Integer Linear Programming in Computational Biology: Overview of ILP, and New Results for Traveling Salesman Problems in Biology

Gusfield, Dan

doi:10.1007/978-3-030-10837-3_15

Cited by 3 publications

(9 citation statements)

References 37 publications

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“…space or the space of feasible solutions (Gusfield, 2019;Morrison et al, 2016). The optimal solution may refer to either the value of the objective function when it is optimized, or the variable values for which the objective function reaches its optimized value, so we refer to the former as our optimal value and the later as our optimal variable values.…”

Section: Overview Of Optimizationmentioning

confidence: 99%

“…The optimal solution may refer to either the value of the objective function when it is optimized, or the variable values for which the objective function reaches its optimized value, so we refer to the former as our optimal value and the later as our optimal variable values. In an optimization problem, there is no difference between minimizing or maximizing the optimal solution, since a minimization problem can be converted to an equivalent maximization problem by maximizing the negation of the objective to be minimized (Gusfield, 2019).…”

Section: Overview Of Optimizationmentioning

confidence: 99%

“…In the case of a linear programming formulation, or an LP formulation, we add what are called linear constraints to our optimization problem, which are equations that limit the choice of variables for our objective function (Gusfield, 2019). These linear constraints can both specify the possible values of each of the variables, as well as relate the variables (Rader, 2010).…”

Section: Lp Descriptionmentioning

confidence: 99%

“…These linear constraints can both specify the possible values of each of the variables, as well as relate the variables (Rader, 2010). The LP may report three possible outcomes: if there is no feasible solution, then the LP will report that there is no solution; if there exists a set of feasible solutions, then the LP will report one optimal solution and one set of optimal variable values (even though there may exist another set of optimal variable values that optimize the objective function); and if there exists a set of feasible solutions but no bound on those solutions, then the LP reports the unboundedness of the problem (Gusfield, 2019).…”

Section: Lp Descriptionmentioning

confidence: 99%

“…One advantage of using LP is that there are solvers that can solve large instances very quickly and it is often much faster to implement than it is to find and implement a polynomial-time algorithm for a problem (Gusfield, 2019). Another benefit to using LPs is that LPs work for both minimization and maximization problems, which eliminates the need for a separate algorithm to either maximize or minimize, respectively (Gusfield, 2019). At practically no cost to the optimality of the solution, LP formulation is helpful in obtaining a solution quickly and easily.…”

Section: Lp Descriptionmentioning

confidence: 99%

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The Use of Maximum Edge Weight Clique and Markov Random Field Problem Formulation to Discover Motifs

Kravchuk¹

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Section: Overview Of Optimizationmentioning

confidence: 99%

Section: Overview Of Optimizationmentioning

confidence: 99%

Section: Lp Descriptionmentioning

confidence: 99%

Section: Lp Descriptionmentioning

confidence: 99%

Section: Lp Descriptionmentioning

confidence: 99%

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The Use of Maximum Edge Weight Clique and Markov Random Field Problem Formulation to Discover Motifs

Kravchuk¹

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Impact of genetic operators on the performance of genetic algorithm (GA) for travelling salesman problem (TSP)

Garg¹,

Kakkar²,

Gupta³

et al. 2022

AIP Conference Proceedings

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Traveling Salesman Problem solution using Magnonic Combinatorial Device

Balinskiy

Khitun

2023

Preprint

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Traveling Salesman Problem (TSP) is a decision-making problem that is essential for a number of practical applications. Today, this problem is solved on digital computers exploiting Boolean-type architecture by checking one by one a number of possible routes. In this work, we describe a special type of hardware for the TSP solution. It is a magnonic combinatorial device comprising magnetic and electric parts connected in the active ring circuit. There is a number of possible propagation routes in the magnetic mesh made of phase shifters, frequency filters, and attenuators. The phase shifters mimic cities in TSP while the distance between the cities is encoded in the signal attenuation. The set of frequency filters makes the waves on different frequencies propagate through the different routes. The principle of operation is based on the classical wave superposition. There is a number of waves coming in all possible routes in parallel accumulating different phase shifts and amplitude damping. However, only the wave(s) that accumulates the certain phase shift will be amplified by the electric part. The amplification comes first to the waves that possess the minimum propagation losses. It makes this type of device suitable for TSP solution, where waves are similar to the salesmen traveling in all possible routes at a time. We present the results of numerical modeling illustrating the TSP solutions for four and six cities. Also, we present experimental data for the TSP solution with four cities. The prototype device is built of commercially available components including magnetic phase shifters/filters, coaxial cables, splitters, attenuators, and a broadband amplifier. The device literally shows the shortest route between the four selected cities. There are three examples of finding the shortest route between the cities for three different sets of city-to-city distances. The ability to exploit classical wave superposition is the most appealing property of the demonstrated device. It allows us to check a number of possible routes in parallel without any time overhead. It provides a fundamental advantage over conventional digital computers in functional throughput. The proposed approach is scalable to TSP with a larger number of cities. The estimated functional throughput of the combinatorial device for TSP with 25 cities exceeds 1035 Ops/s∙m2 which is above the limits of the existing supercomputers combined. Physical limits and challenges are also discussed.

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Integer Linear Programming in Computational Biology: Overview of ILP, and New Results for Traveling Salesman Problems in Biology

Cited by 3 publications

References 37 publications

The Use of Maximum Edge Weight Clique and Markov Random Field Problem Formulation to Discover Motifs

The Use of Maximum Edge Weight Clique and Markov Random Field Problem Formulation to Discover Motifs

Impact of genetic operators on the performance of genetic algorithm (GA) for travelling salesman problem (TSP)

Traveling Salesman Problem solution using Magnonic Combinatorial Device

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