scholarly journals Learning MAX-SAT from Contextual Examples for Combinatorial Optimisation

2020 ◽  
Vol 34 (04) ◽  
pp. 4493-4500
Author(s):  
Mohit Kumar ◽  
Samuel Kolb ◽  
Stefano Teso ◽  
Luc De Raedt
Keyword(s):  
Artificial Intelligence ◽  
Optimization Problems ◽  
Combinatorial Optimisation ◽  
Limiting Factor ◽  
Soft Constraints ◽  
Combinatorial Optimization Problems ◽  
Hard Constraints ◽  
Benchmark Instances ◽  
Hard And Soft Constraints ◽  
Max Sat

Combinatorial optimization problems are ubiquitous in artificial intelligence. Designing the underlying models, however, requires substantial expertise, which is a limiting factor in practice. The models typically consist of hard and soft constraints, or combine hard constraints with a preference function. We introduce a novel setting for learning combinatorial optimisation problems from contextual examples. These positive and negative examples show – in a particular context – whether the solutions are good enough or not. We develop our framework using the MAX-SAT formalism. We provide learnability results within the realizable and agnostic settings, as well as hassle, an implementation based on syntax-guided synthesis and showcase its promise on recovering synthetic and benchmark instances from examples.

Chapter 23. MaxSAT, Hard and Soft Constraints

2021 ◽  
Author(s):  
Chu Min Li ◽  
Felip Manyà
Keyword(s):  
Combinatorial Optimization ◽  
Lower Bounds ◽  
Branch And Bound ◽  
Data Structures ◽  
Optimization Problems ◽  
Soft Constraints ◽  
Inference Rules ◽  
Combinatorial Optimization Problems ◽  
Definition Of ◽  
Hard And Soft Constraints

MaxSAT solving is becoming a competitive generic approach for solving combinatorial optimization problems, partly due to the development of new solving techniques that have been recently incorporated into modern MaxSAT solvers, and to the challenge problems posed at the MaxSAT Evaluations. In this chapter we present the most relevant results on both approximate and exact MaxSAT solving, and survey in more detail the techniques that have proven to be useful in branch and bound MaxSAT and Weighted MaxSAT solvers. Among such techniques, we pay special attention to the definition of good quality lower bounds, powerful inference rules, clever variable selection heuristics and suitable data structures. Moreover, we discuss the advantages of dealing with hard and soft constraints in the Partial MaxSAT formalims, and present a summary of the MaxSAT Evaluations that have been organized so far as affiliated events of the International Conference on Theory and Applications of Satisfiability Testing.

scholarly journals University Course Timetabling using Bayesian based Optimization Algorithm

2018 ◽  
Vol 6 (2) ◽  
pp. 14
Author(s):  
Alinaswe Siame ◽  
Douglas Kunda
Keyword(s):  
Mathematical Optimization ◽  
Soft Constraints ◽  
Simulation Research ◽  
Timetabling Problem ◽  
University Course Timetabling ◽  
Hard Constraints ◽  
Time Simulation ◽  
Feasible Solutions ◽  
Hard And Soft Constraints ◽  
University Course

<p>The timetabling problem has traditionally been treated as a mathematical optimization, heuristic, or human-machine interactive problem. The timetabling problem comprises hard and soft constraints. Hard constraints must be satisfied in order to generate feasible solutions. Soft constraints are sometimes referred to as preferences that can be contravened if necessary. In this research, we present is as both a mathematical and a human-machine problem that requires acceptable and controlled human input, then the algorithm gives options available without conflicting the hard constraints. In short, this research allows the human agents to address the soft-constraints as the algorithm works on the hard constraints, as well as the algorithm being able to learn the soft constraints over time. Simulation research was used to investigate the timetabling problem. Our proposed model employs the use a naïve Bayesian Algorithm, to learn preferred days and timings by lecturers and use them to resolve the soft constraints.  </p>

scholarly journals Solving the Quadratic Assignment Problem using the Swallow Swarm Optimization Problem

2019 ◽  
Vol 8 (6) ◽  
pp. 3116-3120
Keyword(s):  
Assignment Problem ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Combinatorial Problems ◽  
Computational Method ◽  
Quadratic Assignment ◽  
Swarm Optimization ◽  
Natural Behavior ◽  
Combinatorial Optimization Problems ◽  
Benchmark Instances

In recent years, there is a growing interest in swarm intelligent algorithms inspired by the observation of the natural behavior of swarm to define a computational method, which may resolve the hardest combinatorial optimization problems. The Quadratic Assignment Problem is one of the well-known combinatorial problems, which simulate with the assignment problem in several domains such as the industrial domain. This paper proposes an adaptation of a recent algorithm called the swallow swarm optimization to solve the Quadratic Assignment Problem; this algorithm is characterized by a hierarchy of search who allow it to search in a totality of research space. The obtained results in solving some benchmark instances from QAPLIB are compared with those obtained from other know metaheuristics in other to evaluate the performance of the proposed adaptation.

