Quantum-inspired evolutionary computation offers a practical approach to complex optimization by simulating quantum principles on classical systems. This study proposes a multi-objective weighted portfolio model (MoWPM) based on trend ratio evaluation, along with a multi-objective quantum-inspired tabu search algorithm (MoQTS) for portfolio allocation. MoQTS incorporates superposition and an enhanced entanglement mechanism, which effectively improves convergence and expands the Pareto front. Experimental results indicate that the proposed method performs robustly and shows strong potential in supporting diverse financial decision-making needs.

Quantum-inspired evolutionary computation integrates quantum mechanics with classical optimization techniques, offering innovative solutions to complex real-world problems and gaining attention. Among them, portfolio optimization presents a critical issue. Enhancing real-world applicability requires further consideration of fund allocation alongside various investor risk preferences. However, traditional methods face challenges in handling high-dimensional, multi-objective optimization, particularly in maintaining solution diversity and offering interpretable results. To address this challenge, this study proposes a multi-objective weighted portfolio model (MoWPM) incorporating trend ratio-based evaluation. The multi-objective quantum-inspired tabu search (MoQTS) designs for MoWPM, leveraging superposition and enhanced entanglement mechanisms to explore the Pareto front. MoQTS enables the generation of high-quality solutions tailored to various risk levels. In-depth empirical analysis shows that MoQTS and MoWPM outperform equal-weighted approaches, demonstrating robustness across various performance indicators and through statistical validation. Experiments with classical multi-objective algorithms, supported by clear visualizations, underscore the strong potential of quantum-inspired techniques for practical financial optimization.

Portfolio strategy search is an essential topic in the financial and economic networks. Various risk preferences of investors should be considered to accommodate their investment choices, thereby introducing multi-objective portfolio optimization. This study utilizes an innovative and accurate evaluation model, the trend ratio (TR), to assess return and risk and construct a multi-objective optimization (MOO) model. Within a huge search space, computational intelligence techniques achieve high-performance computing through effective nature-inspired computing. The proposed TR-based MOO quantum-inspired model with an entanglement-enhanced local search (EL) mech-anism can search for Pareto optimal solutions (POSs) in global investment markets. The experimental results demonstrate that the TR-based EL mechanism effectively achieves a larger number of POSs and improves efficient frontiers to meet the different risk profiles of investors across global markets. A visualized Pareto front (PF) of the TR model helps a user identify a more straightforward return and risk balance evaluation, helping investors make informed decisions. The entanglement-simulated local search mechanism has been proven to improve the search for a better PF significantly. The TR-based, quantum-inspired MOO portfolio strategy search has paved the way for flexible solutions in global financial networks.

Hybrid quantum computing (QC) combines classical and quantum resources to tackle challenging optimization problems, leveraging the strengths of both within the current constraints of quantum computers, which are limited in size and power. Therefore, we explore the efficacy of a hybrid quantum annealing (QA) search algorithm in improving portfolio optimization. This study pioneers the application of the trend ratio (TR) to a quantum annealing computer, converting it into a constrained quadratic model with a flexible presentation. The TR serves as a promising indicator in portfolio evaluation, considering the great balance between expected returns and risks. Utilizing D- Wave's hybrid solver, we present a thorough analysis and discussion of the proposed model realized in the QA structure. The experimental results demonstrate that our model can discover solutions of comparable quality in a significantly shorter amount of time than an exhaustive search. When extending the search space to sizes challenging for exhaustive search, we conducted experiments comparing our approach with state-of-the-art quantum-inspired artificial intelligence (AI) algorithms. The results show that our method not only constructs higher-quality solutions but also requires the least computation time. The hybrid quantum-classical AI represents a forward-looking technology paradigm poised to revolutionize problem-solving methods.

Quantum-inspired optimization is an emerging computational intelligence technique that achieves quantum advan-tages through inspiration from the mechanisms of quantum properties. Parameter control is vital for optimization methods to address complex problems with extensive solution spaces. However, static parameters lack adaptability, leading to issues like premature convergence, becoming trapped in local optima, and failing to uncover the global optimum. Therefore, we develop a novel adaptive mechanism to dynamically adjust parameters during algorithm execution to strike a remarkable balance between exploration and exploitation. This study first proposes the knowledge-navigated quantum-inspired tabu search (KNQTS) algorithm, which acquires insights from the ongoing process to adjust the environment-sensitive parameters adaptively and non-linearly. Differences between inter-iteration solutions can signal the extent of convergence and guide bidirectional adjustments of a parameter, facilitating the handling of com-plex optimization problems. KNQTS is applied to tackle real-world application portfolio construction problems in the financial technology field. Comprehensive experiments are conducted to demonstrate the substantial potential and robustness of KNQTS in rapidly identifying better solutions with higher probabilities in shorter durations compared to the other state-of-the-art methods. Statistical tests substantiate the significant superiority of KNQTS over these comparative algorithms.

