to obtain the minimization of the backtracking and the maximization of the parallelism are illustrated. The school timetabling problem is discussed in detail as a case study. The genetic algorithm approach is particularly well suited for this kind of problem, since there exists an easy way to assess a good timetable but not a well-structured automatic technique for constructing it. So, a population of timetables is created that evolves toward the best solutions. The evaluation function and the genetic operators are well separated from the domain-specific parts, such as the problem knowledge and the heuristics, i.e., from the timetable builder. A fundamental issue and a general problem in the decision process and automated reasoning is how to efficiently obtain logic decisions under disjunctive constraints. Logic constraint satisfaction problems are in general NP-hard and a general deterministic polynomial time algorithm is not known. The present article illustrates an approach based on the hybridization of constrained heuristic search with novel genetic algorithm techniques. It compares favorably with the best-known programs to solve decisions problems under logic constraints. Complexity of the new algorithms and results of significant experiments are reported. © 1996 John Wiley & Sons, Inc.
Data and Knowledge Engineering, Aug 1, 1988
ABSTRACT Timetabling and Constraint Satisfaction are very hard problems and a general polynomial ... more ABSTRACT Timetabling and Constraint Satisfaction are very hard problems and a general polynomial time deterministic algorithm is not known. An Artificial Intelligence approach, in a logic programming environment may be useful for such problems. The decomposition and classification of constraints and the constraint ordering to obtain the minimization of the backtracking and the maximization of the parallelism are illustrated. The timetabling problem is discussed in detail as a case study: a PROLOG system and a PARLOG system which solve the problem are described and their performances in significant tests are assessed. Finally, a General Constraint Solver is proposed that may be useful for several Resource Allocation, Engineering, DBMS, Decision Support Systems.
Social Science Research Network, 2023
A novel representation is described that models some important NP-hard problems, such as the prop... more A novel representation is described that models some important NP-hard problems, such as the propositional satisfiability problem (SAT), the Traveling Salesperson Problem (TSP), and the Minimal Set Covering Problem (MSCP) by means of only two types of constraints:'choiceconstraints'and 'exclusion constraints'. In its main section the paper presents an approach for solving a m-CNF-SAT problem (Conjunctive Normal Form Satisfaction: n variables, p clauses, clause length m) by integer programming. The paper presents a 0/1 Simplex for solving the obtained integer program. A main theorem of the paper is that this algorithm always finds a 0-1 integer solution. A solution of the integer program corresponds to a solution of the m-CNF-SAT and vice versa. The same modelling technique is then used for the Traveling Salesperson Problem and for the Minimal Set Covering: it is shown that a uniform approach is thus useful. Black A., J.A. De Loera, S. Kafer and Laura Sanità [Bla21] present new pivot rules for the Simplex method for LP over 0/1 polytopes such as ours, that require only polynomial steps in the number of variables, and give the proof. Thus, based on this result and using these pivot rules for our CNF-SAT solver Simplex algorithm, we find a solution in polynomial time. The complexity of CNF-SAT is NP-complete.
Theoretical Computer Science, Apr 1, 1992
Monfroglio, A., Integer programs for logic constraint satisfaction, Theoretical Computer Science ... more Monfroglio, A., Integer programs for logic constraint satisfaction, Theoretical Computer Science 97 (1992) 105-130. Logic constraint satisfaction problems are in general NP-hard and a general deterministic polynomial time algorithm is not known. Since several logic constraint problems can be reduced in polynomial time to the satisfaction of a conjunctive normal form (CNF-SAT), this case is very important. We present here a technique to transform a CNF-SAT problem in an integer optimization problem that can be solved by linear programming. The size of the obtained integer program has a polynomial growth in comparison with the original problem size.
Neurocomputing, Aug 1, 1991
ABSTRACT Logic Constraint Satisfaction problems are in general NP-hard and a general deterministi... more ABSTRACT Logic Constraint Satisfaction problems are in general NP-hard and a general deterministic polynomial time algorithm is not known. Since several Logic Constraint Problems can be reduced in polynomial time to the satisfaction of a Conjunctive Normal Form (CNF-SAT), this case is very important. We present here a technique to solve CNF-SAT by means of a class of simulated neural networks which are trained through a supervised procedure. The results of significant tests are described.
