scholarly journals Recent Advancements in Commercial Integer Optimization Solvers for Business Intelligence Applications

2021 ◽  
Author(s):  
Cheng Seong Khor
Keyword(s):  
Business Intelligence ◽  
Mixed Integer Linear Programming ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Neighborhood Search ◽  
Integer Optimization ◽  
Computational Performance ◽  
Solution Methods ◽  
Future Work ◽  
Optimization Solvers

The chapter focuses on the recent advancements in commercial integer optimization solvers as exemplified by the CPLEX software package particularly but not limited to mixed-integer linear programming (MILP) models applied to business intelligence applications. We provide background on the main underlying algorithmic method of branch-and-cut, which is based on the established optimization solution methods of branch-and-bound and cutting planes. The chapter also covers heuristic-based algorithms, which include preprocessing and probing strategies as well as the more advanced methods of local or neighborhood search for polishing solutions toward enhanced use in practical settings. Emphasis is given to both theory and implementation of the methods available. Other considerations are offered on parallelization, solution pools, and tuning tools, culminating with some concluding remarks on computational performance vis-à-vis business intelligence applications with a view toward perspective for future work in this area.

scholarly journals Benchmarks for Current Linear and Mixed Integer Optimization Solvers

2015 ◽  
Vol 63 (6) ◽  
pp. 1923-1928 ◽  
Author(s):  
Josef Jablonský
Keyword(s):  
Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Large Scale ◽  
Optimization Problems ◽  
Academic Research ◽  
Mixed Integer ◽  
Important Class ◽  
Integer Optimization ◽  
Computational Performance ◽  
Optimization Solvers

Linear programming (LP) and mixed integer linear programming (MILP) problems belong among very important class of problems that find their applications in various managerial consequences. The aim of the paper is to discuss computational performance of current optimization packages for solving large scale LP and MILP optimization problems. Current market with LP and MILP solvers is quite extensive. Probably among the most powerful solvers GUROBI 6.0, IBM ILOG CPLEX 12.6.1, and XPRESS Optimizer 27.01 belong. Their attractiveness for academic research is given, except their computational performance, by their free availability for academic purposes. The solvers are tested on the set of selected problems from MIPLIB 2010 library that contains 361 test instances of different hardness (easy, hard, and not solved).

scholarly journals Optimal Pump Scheduling for Urban Drainage under Variable Flow Conditions

Resources ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 73 ◽  
Author(s):  
Oreste Fecarotta ◽  
Armando Carravetta ◽  
Maria Morani ◽  
Roberta Padulano
Keyword(s):  
Power Efficiency ◽  
Drainage System ◽  
Mixed Integer ◽  
Urban Drainage ◽  
Integer Optimization ◽  
Average Value ◽  
Computational Performance ◽  
Set Up ◽  
Mixed Integer Optimization Model ◽  
Inflow Discharge

The paper is focused on the optimal scheduling of a drainage pumping station, complying with variations in the pump rotational speed and a recurrent pattern for the inflow discharge. The paper is structured in several consecutive steps. In the first step, the experimental set-up is described and results of calibration tests on different pumping machines are presented to obtain equations linking significant variables (discharge, head, power, efficiency). Then, those equations are utilized to build a mixed-integer optimization model able to find the scheduling solution that minimizes required pumping energy. The model is solved with respect to a case study referred to a urban drainage system in Naples (Italy) and optimization results are analysed to provide insights on the algorithm computational performance and on the influence of pumping machine characteristics on the overall efficiency savings. With reference to the simulated scenarios, an average value of 32% energy can be saved with an optimized control. Its actual value depends on the hydraulic characteristics of the system.

scholarly journals Polyhedral Results and Branch-and-Cut for the Resource Loading Problem

2020 ◽  
Author(s):  
Guopeng Song ◽  
Tamás Kis ◽  
Roel Leus
Keyword(s):  
Resource Use ◽  
Capacity Planning ◽  
Mixed Integer Linear Programming ◽  
Branch And Cut ◽  
Mixed Integer ◽  
The Novel ◽  
Due Dates ◽  
Capacity Limits ◽  
Resource Loading ◽  
Loading Problem

We study the resource loading problem, which arises in tactical capacity planning. In this problem, one has to plan the intensity of execution of a set of orders to minimize a cost function that penalizes the resource use above given capacity limits and the completion of the orders after their due dates. Our main contributions include a novel mixed-integer linear-programming (MIP)‐based formulation, the investigation of the polyhedra associated with the feasible intensity assignments of individual orders, and a comparison of our branch-and-cut algorithm based on the novel formulation and the related polyhedral results with other MIP formulations. The computational results demonstrate the superiority of our approach. In our formulation and in one of the proofs, we use fundamental results of Egon Balas on disjunctive programming.

scholarly journals Learning to Solve Large-Scale Security-Constrained Unit Commitment Problems

2020 ◽  
Author(s):  
Álinson S. Xavier ◽  
Feng Qiu ◽  
Shabbir Ahmed
Keyword(s):  
Machine Learning ◽  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Large Scale ◽  
Unit Commitment ◽  
Energy Sector ◽  
Mixed Integer ◽  
Data Set ◽  
Computational Performance