Population Based Equilibrium in Hybrid SA/PSO for Combinatorial Optimization

2020 ◽  
Vol 12 (2) ◽  
pp. 74-86 ◽  
Author(s):  
Kenneth Brezinski ◽  
Michael Guevarra ◽  
Ken Ferens
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Parameter Tuning ◽  
Population Based ◽  
Convergence Time ◽  
Benchmark Problems ◽  
Swarm Optimization ◽  
Combinatorial Optimization Problems ◽  
Benchmark Instances

This article introduces a hybrid algorithm combining simulated annealing (SA) and particle swarm optimization (PSO) to improve the convergence time of a series of combinatorial optimization problems. The implementation carried out a dynamic determination of the equilibrium loops in SA through a simple, yet effective determination based on the recent performance of the swarm members. In particular, the authors demonstrated that strong improvements in convergence time followed from a marginal decrease in global search efficiency compared to that of SA alone, for several benchmark instances of the traveling salesperson problem (TSP). Following testing on 4 additional city list TSP problems, a 30% decrease in convergence time was achieved. All in all, the hybrid implementation minimized the reliance on parameter tuning of SA, leading to significant improvements to convergence time compared to those obtained with SA alone for the 15 benchmark problems tested.

scholarly journals Optimized Hybrid Resource Allocation in Wireless Cellular Networks with and without Channel Reassignment

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Xin Wu ◽  
Arunita Jaekel ◽  
Ataul Bari ◽  
Alioune Ngom
Keyword(s):  
Cellular Networks ◽  
Channel Assignment ◽  
Network Performance ◽  
Resonance Condition ◽  
Soft Constraints ◽  
Hard Constraints ◽  
Call Dropping ◽  
Incoming Call ◽  
Hard And Soft Constraints ◽  
Assignment Scheme

In cellular networks, it is important to determine an optimal channel assignment scheme so that the available channels, which are considered as “limited” resources in cellular networks, are used as efficiently as possible. The objective of the channel assignment scheme is to minimize thecall-blockingand thecall-droppingprobabilities. In this paper, we present two efficient integer linear programming (ILP) formulations, foroptimallyallocating a channel (from a pool of available channels) to an incoming call such that both “hard” and “soft” constraints are satisfied. Our first formulation, ILP1, does not allow channel reassignment of the existing calls, while our second formulation, ILP2, allows such reassignment. Both formulations can handle hard constraints, which includesco-siteandadjacent channelconstraints, in addition to the standardco-channelconstraints. The simplified problem (with only co-channel constraints) can be treated as a special case of our formulation. In addition to the hard constraints, we also consider soft constraints, such as, thepacking condition, resonance condition,andlimiting rearrangements, to further improve the network performance. We present the simulation results on a benchmark 49 cell environment with 70 channels that validate the performance of our approach.

scholarly journals Which Are the Effects of Hard and Soft Equality Constraints on the Iterative Outlier Elimination Procedure?

2020 ◽  
Author(s):  
Vinicius Francisco Rofatto ◽  
Marcelo Tomio Matsuoka ◽  
Ivandro Klein ◽  
Mauricio Roberto Veronez ◽  
Luiz Gonzaga Da Silveira, Jr.
Keyword(s):  
Geodetic Network ◽  
Model Parameters ◽  
Soft Constraints ◽  
Test Statistics ◽  
Elimination Procedure ◽  
Outlier Test ◽  
Hard Constraints ◽  
Absolute Correlation ◽  
Hard And Soft Constraints ◽  
Detectable Bias

In this paper we evaluate the effects of hard and soft constraints on the Iterative Data Snooping (IDS), an iterative outlier elimination procedure. Here, the measurements of a levelling geodetic network were classified according to the local redundancy and maximum absolute correlation between the outlier test statistics, referred to as clusters. We highlight that the larger the relaxation of the constraints, the higher the sensitivity indicators MDB (Minimal Detectable Bias) and MIB (Minimal Identifiable Bias) for both the clustering of measurements and the clustering of constraints. There are circumstances that increase the family-wise error rate (FWE) of the test statistics, increase the performance of the IDS. Under a scenario of soft constraints, one should set out at least three soft constraints in order to identify an outlier in the constraints. In general, hard constraints should be used in the stage of pre-processing data for the purpose of identifying and removing possible outlying measurements. In that process, one should opt to set out the redundant hard constraints. After identifying and removing possible outliers, the soft constraints should be employed to propagate their uncertainties to the model parameters during the process of least-squares estimation.

