scholarly journals Xeggora: Exploiting Immune-to-Evidence Symmetries with Full Aggregation in Statistical Relational Models (Extended Abstract)

2020 ◽  
Author(s):  
Mohammad Mahdi Amirian ◽  
Saeed Shiry Ghidary
Keyword(s):  
Linear Programs ◽  
A Posteriori ◽  
Constraint Aggregation ◽  
Relational Models ◽  
Markov Logic ◽  
Integer Linear Programs ◽  
Query Engine ◽  
Overall Performance ◽  
Context Specific ◽  
Constraint Relaxations

We present improvements in maximum a-posteriori inference for Markov Logic, a widely used SRL formalism. Several approaches, including Cutting Plane Aggregation (CPA), perform inference through translation to Integer Linear Programs. Aggregation exploits context-specific symmetries independently of evidence and reduces the size of the program. We illustrate much more symmetries occurring in long ground clauses that are ignored by CPA and can be exploited by higher-order aggregations. We propose Full-Constraint-Aggregation, a superior algorithm to CPA which exploits the ignored symmetries via a lifted translation method and some constraint relaxations. RDBMS and heuristic techniques are involved to improve the overall performance. We introduce Xeggora as an evolutionary extension of RockIt, the query engine that uses CPA. Xeggora evaluation on real-world benchmarks shows progress in efficiency compared to RockIt especially for models with long formulas.

scholarly journals Xeggora: Exploiting Immune-to-Evidence Symmetries with Full Aggregation in Statistical Relational Models

2019 ◽  
Vol 66 ◽  
pp. 33-56
Author(s):  
Mohammad Mahdi Amirian ◽  
Saeed Shiry Ghidary
Keyword(s):  
Linear Programs ◽  
A Posteriori ◽  
Constraint Aggregation ◽  
Relational Models ◽  
Markov Logic ◽  
Integer Linear Programs ◽  
Query Engine ◽  
Overall Performance ◽  
Context Specific ◽  
Constraint Relaxations

We present improvements in maximum a-posteriori inference for Markov Logic, a widely used SRL formalism. Inferring the most probable world for Markov Logic is NP-hard in general. Several approaches, including Cutting Plane Aggregation (CPA), perform inference through translation to Integer Linear Programs. Aggregation exploits context-specific symmetries independently of evidence and reduces the size of the program. We illustrate much more symmetries occurring in long ground clauses that are ignored by CPA and can be exploited by higher-order aggregations. We propose Full-Constraint-Aggregation, a superior algorithm to CPA which exploits the ignored symmetries via a lifted translation method and some constraint relaxations. RDBMS and heuristic techniques are involved to improve the overall performance. We introduce Xeggora as an evolutionary extension of RockIt, the query engine that uses CPA. Xeggora evaluation on real-world benchmarks shows progress in efficiency compared to RockIt especially for models with long formulas.

scholarly journals Balanced Ranking with Diversity Constraints

2019 ◽  
Author(s):  
Ke Yang ◽  
Vasilis Gkatzelis ◽  
Julia Stoyanovich
Keyword(s):  
Optimization Problems ◽  
Unintended Consequence ◽  
Linear Programs ◽  
Disadvantaged Populations ◽  
Ranking Algorithms ◽  
Integer Linear Programs ◽  
Trade Offs ◽  
Overall Performance ◽  
Additional Constraints ◽  
Selection And Ranking

Many set selection and ranking algorithms have recently been enhanced with diversity constraints that aim to explicitly increase representation of historically disadvantaged populations, or to improve the over-all representativeness of the selected set. An unintended consequence of these constraints, however, is reduced in-group fairness: the selected candidates from a given group may not be the best ones, and this unfairness may not be well-balanced across groups. In this paper we study this phenomenon using datasets that comprise multiple sensitive attributes. We then introduce additional constraints, aimed at balancing the in-group fairness across groups, and formalize the induced optimization problems as integer linear programs. Using these programs, we conduct an experimental evaluation with real datasets, and quantify the feasible trade-offs between balance and overall performance in the presence of diversity constraints. 

