On modelling hard combinatorial optimisation problems as linear programs: refutations of the 'unconditional impossibility' claims

2021 ◽  
Vol 40 (2) ◽  
pp. 261
Author(s):  
Moustapha Diaby ◽  
Mark H. Karwan ◽  
Lei Sun
Keyword(s):  
Combinatorial Optimisation ◽  
Linear Programs

Sequential Optimization of an Emergency Response Vehicle’s Intra-Link Movement in a Partially Connected Vehicle Environment

2021 ◽  
pp. 036119812110179
Author(s):  
Gaby Joe Hannoun ◽  
Pamela Murray-Tuite ◽  
Kevin Heaslip ◽  
Thidapat Chantem
Keyword(s):  
Emergency Response ◽  
Lateral Position ◽  
Automated System ◽  
Sequential Optimization ◽  
Connected Vehicles ◽  
Linear Programs ◽  
Connected Vehicle ◽  
Market Penetration ◽  
Short Term ◽  
New Approach

This paper introduces a semi-automated system that facilitates emergency response vehicle (ERV) movement through a transportation link by providing instructions to downstream non-ERVs. The proposed system adapts to information from non-ERVs that are nearby and downstream of the ERV. As the ERV passes stopped non-ERVs, new non-ERVs are considered. The proposed system sequentially executes integer linear programs (ILPs) on transportation link segments with information transferred between optimizations to ensure ERV movement continuity. This paper extends a previously developed mathematical program that was limited to a single short segment. The new approach limits runtime overhead without sacrificing effectiveness and is more suitable to dynamic systems. It also accommodates partial market penetration of connected vehicles using a heuristic reservation approach, making the proposed system beneficial in the short-term future. The proposed system can also assign the ERV to a specific lateral position at the end of the link, a useful capability when next entering an intersection. Experiments were conducted to develop recommendations to reduce computation times without compromising efficiency. When compared with the current practice of moving to the nearest edge, the system reduces ERV travel time an average of 3.26 s per 0.1 mi and decreases vehicle interactions.

scholarly journals Solving Linear Programs in the Current Matrix Multiplication Time

2021 ◽  
Vol 68 (1) ◽  
pp. 1-39
Author(s):  
Michael B. Cohen ◽  
Yin Tat Lee ◽  
Zhao Song
Keyword(s):  
Matrix Multiplication ◽  
Linear Programs

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 Bi-objective design-for-control of water distribution networks with global bounds

2021 ◽  
Author(s):  
Aly-Joy Ulusoy ◽  
Filippo Pecci ◽  
Ivan Stoianov
Keyword(s):  
Water Distribution ◽  
Distribution Networks ◽  
Water Distribution Networks ◽  
Mixed Integer ◽  
Global Optimality ◽  
Linear Programs ◽  
Design For Control ◽  
Non Linear ◽  
Feasible Solutions

AbstractThis manuscript investigates the design-for-control (DfC) problem of minimizing pressure induced leakage and maximizing resilience in existing water distribution networks. The problem consists in simultaneously selecting locations for the installation of new valves and/or pipes, and optimizing valve control settings. This results in a challenging optimization problem belonging to the class of non-convex bi-objective mixed-integer non-linear programs (BOMINLP). In this manuscript, we propose and investigate a method to approximate the non-dominated set of the DfC problem with guarantees of global non-dominance. The BOMINLP is first scalarized using the method of $$\epsilon $$ ϵ -constraints. Feasible solutions with global optimality bounds are then computed for the resulting sequence of single-objective mixed-integer non-linear programs, using a tailored spatial branch-and-bound (sBB) method. In particular, we propose an equivalent reformulation of the non-linear resilience objective function to enable the computation of global optimality bounds. We show that our approach returns a set of potentially non-dominated solutions along with guarantees of their non-dominance in the form of a superset of the true non-dominated set of the BOMINLP. Finally, we evaluate the method on two case study networks and show that the tailored sBB method outperforms state-of-the-art global optimization solvers.

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