scholarly journals Effects of Hard and Soft Equality Constraints on Reliability Analysis

2020 ◽  
Author(s):  
Vinicius Francisco Rofatto ◽  
Marcelo Tomio Matsuoka ◽  
Ivandro Klein ◽  
Mauricio Roberto Veronez ◽  
Luiz Gonzaga Da Silveira, Jr.
Keyword(s):  
Reliability Analysis ◽  
Normal Operation ◽  
Model Parameters ◽  
Soft Constraints ◽  
Optical Investigation ◽  
Functional Relations ◽  
Hard Constraints ◽  
Detection And Identification ◽  
Set Up ◽  
Hard And Soft Constraints

The reliability analysis allows to estimate the system's probability of detecting and identifying outlier. Failure to identify an outlier can jeopardise the reliability level of a system. Due to its importance, outliers must be appropriately treated to ensure the normal operation of a system. The system models are usually developed from certain constraints. Constraints play a central role in model precision and validity. In this work, we present a detailed optical investigation of the effects of the hard and soft constraints on the reliability of a measurement system model. Hard constraints represent a case in which there exist known functional relations between the unknown model parameters, whereas the soft constraints are employed for the case where such functional relations can slightly be violated depending on their uncertainty. The results highlighted that the success rate of identifying an outlier for the case of hard constraints is larger than soft constraints. This suggested that hard constraints should be used in the stage of pre-processing data for the purpose of identifying and removing possible outlying measurements. After identifying and removing possible outliers, one should set up the soft constraints to propagate the uncertainties of the constraints during the data processing. This recommendation is valid for outlier detection and identification purpose.

scholarly journals Courses timetabling based on hill climbing algorithm

2020 ◽  
Vol 10 (6) ◽  
pp. 6558
Author(s):  
Abdoul Rjoub
Keyword(s):  
Optimal Solution ◽  
Initial Solution ◽  
Hill Climbing ◽  
Soft Constraints ◽  
Hill Climbing Algorithm ◽  
Hard Constraints ◽  
Side Constraints ◽  
Time Requirements ◽  
Hard And Soft Constraints ◽  
Hill Climbing Algorithms

In addition to its monotonous nature and excessive time requirements, the manual school timetable scheduling often leads to more than one class being assigned to the same instructor, or more than one instructor being assigned to the same classroom during the same slot time, or even leads to exercise in intentional partialities in favor of a particular group of instructors. In this paper, an automated school timetable scheduling is presented to help overcome the traditional conflicts inherent in the manual scheduling approach. In this approach, hill climbing algorithms have been modified to transact hard and soft constraints. Soft constraints are not easy to be satisfied typically, but hard constraints are obligated. The implementation of this technique has been successfully experimented in different schools with various kinds of side constraints. Results show that the initial solution can be improved by 72% towards the optimal solution within the first 5 seconds and by 50% from the second iteration while the optimal solution will be achieved after 15 iterations ensuring that more than 50% of scientific courses will take place in the early slots time while more than 50% of non-scientific courses will take place during the later time's slots.

scholarly journals An Intelligent Technique for Solving Timetable Problem

2021 ◽  
Vol 23 (04) ◽  
pp. 317-327
Author(s):  
Abdalla El-Dhshan ◽  
◽  
Hegazy Zaher ◽  
Naglaa Ragaa ◽  
◽  
...  
Keyword(s):  
Search Algorithm ◽  
Optimization Techniques ◽  
Separate Experiment ◽  
Soft Constraints ◽  
Intelligent Technique ◽  
Hard Constraints ◽  
Intelligent Behavior ◽  
Best Parameter ◽  
Hard And Soft Constraints ◽  
Timetable Problem

Timetabling problem is complex combinatorial resources allocation problems. There are two hard and soft constraints to be satisfied. The timetable is feasible if all hard constraints are satisfied. Besides, satisfying more of the soft constraints produces a high-quality timetable. Crow Search Algorithm (CSA) as an intelligence technique presents for solving timetable problem. CSA like all meta-heuristic optimization techniques is a nature-inspire of intelligent behavior of crows. The proposed CSA tested using the well-known benchmark of hard timetabling datasets (hdtt). Taguchi’s method used to tune the best parameter combinations for the factors and levels. The tuned parameters of CSA are applied on datasets in separate experiment. The results show that the proposed CSA is superior to generate solutions in reasonable CPU time when compared with other literature techniques.

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