International Journal of Neural Systems, Feb 1, 1999
First a Linear Programming formulation is considered for the satisfiability problem, in particula... more First a Linear Programming formulation is considered for the satisfiability problem, in particular for the satisfaction of a Conjunctive Normal Form in the Propositional Calculus and the Simplex algorithm for solving the optimization problem. The use of Recurrent Neural Networks is then described for choosing the best pivot positions and greatly improving the algorithm performance. The result of hard cases testing is reported and shows that the technique can be useful even if it requires a huge amount of size for the constraint array and Neural Network Data Input.
Connection science, 1993
Constraint satisfaction problems (CSPs) play a central role in the real world and in computer sci... more Constraint satisfaction problems (CSPs) play a central role in the real world and in computer science. CSPs are in general NP-hard and a general deterministic polynomial time algorithm is not known. CSPs with finite domains for the variables (finite constraint satisfaction problems) are considered. They (and all NP-complete problems) can be reduced in polynomial time to the satisfaction of a
Neurocomputing, May 1, 1995
ABSTRACT Linear programming (LP) has sparked great interest among scientists due to its practical... more ABSTRACT Linear programming (LP) has sparked great interest among scientists due to its practical and theoretical importance.LP plays a special role in optimization theory: in one sense, it is a continuous optimization problem (first optimization problem) because the decision variables are real numbers, but it also may be considered a combinatorial optimization problem to identify an optimal basis containing certain columns from the constraint matrix (second optimization problem).As a case study, we describe a novel transformation from clausal form Conjunctive Normal Form Satisfaction problem (CNF-SAT) to an integer linear programming model. The resulting matrix has a regular structure and is no longer problem-specific. It depends just on the number of clauses and the number of variables, but not on the structure of the clauses.The structure of the integer program allows to solve it by means of standard linear programming techniques.Then we describe several connectionist network paradigms to solve the second optimization problem. Some of these networks are effective in solving this problem as shown in significant tests.The connectionist approach is compared with a standard Linear Programming (LP) procedure, and with a more recent hybrid LP technique.A performance summary and final comments show the usefulness of the neural network proposal.
SIGART newsletter, Jul 1, 1995
The chapter on knowledge acquisition (KA) techniques provides a succint definition of the term KA... more The chapter on knowledge acquisition (KA) techniques provides a succint definition of the term KA followed by a discussion of pitfalls to be avoided. The chapter ends with a brief descriptions of the most familiar techniques such as interviews and observations, accompanied by a list of the pros and cons of each. The chapter dealing with knowledge representation and problem solving draws the necessary connections between the model design and known AI techniques. While these chapters function effectively as ready reference, inexperienced readers may have to consult other sources [4] in order to obtain all the information they need to apply these techniques.
Computers & Operations Research, Jun 1, 1998
ABSTRACT Minimal Set Covering (MSC) is a known NP-hard problem. It is the model of many important... more ABSTRACT Minimal Set Covering (MSC) is a known NP-hard problem. It is the model of many important real-world problems and plays a central role in rostering (crew scheduling) problems. Large-size set covering problems (constraint matrix of about 10,000 * 100,000 elements) are considered. First, the traditional model of MSC as integer program is recalled, then a new representation in Linear Programming (LP) is described. Finally, a new algorithm based on recurrent neural networks is introduced for the optimization of the pivot positions selection. This algorithm is combined with the LP algorithm to guarantee an optimal solution. The heuristic part serves for choosing the pivot positions in the Simplex algorithm for LP. The results of significant tests on real data are reported. They compare favourably with the best-known results on set covering, both in terms of execution time and solution accuracy.
SIGART newsletter, Jul 1, 1987
system. It is possible to set up an environment of tasks of varying difficulty, some of simple di... more system. It is possible to set up an environment of tasks of varying difficulty, some of simple discrimination, others more complex, and select by (automated) competitive breeding the best system parameter values for particular tasks. This will be possible on a 500K machine. The results would then help form a rigorous analysis of the system.
