Solving Constrained Slot Placement Problems Using an Ising Machine and Its Evaluations

Kanamaru, Sho; Kawamura, Kazushi; Tanaka, Shu; Tomita, Yoshinori; Togawa, Nozomu

doi:10.1587/transinf.2019edp7254

Cited by 4 publications

(1 citation statement)

References 22 publications

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“…In most combinatorial optimization problem, as the number of combinations increases, the variable combination increases exponentially, which makes it difficult for a von Neumann architecture to find an optimal or a quasi-optimal solution in a realistic time. On the other hand, Ising machines have recently been developed which are specialized for solving combinatorial optimization problems [8], [9]. The Ising machines transform the original problem onto the Ising models or quadratic unconstrained binary optimization (QUBO) models [10], and the Ising machines search for the ground state of the Ising or QUBO models, that leads to the optimal solution of the original problem.…”

Section: B Ising Machinementioning

confidence: 99%

Trip Planning Based on subQUBO Annealing

Noguchi,

Fukada,

Bao

et al. 2023

IEEE Access

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The trip planning problem (TPP) can be formulated as a combinatorial optimization problem that searches for the best route to visit a series of landmarks and hotels. Meanwhile, Ising machines have attracted attention due to their efficiency in solving combinatorial optimization problems. The Ising machines solve the combinatorial optimization problems by transforming the problems into quadratic unconstrained binary optimization (QUBO) models. However, the possible input QUBO size of current Ising machines is quite limited. Thus, it is hard to directly embed a large-scale TPP onto the current Ising machines. In this paper, we propose a novel subQUBO annealing method based on the combined variable selection method to solve the TPP. The proposed method finds a quasi-optimal solution to a large problem by repeatedly partitioning the original QUBO model into small subQUBOs that can be embedded onto the Ising machine. Specifically, to construct a subQUBO, we select variables from the original QUBO model, which have small deviation values. Further, we select variables randomly from the original QUBO model, so as not to fall into the local optimum. We have conducted an evaluation experiment using Ising machines on TPP and confirmed that the proposed method outperforms the state-of-the-art methods in terms of POI satisfaction and POI cost.

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Section: B Ising Machinementioning

confidence: 99%

Trip Planning Based on subQUBO Annealing

Noguchi,

Fukada,

Bao

et al. 2023

IEEE Access

Self Cite

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Performance Comparison of Typical Binary-Integer Encodings in an Ising Machine

et al. 2021

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The differences in performance among binary-integer encodings in an Ising machine, which can solve combinatorial optimization problems, are investigated. Many combinatorial optimization problems can be mapped to find the lowest-energy (ground) state of an Ising model or its equivalent model, the Quadratic Unconstrained Binary Optimization (QUBO). Since the Ising model and QUBO consist of binary variables, they often express integers as binary when using Ising machines. A typical example is the combinatorial optimization problem under inequality constraints. Here, the quadratic knapsack problem is adopted as a prototypical problem with an inequality constraint. It is solved using typical binaryinteger encodings: one-hot encoding, binary encoding, and unary encoding. Unary encoding shows the best performance for large-sized problems.

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Partitioning QUBO with two-way one-hot conditions on traveling salesman problems for city distributions with multiple clusters

Yatabe

2024

Front. Comput. Sci.

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We introduce a method for solving a quadratic unconstrained binary optimization (QUBO) with the two-way one-hot constraints by dividing the QUBO into parts and solving it with an Ising machine. The one-hot constraint is a constraint condition in that only one binary variable takes the value one for a set of multiple binary variables. The two-way one-hot constraint imposes one-hot constraint conditions on every row and every column of a two-dimensional array of binary variables with equal numbers of rows and columns. For example, traveling salesman problems (TSPs) have two-way one-hot constraints. We propose two methods to solve a TSP by dividing the cities into clusters based on information in the QUBO matrix. The proposed methods decompose cities into clusters and solve TSPs for each cluster. We solve TSPs such that the cities are distributed in clusters and compare the results of the two proposed methods with the results of solving the problem without partitioning. The results show that the proposed methods are robust to the coefficient parameters in the Hamiltonian of QUBO and can obtain a solution closer to the optimal solution when solving the problem without partitioning is hard. We also discuss the application of the methods proposed in the TSPs to the quadratic assignment problems and to the problems of ordering things.

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Solving Constrained Slot Placement Problems Using an Ising Machine and Its Evaluations

Cited by 4 publications

References 22 publications

Trip Planning Based on subQUBO Annealing

Trip Planning Based on subQUBO Annealing

Performance Comparison of Typical Binary-Integer Encodings in an Ising Machine

Partitioning QUBO with two-way one-hot conditions on traveling salesman problems for city distributions with multiple clusters

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