Security-constrained unit commitment (SCUC) is a fundamental problem in power systems and electricity markets. In practical settings, SCUC is repeatedly solved via mixed-integer linear programming (MIP), sometimes multiple times per day, with only minor changes in input data. In this work, we propose a number of machine learning techniques to effectively extract information from previously solved instances in order to significantly improve the computational performance of MIP solvers when solving similar instances in the future. Based on statistical data, we predict redundant constraints in the formulation, good initial feasible solutions, and affine subspaces where the optimal solution is likely to lie, leading to a significant reduction in problem size. Computational results on a diverse set of realistic and large-scale instances show that using the proposed techniques, SCUC can be solved on average 4.3 times faster with optimality guarantees and 10.2 times faster without optimality guarantees, with no observed reduction in solution quality. Out-of-distribution experiments provide evidence that the method is somewhat robust against data-set shift. Summary of Contribution. The paper describes a novel computational method, based on a combination of mixed-integer linear programming (MILP) and machine learning (ML), to solve a challenging and fundamental optimization problem in the energy sector. The method advances the state-of-the-art, not only for this particular problem, but also, more generally, in solving discrete optimization problems via ML. We expect that the techniques presented can be readily used by practitioners in the energy sector and adapted, by researchers in other fields, to other challenging operations research problems that are solved routinely.

scholarly journals Strengthened Formulations and Valid Inequalities for Single Delay Management in Public Transportation

2019 ◽  
Vol 53 (5) ◽  
pp. 1271-1286
Author(s):  
Veronica Dal Sasso ◽  
Luigi De Giovanni ◽  
Martine Labbé
Keyword(s):  
Linear Programming ◽  
Public Transportation ◽  
Mixed Integer Linear Programming ◽  
Transportation Networks ◽  
Valid Inequalities ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Management Problem ◽  
Delay Management ◽  
Initial Delay

The delay management problem arises in public transportation networks, often characterized by the necessity of connections between different vehicles. The attractiveness of public transportation networks is strongly related to the reliability of connections, which can be missed when delays or other unpredictable events occur. Given a single initial delay at one node of the network, the delay management problem is to determine which vehicles have to wait for the delayed ones, with the aim of minimizing the dissatisfaction of the passengers. In this paper, we present strengthened mixed integer linear programming formulations and new families of valid inequalities. The implementation of branch-and-cut methods and tests on a benchmark of instances taken from real networks show the potential of the proposed formulations and cuts.

scholarly journals A Comparison of Algorithms for Finding an Efficient Theme Park Tour

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Elizabeth L. Bouzarth ◽  
Richard J. Forrester ◽  
Kevin R. Hutson ◽  
Rahul Isaac ◽  
James Midkiff ◽  
...  
Keyword(s):  
Mixed Integer Linear Programming ◽  
Search Algorithm ◽  
Computational Study ◽  
Branch And Cut ◽  
Time Dependent ◽  
Mixed Integer ◽  
Theme Park ◽  
Linear Programming Formulation ◽  
The Traveling Salesman Problem ◽  
Integer Linear Programming Formulation

The problem of efficiently touring a theme park so as to minimize the amount of time spent in queues is an instance of the Traveling Salesman Problem with Time-Dependent Service Times (TSP-TS). In this paper, we present a mixed-integer linear programming formulation of the TSP-TS and describe a branch-and-cut algorithm based on this model. In addition, we develop a lower bound for the TSP-TS and describe two metaheuristic approaches for obtaining good quality solutions: a genetic algorithm and a tabu search algorithm. Using test instances motivated by actual theme park data, we conduct a computational study to compare the effectiveness of our algorithms.

scholarly journals Multidepot UAV Routing Problem with Weapon Configuration and Time Window

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Tianren Zhou ◽  
Jiaming Zhang ◽  
Jianmai Shi ◽  
Zhong Liu ◽  
Jincai Huang
Keyword(s):  
Unmanned Aerial Vehicles ◽  
Mixed Integer Linear Programming ◽  
Time Window ◽  
Programming Model ◽  
Mixed Integer ◽  
Neighborhood Search ◽  
Large Neighborhood Search ◽  
Routing Problem ◽  
Routing Strategy ◽  
Increasing Trend

In recent wars, there is an increasing trend that unmanned aerial vehicles (UAVs) are utilized to conduct military attacking missions. In this paper, we investigate a novel multidepot UAV routing problem with consideration of weapon configuration in the UAV and the attacking time window of the target. A mixed-integer linear programming model is developed to jointly optimize three kinds of decisions: the weapon configuration strategy in the UAV, the routing strategy of target, and the allocation strategy of weapons to targets. An adaptive large neighborhood search (ALNS) algorithm is proposed for solving the problem, which is tested by randomly generated instances covering the small, medium, and large sizes. Experimental results confirm the effectiveness and robustness of the proposed ALNS algorithm.

scholarly journals Fast Best Subset Selection: Coordinate Descent and Local Combinatorial Optimization Algorithms

2020 ◽  
Vol 68 (5) ◽  
pp. 1517-1537 ◽  
Author(s):  
Hussein Hazimeh ◽  
Rahul Mazumder
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Algorithms ◽  
Subset Selection ◽  
Optimization Methods ◽  
Industrial Applications ◽  
Coordinate Descent ◽  
Mixed Integer ◽  
Greedy Heuristics ◽  
Integer Optimization ◽  
Optimization Solvers

In several scientific and industrial applications, it is desirable to build compact, interpretable learning models where the output depends on a small number of input features. Recent work has shown that such best-subset selection-type problems can be solved with modern mixed integer optimization solvers. Despite their promise, such solvers often come at a steep computational price when compared with open-source, efficient specialized solvers based on convex optimization and greedy heuristics. In “Fast Best-Subset Selection: Coordinate Descent and Local Combinatorial Optimization Algorithms,” Hussein Hazimeh and Rahul Mazumder push the frontiers of computation for best-subset-type problems. Their algorithms deliver near-optimal solutions for problems with up to a million features—in times comparable with the fast convex solvers. Their work suggests that principled optimization methods play a key role in devising tools central to interpretable machine learning, which can help in gaining a deeper understanding of their statistical properties.

Sign in / Sign up

Export Citation Format

Share Document