Theorems Supporting r-flip Search for Pseudo-Boolean Optimization

Alidaee, Bahram; Kochenberger, Gary A.; Wang, Haibo

doi:10.4018/jamc.2010102605

Cited by 14 publications

(12 citation statements)

References 19 publications

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“…However, due to the complexity and practicality of QUBO, it is still necessary to provide results suitable for solving large-scale problems. In recent years, researchers have developed theoretical results to reduce the algorithmic implementation difficulty of QUBO, [11][12][13][14][15][16]. Our results in this paper also help to reduce the size and difficulty of the algorithmic implementation of these problems.…”

Section: Introductionmentioning

confidence: 78%

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An Efficient Closed-Form Formula for Evaluating r-Flip Moves in Quadratic Unconstrained Binary Optimization

Alidaee,

Wang,

Sua

2023

Algorithms

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Quadratic unconstrained binary optimization (QUBO) is a classic NP-hard problem with an enormous number of applications. Local search strategy (LSS) is one of the most fundamental algorithmic concepts and has been successfully applied to a wide range of hard combinatorial optimization problems. One LSS that has gained the attention of researchers is the r-flip (also known as r-Opt) strategy. Given a binary solution with n variables, the r-flip strategy “flips” r binary variables to obtain a new solution if the changes improve the objective function. The main purpose of this paper is to develop several results for the implementation of r-flip moves in QUBO, including a necessary and sufficient condition that when a 1-flip search reaches local optimality, the number of candidates for implementation of the r-flip moves can be reduced significantly. The results of the substantial computational experiments are reported to compare an r-flip strategy-embedded algorithm and a multiple start tabu search algorithm on a set of benchmark instances and three very-large-scale QUBO instances. The r-flip strategy implemented within the algorithm makes the algorithm very efficient, leading to very high-quality solutions within a short CPU time.

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Section: Introductionmentioning

confidence: 78%

“…The basic ingredient of almost all sophisticated heuristics is some variation of LSS. One LSS that has been used by many researchers as a stand-alone or as a basic component of more sophisticated algorithms is the r-flip (also known as r-Opt) strategy [11,[18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Closed-Form Formula for Evaluating r-Flip Moves in Quadratic Unconstrained Binary Optimization

Alidaee,

Wang,

Sua

2023

Algorithms

Self Cite

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“…The algorithm can be randomized by repeatedly restarting the procedure from randomly drawn starting points. There are more sophisticated versions of local search algorithms exploit the properties of the objective function but even a simple local search procedure can produce good results Alidaee et al (2010). Algorithm 3 describes the 1-opt local search procedure we use in our numerical experiments in Section 5.3.3.…”

Section: Randomized Local Searchmentioning

confidence: 99%

Particle Algorithms for Optimization on Binary Spaces

Schäfer

2013

ACM Trans. Model. Comput. Simul.

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We discuss a unified approach to stochastic optimization of pseudo-Boolean objective functions based on particle methods, including the cross-entropy method and simulated annealing as special cases. We point out the need for auxiliary sampling distributions, that is parametric families on binary spaces, which are able to reproduce complex dependency structures, and illustrate their usefulness in our numerical experiments. We provide numerical evidence that particle-driven optimization algorithms based on parametric families yield superior results on strongly multi-modal optimization problems while local search heuristics outperform them on easier problems.

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“…Max-Cut problem is a popular testbed for Quantum Computing platforms and algorithms due to its natural formulations. Recent developments in quantum computing, especially quantum annealing solvers, put Max-Cut in the spotlight [15][16][17][18][19][20][21][22][23][24]. Alam et al used the graph Max-Cut problem as a prototype while using the quantum approximate optimization algorithm (QAOA) where a quantum circuit and a classical optimizer operate in a closed loop solving hard combinatorial optimization problems [15].…”

Section: Introductionmentioning

confidence: 99%

“…In this research, we introduce a local search strategy based on the r-flip strategy for QUBO [24]. The dynamic adjustment of the r value in the r-flip strategy strikes a balance between computational cost and solution quality.…”

Section: Introductionmentioning

confidence: 99%

Efficient Solutions for Large-Scale Max-Cut Problems: A Hybrid Local Search Heuristic Approach and Comparative Analysis with Quantum Annealing

Wang,

Alidaee,

Sagbansua

2024

Preprint

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In this study, we address the formidable challenge of solving large-scale Max-Cut problems (MCP). We introduce a rapid computational procedure utilizing a hybrid 1-flip/r-flip local search heuristic. This innovative strategy significantly reduces the computational time required for MCP problems while consistently generating solutions of exceptional quality. The paper presents substantial computational insights, showcasing the effectiveness of our approach on very-large-scale Max-Cut instances with varying densities. Our proposed heuristic is rigorously evaluated by comparing its performance against a quantum annealing solver, leveraging a multi-start Tabu Search framework. The results underscore the potency of this unique combination as an efficient and effective solution for large-scale QUBO problems. Notably, our hybrid heuristic consistently delivers high-quality solutions within the stringent CPU time limits of 600 seconds, demonstrating its efficacy across Max-Cut instances ranging from 10,000 to 40,000 variables. This research contributes to advancing the state-of-the-art in large-scale QUBO problem-solving, offering a powerful and time-efficient approach with broad applicability.

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Theorems Supporting r-flip Search for Pseudo-Boolean Optimization

Cited by 14 publications

References 19 publications

An Efficient Closed-Form Formula for Evaluating r-Flip Moves in Quadratic Unconstrained Binary Optimization

An Efficient Closed-Form Formula for Evaluating r-Flip Moves in Quadratic Unconstrained Binary Optimization

Particle Algorithms for Optimization on Binary Spaces

Efficient Solutions for Large-Scale Max-Cut Problems: A Hybrid Local Search Heuristic Approach and Comparative Analysis with Quantum Annealing

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