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 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 Representative Solutions for Bi-Objective Optimisation

2020 ◽  
Vol 34 (02) ◽  
pp. 1436-1443
Author(s):  
Emir Demirovi? ◽  
Nicolas Schwind
Keyword(s):  
Polynomial Time ◽  
Pareto Front ◽  
Mixed Integer ◽  
Linear Programs ◽  
Objective Functions ◽  
Nondominated Solutions ◽  
Integer Linear Programs ◽  
Trade Offs ◽  
Continuous Problems ◽  
Discrete Problems

Bi-objective optimisation aims to optimise two generally competing objective functions. Typically, it consists in computing the set of nondominated solutions, called the Pareto front. This raises two issues: 1) time complexity, as the Pareto front in general can be infinite for continuous problems and exponentially large for discrete problems, and 2) lack of decisiveness. This paper focusses on the computation of a small, “relevant” subset of the Pareto front called the representative set, which provides meaningful trade-offs between the two objectives. We introduce a procedure which, given a pre-computed Pareto front, computes a representative set in polynomial time, and then we show how to adapt it to the case where the Pareto front is not provided. This has three important consequences for computing the representative set: 1) does not require the whole Pareto front to be provided explicitly, 2) can be done in polynomial time for bi-objective mixed-integer linear programs, and 3) only requires a polynomial number of solver calls for bi-objective problems, as opposed to the case where a higher number of objectives is involved. We implement our algorithm and empirically illustrate the efficiency on two families of benchmarks.

scholarly journals Solving Integer Linear Programs by Exploiting Variable-Constraint Interactions: A Survey

Algorithms ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 248
Author(s):  
Robert Ganian ◽  
Sebastian Ordyniak
Keyword(s):  
Linear Programming ◽  
Computer Science ◽  
Integer Linear Programming ◽  
Systematic Study ◽  
Optimization Problems ◽  
Linear Programs ◽  
Integer Linear Programs ◽  
Diverse Backgrounds ◽  
Recent Developments ◽  
Np Complete

Integer Linear Programming (ILP) is among the most successful and general paradigms for solving computationally intractable optimization problems in computer science. ILP is NP-complete, and until recently we have lacked a systematic study of the complexity of ILP through the lens of variable-constraint interactions. This changed drastically in recent years thanks to a series of results that together lay out a detailed complexity landscape for the problem centered around the structure of graphical representations of instances. The aim of this survey is to summarize these recent developments, put them into context and a unified format, and make them more approachable for experts from many diverse backgrounds.

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 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 A Shuffle-Based Artificial Bee Colony Algorithm for Solving Integer Programming and Minimax Problems

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1211
Author(s):  
Ivona Brajević
Keyword(s):  
Integer Programming ◽  
Artificial Bee Colony ◽  
Optimization Problems ◽  
Minimax Problems ◽  
Abc Algorithm ◽  
Bee Colony ◽  
Effective Performance ◽  
Complex Optimization ◽  
Overall Performance ◽  
Integer Programming Problems

The artificial bee colony (ABC) algorithm is a prominent swarm intelligence technique due to its simple structure and effective performance. However, the ABC algorithm has a slow convergence rate when it is used to solve complex optimization problems since its solution search equation is more of an exploration than exploitation operator. This paper presents an improved ABC algorithm for solving integer programming and minimax problems. The proposed approach employs a modified ABC search operator, which exploits the useful information of the current best solution in the onlooker phase with the intention of improving its exploitation tendency. Furthermore, the shuffle mutation operator is applied to the created solutions in both bee phases to help the search achieve a better balance between the global exploration and local exploitation abilities and to provide a valuable convergence speed. The experimental results, obtained by testing on seven integer programming problems and ten minimax problems, show that the overall performance of the proposed approach is superior to the ABC. Additionally, it obtains competitive results compared with other state-of-the-art algorithms.

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