scholarly journals Empowering the configuration-IP: new PTAS results for scheduling with setup times

2021 ◽  
Author(s):  
Klaus Jansen ◽  
Kim-Manuel Klein ◽  
Marten Maack ◽  
Malin Rau
Keyword(s):  
Approximation Scheme ◽  
Constant Factor ◽  
Setup Times ◽  
Linear Programs ◽  
Scheduling Problems ◽  
Design Of Algorithms ◽  
Packing Problems ◽  
Integer Linear Programs ◽  
One Machine ◽  
Target Locations

AbstractInteger linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms for scheduling and packing problems where a set of items has to be placed in multiple target locations. Herein, a configuration describes a possible placement on one of the target locations, and the IP is used to choose suitable configurations covering the items. We give an augmented IP formulation, which we call the module configuration IP. It can be described within the framework of n-fold integer programming and, therefore, be solved efficiently. As an application, we consider scheduling problems with setup times in which a set of jobs has to be scheduled on a set of identical machines with the objective of minimizing the makespan. For instance, we investigate the case that jobs can be split and scheduled on multiple machines. However, before a part of a job can be processed, an uninterrupted setup depending on the job has to be paid. For both of the variants that jobs can be executed in parallel or not, we obtain an efficient polynomial time approximation scheme (EPTAS) of running time $$f(1/\varepsilon )\cdot \mathrm {poly}(|I|)$$ f ( 1 / ε ) · poly ( | I | ) . Previously, only constant factor approximations of 5/3 and $$4/3 + \varepsilon $$ 4 / 3 + ε , respectively, were known. Furthermore, we present an EPTAS for a problem where classes of (non-splittable) jobs are given, and a setup has to be paid for each class of jobs being executed on one machine.

scholarly journals Distributionally robust mixed integer linear programs: Persistency models with applications

2014 ◽  
Vol 233 (3) ◽  
pp. 459-473 ◽  
Author(s):  
Xiaobo Li ◽  
Karthik Natarajan ◽  
Chung-Piaw Teo ◽  
Zhichao Zheng
Keyword(s):  
Mixed Integer ◽  
Linear Programs ◽  
Integer Linear Programs ◽  
Distributionally Robust

scholarly journals Robot Task Planning in Deterministic and Probabilistic Conditions Using Semantic Knowledge Base

2016 ◽  
Vol 7 (1) ◽  
pp. 56-77 ◽  
Author(s):  
Ahmed Abdulhadi Al-Moadhen ◽  
Michael Packianather ◽  
Rossitza Setchi ◽  
Renxi Qiu
Keyword(s):  
Domain Knowledge ◽  
Semantic Knowledge ◽  
Task Planning ◽  
Relational Models ◽  
Markov Logic ◽  
Plan Generation ◽  
Knowledge Based ◽  
Probabilistic Values ◽  
Robot Task ◽  
Semantic Knowledge Base

A new method is proposed to increase the reliability of generating symbolic plans by extending the Semantic-Knowledge Based (SKB) plan generation to take into account the amount of information and uncertainty related to existing objects, their types and properties, as well as their relationships with each other. This approach constructs plans by depending on probabilistic values which are derived from learning statistical relational models such as Markov Logic Networks (MLN). An MLN module is established for probabilistic learning and inference together with semantic information to provide a basis for plausible learning and reasoning services in support of robot task-planning. The MLN module is constructed by using an algorithm to transform the knowledge stored in SKB to types, predicates and formulas which represent the main building block for this module. Following this, the semantic domain knowledge is used to derive implicit expectations of world states and the effects of the action which is nominated for insertion into the task plan. The expectations are matched with MLN output.

An optimality cut for mixed integer linear programs

1999 ◽  
Vol 119 (3) ◽  
pp. 671-677
Author(s):  
Gilbert Laporte ◽  
Frédéric Semet
Keyword(s):  
Mixed Integer ◽  
Linear Programs ◽  
Integer Linear Programs
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