Journal of Parallel and Distributed Computing, 1994
ABSTRACT Constraint Satisfaction Problems (CSPs) play a crucial role in Artificial Intelligence a... more ABSTRACT Constraint Satisfaction Problems (CSPs) play a crucial role in Artificial Intelligence and in the real world. CSPs are in general NP-hard, and a general deterministic polynomial time algorithm is not known. CSPs can be reduced in polynomial time to the Satisfaction of a Conjunctive Normal Form (CNF-SAT). We present here techniques for solving CNF-SAT by means of several different simulated neural networks. The results of significant tests are described.
European Journal of Operational Research, Feb 1, 1997
ABSTRACT A novel representation is described that models some important NP-hard problems, such as... more ABSTRACT A novel representation is described that models some important NP-hard problems, such as the propositional satisfiability problem (SAT), the Traveling Salesperson Problem (TSP), the Quadratic Assignment Problem (QAP), and the Minimal Set Covering Problem (MSCP) by means of only two types of constraints: ‘choice constraints’ and ‘exclusion constraints’. In its main section the paper presents an approach for solving an m-CNF-SAT problem (Conjunctive Normal Form Satisfaction: n variables, p clauses, clause length m) by integer programming. The approach is unconventional, because 2n distinct 0–1 variables are used for each clause of the m-CNF-SAT problem. The constraint matrix A forces that for every clause exactly one 0–1 variable is set equal to 1 (choice constraint), and no two 0–1 variables, representing a literal and its complement, are both set equal to 1 (exclusion constraints). The particular m-CNF-SAT instance is coded in a cost vector, which serves for maximization of the number of satisfied clauses. The paper presents a modification of the Simplex for solving the obtained integer program. A main theorem of the paper is that this algorithm always finds a 0–1 integer solution. A solution of the integer program corresponds to a solution of the m-CNF-SAT and vice versa. The results of significant experimental tests are reported, and the procedure is compared to other approaches. The same modelling technique is then used for the Traveling Salesperson Problem, for the Minimal Set Covering, and for the Quadratic Assignment Problem: it is shown that a uniform approach is thus useful.
Decision Support Systems, Mar 1, 1994
Abstract A fundamental issue in the decision process and automated reasoning is how to efficientl... more Abstract A fundamental issue in the decision process and automated reasoning is how to efficiently obtain logic decisions under constraints. Logic Constraints Catisfaction problems are in general NP-hard and a general deterministic polynomial time algorithm is not known. The present paper illustrates two different approaches: the first based on Constrained Heuristic Search and the second based on Integer and Linear Programming. Both algorithms compare favourable with the best known techniques to solve decisions problems under logic constraints. Complexity of the algorithms and results of significant tests are reported.
A novel representation is described that models some important NP-hard problems, such as the prop... more A novel representation is described that models some important NP-hard problems, such as the propositional satisfiability problem (SAT), the Traveling Salesperson Problem (TSP), and the Minimal Set Covering Problem (MSCP) by means of only two types of constraints:'choiceconstraints'and 'exclusion constraints'. In its main section the paper presents an approach for solving a m-CNF-SAT problem (Conjunctive Normal Form Satisfaction: n variables, p clauses, clause length m) by integer programming. The paper presents a 0/1 Simplex for solving the obtained integer program. A main theorem of the paper is that this algorithm always finds a 0-1 integer solution. A solution of the integer program corresponds to a solution of the m-CNF-SAT and vice versa. The same modelling technique is then used for the Traveling Salesperson Problem and for the Minimal Set Covering: it is shown that a uniform approach is thus useful. Black A., J.A. De Loera, S. Kafer and Laura Sanità [Bla21] present new pivot rules for the Simplex method for LP over 0/1 polytopes such as ours, that require only polynomial steps in the number of variables, and give the proof. Thus, based on this result and using these pivot rules for our CNF-SAT solver Simplex algorithm, we find a solution in polynomial time. The complexity of CNF-SAT is NP-complete.
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Papers by Angelo Monfroglio