614 research outputs found
A 50-spin surface acoustic wave Ising machine
Time-multiplexed Spinwave Ising Machines (SWIMs) have unveiled a route
towards miniaturized, low-cost, and low-power solvers of combinatorial
optimization problems. While the number of supported spins is limited by the
nonlinearity of the spinwave dispersion, other collective excitations, such as
surface acoustic waves (SAWs), offer a linear dispersion. Here, we demonstrate
an all-to-all, fully FPGA reprogrammable, 50-spin surface acoustic wave-based
Ising machine (SAWIM), using a 50-mm-long Lithium Niobate SAW delay line,
off-the-shelf microwave components, and a low-cost FPGA. The SAWIM can solve
any 50-spin MAX-CUT problem, with arbitrary coupling matrices, in less than 340
s consuming only 0.62 mJ, corresponding to close to 3000 solutions per
second and a figure of merit of 1610 solutions/W/s. We compare the SAWIM
computational results with those of a 100-spin optical Coherent Ising machine
and find a higher probability of solution. Moreover, we demonstrate that there
is an optimum overall coupling strength between spins at which the probability
of the exact solution reaches 100%. The SAWIM illustrates the general merits of
solid state wave-based time-multiplexed Ising machines in the microwave domain
as versatile platforms for commercially feasible high-performance solvers of
combinatorial optimization problems
End-to-End Decision Focused Learning using Learned Solvers
Achieving fusion of deep learning with combinatorial algorithms promises transformativechanges to AI. Creating an impact in a real-world setting requires AI techniques to span a pipeline from data, to predictive models, to decisions. Aligning these components together requires careful consideration, as having these components trained separately does not account for the end goal of the model. This work surveys general frameworks for melding these components, we focus on the integration of optimization methods with machine learning architectures. We address some challenges and limitations associated with these methods and propose a novel approach to address some of the bottlenecks that arise
A Study in Three Practical Management Science Problems
This study of practical problems in Management Science (MS) describes novel mathematical models for three different decision settings. It addresses questions of: (a) what optimal route should be taken through a time-windows and topographically complex network; (b) what optimal sequencing of scheduled surgeries best coordinates flow of patients through central recovery; and (c) what prices should be charged and what stock amounts should be produced for two markets or channels to maximize profit explicitly, given various capacity and uncertainty conditions.
The first problem is in a sport analytics context, using a novel Integer Programming and big data from Whistler-Blackcomb ski resort. The second is to coordinate dozens of surgeries at London Health Sciences Centre, using a novel Constraint Programming model mapped to and parameterized with hospital data, including a tool for visualizing process and patient flow. The third problem is relevant to almost any business with a secondary market or sales channel, as it helps them identify profit optimal prices based on simple demand estimates and cost information they can easily provide for their own setting.
The studies use fundamentally different operational research techniques, in each case uniquely extended to the problem setting. The first two are combinatorial problems, neither one extremely beyond human cognitive ability, and both involving lots of uncertainty, and thus the sort of problem managers tend to dismiss as not efficient or practical to solve analytically. We show in the first study that vastly more skiers could achieve the challenge by following our route recommendation, unintuitive as are some of its elements, initially. In the second study, our scheduling model consistently outperforms currently unstructured-independent approach at the hospital. The final study is mathematical but demonstrates that by considering distinct market costs in pricing a firm can invariably earn more profit
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Simulated annealing based symbiotic organisms search optimization algorithm for traveling salesman problem
Symbiotic Organisms Search (SOS) algorithm is an effective new metaheuristic search algorithm, which has recently recorded wider application in solving complex optimization problems. SOS mimics the symbiotic relationship strategies adopted by organisms in the ecosystem for survival. This paper, presents a study on the application of SOS with Simulated Annealing (SA) to solve the well-known traveling salesman problems (TSPs). The TSP is known to be NP-hard, which consist of a set of (n − 1)!