Recently, there has been a great deal of research interest in solving quadratic unconstrained binary optimization (QUBO) problems. Physics-inspired optimization algorithms have been proposed to derive optimal or suboptimal solutions for QUBO. These methods are particularly attractive within the context of using specialized hardware such as quantum computers, application-specific CMOS, and other high-performance computing resources to solve optimization problems. These solvers are applied to his QUBO formulation of combinatorial optimization problems. Quantum and quantum-inspired optimization algorithms show promising performance when applied to academic benchmarks and real-world problems. However, the QUBO solver is a single-objective solver. To solve multi-objective problems more efficiently, we need to decide how to transform such multi-objective problems into single-objective problems. In this work, we compare methods of deriving scalarized weights when combining his two objectives of the cardinality-constrained mean-variance portfolio optimization problem into one. Compared to the aive approach with uniformly generated weights, we show a significant performance improvement (measured in hypervolume) using the method that iteratively fills the maximum space of the Pareto front.

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