/2 feasible solutions. The intent of the proposed hybrid method is to evaluate the convergence behaviour and scalability of the symbiotic organism’s search with simulated annealing to solve both small and large-scale travelling salesman problems. The implementation of the SA based SOS (SOS-SA) algorithm was done in the MATLAB environment. To inspect the performance of the proposed hybrid optimization method, experiments on the solution convergence, average execution time, and percentage deviations of both the best and average solutions to the best known solution were conducted. Similarly, in order to obtain unbiased and comprehensive comparisons, descriptive statistics such as mean, standard deviation, minimum, maximum and range were used to describe each of the algorithms, in the analysis section. The oneway ANOVA and Kruskal-Wallis test were further used to compare the significant difference in performance between SOS-SA and the other selected state-of-the-art algorithms. The performances of SOS-SA and SOS are evaluated on different sets of TSP benchmarks obtained from TSPLIB (a library containing samples of TSP instances). The empirical analysis’ results show that the quality of the final results as well as the convergence rate of the new algorithm in some cases produced even more superior solutions than the best known TSP benchmarked results
A Decision Support System for Dynamic Integrated Project Scheduling and Equipment Operation Planning
Common practice in scheduling under limited resource availability is to first schedule activities with the assumption of unlimited resources, and then assign required resources to activities until available resources are exhausted. The process of matching a feasible resource plan with a feasible schedule is called resource allocation. Then, to avoid sharp fluctuations in the resource profile, further adjustments are applied to both schedule and resource allocation plan within the limits of feasibility constraints. This process is referred to as resource leveling in the literature. Combination of these three stages constitutes the standard approach of top-down scheduling.
In contrast, when scarce and/or expensive resource is to be scheduled, first a feasible and economical resource usage plan is established and then activities are scheduled accordingly. This practice is referred to as bottom-up scheduling in the literature. Several algorithms are developed and implemented in various commercial scheduling software packages to schedule based on either of these approaches.
However, in reality resource loaded scheduling problems are somewhere in between these two ends of the spectrum. Additionally, application of either of these conventional approaches results in just a feasible resource loaded schedule which is not necessarily the cost optimal solution. In order to find the cost optimal solution, activity scheduling and resource allocation problems should be considered jointly. In other words, these two individual problems should be formulated and solved as an integrated optimization problem.
In this research, a novel integrated optimization model is proposed for solving the resource loaded scheduling problems with concentration on construction heavy equipment being the targeted resource type. Assumptions regarding this particular type of resource along with other practical assumptions are provided for the model through inputs and constraints. The objective function is to minimize the fraction of the execution cost of resource loaded schedule which varies based on the selected solution and thus, considered to be the model's decision making criterion. This fraction of cost which hereafter is referred to as operation cost, encompasses four components namely schedule delay cost, shipping, rental and ownership costs for equipment
Strategic Network Design for Delivery by Drones under Service-based Competition
In today’s world, E-commerce is a fast growing industry and e-retailers are looking for innovative ways to deliver customer orders within short delivery times at a low cost. Currently, the use of drone technology for last-mile delivery is being developed by such companies as Amazon, FedEx, and UPS. Drones are relatively cheaper and faster than trucks but are limited in range and may be restricted in landing and takeoff. Most of the work in the Operations Research literature focusses on the operational challenges of integrating drones with truck delivery. The more strategic questions of whether it is economically feasible to use drones and the effects on distribution network design are rarely addressed. These questions are the focus of this work. We consider an e-retailer offering multiple same day services using both existing vehicles and drones, and develop a facility location problem under service-based competition where the services offered by the e-retailer not only compete with the stores (convenience, grocery, etc.), but also with each other. The competition in the market is incorporated using the Multinomial Logit (MNL) market share model. To solve the resulting nonlinear mathematical formulation we develop a novel logic-based Benders decomposition approach. We also show that the nonlinear model can be transformed into a linear mixed integer formulation. Computational experiments show that our algorithm outperforms direct solution of the linear formulation. We carry out extensive numerical testing of the model and perform sensitivity analyses over pricing, delivery time, government regulations, technological limitations, customer behavior, and market size. The results show that government regulations play a vital role in determining the future of drone delivery
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