Quantum-inspired optimization (QIO) has garnered attention for attempting to retain quantum benefits on classical computers, thereby improving search efficiency in solving complex optimization problems. Portfolio optimization is one of the complicated real-world applications that concerns conflicting objectives of profit and risk simultaneously, making it a biobjective problem. This study exploits the advantage of the QIO to propose a multi-objective quantum-inspired tabu search algorithm (MoQTS) for constructing the Pareto front (PF) for portfolio optimization based on the innovative bi-objective trend ratio model. MoQTS initially employs the superposition encoding mechanism and Q-gate to search for potential areas quickly while maintaining the memory of PF information. Then, the entanglement move expands the search direction along with the current PF with more diversity. This study provides exhaustive search results to examine the completeness of optimal solutions in PF. The experimental results demonstrate that MoQTS exhibits competitive performance compared to classical methods across various metrics, including inverted generational distance (IGD), hypervolume (HV), and others. MoQTS shows significant potential in generating the PF using fewer computational resources.

Financial management is a critical and complicated issue. People tend to invest in the stock market and expect a stable uptrend portfolio to spread the investment risk effectively. As global economies affect each other, investing in global markets is the best way to address systematic risk for effective financial management. Selecting an appropriate portfolio across global markets involves a substantial solution space; thus, an efficient and effective evolutionary computation is proposed. The novel entanglement-enhanced quantum-inspired optimization technique is proposed as an efficient mechanism to search for the relationship between stocks with high-dependency solutions. The novel indicator trend ratio aims to evaluate the investor-desired portfolio with a stable uptrend under a perfect balance between return and risk. Therefore, this study is the first attempt to evaluate the major global markets in the Group of Seven (G7) countries to expand the generality of trend ratio usage. The experiments demonstrate that the proposed novel approach has better and more precise searchability than other state-of-the-art optimization. The proposed intelligent model outperforms the Sharpe ratio, benchmark strategy, and index performance regarding the trend ratio, risk, maximum drawdown, and profit factor. The results reveal that risk dispersion substantially improves investment performance. Under the evaluation of the trend ratio, the proposed system integrates G7 markets as an expansion of a prospective avenue for global asset management,

Computational intelligence (CI) has been extensively used in financial technology areas to help make smart decisions within enormous solution spaces. This study proposes a new portfolio optimization model using hybrid strategies to concurrently consider long and short investments and compose effective portfolios assessed by an emerging indicator to reach an excellent balance between return and risk. It exploits the trend ratio investment strategy to a detailed extent to evaluate the steady uptrend and downtrend portfolios and provides an in-depth discussion of the U.S. stock market. The proposed method combines long and short selling through a single fund to enhance investment efficiency. Quantum-inspired CI is adopted to construct a near-optimal portfolio efficiently and effectively, and sliding windows are applied to rebalance the portfolio and dynamically discover appropriate periods. The experiment conducts comprehensive statistical tests to show that hybrid strategies significantly improve traditional approaches. The comparison with other traditional methods shows outstanding performances in MDD, PF, RoMaD, return, and trend ratio. The proposed hybrid portfolio optimization application can be complementary, offset the volatility and increase the return, and show great potential in the financial industry.

With the growing popularity of online trading platforms, investors can consider investing in the global market without regard to their geographical location. This study analyzes the investment performance of Group of Seven (G7) members, who greatly influence the global economy and stock market. Regardless of the market in which they invest, investors seek long-term and stable gains in the stock market; therefore, investing in a risk diversification option is paramount. By constructing a portfolio, investment risk can be decreased. The relationship between return and risk is crucial. In this study, the proposed intelligent investing system with a novel trend ratio indicator aids in constructing an efficient portfolio. In a volatile stock market, the daily ups and downs are all profit opportunities; therefore, the proposed intelligent system constructs long-selling and short-selling portfolios. This study expands the investment discussion market to the G7 market and combines trading strategies into an innovative hybrid trading strategy to evaluate the G7 market's overall performance. As the trading strategies and markets under consideration are more inclusive, the proposed quantum-inspired algorithm with the entanglement technique can address the vast portfolio construction solution space. This study generalizes trend ratios in long-selling and short-selling portfolios and G7 markets. The experiment's result reveals that the hybrid strategy can increase portfolio profitability and efficiency.

Reversible circuits are the essential building blocks of quantum computers and have zero energy dissipation. However, there is no general rule on how to synthesize an effective circuit with minimal cost. Many researchers have placed a high value on the design of algorithms for reversible circuit synthesis as it is the fundamental component to implement in many paradigms, such as Shor’s algorithm. In this paper, the knowledge navigated quantum-inspired tabu search algorithm (KNQTS) is proposed to synthesize several benchmark functions. KNQTS is a quantum-inspired algorithm with the concept of getting closer to the best solution and keeping away from the worst solution, and it has a great search ability. Furthermore, the proposed algorithm uses self-adaptive, global-best guided and Quantum-Not gate mechanisms to make all procedures more efficient and avoid sticking to the local optimum. This paper also compares the KNQTS approach’s experimental results with those obtained via other metaheuristics and previous algorithms. Finally, the result shows that the proposed KNQTS method outperforms other state-of-the-art methods and achieves the same functionality at a lower cost. The solutions are optimal or near-optimal.

When investors invest in the stock market, the first decision is invested in which stock market and how to decide on the invested stock. The high return stock is accompanied by high risk. Constructing a portfolio can help to diversify the risk in the investment. This paper proposes a decision support system that can help select stocks and construct a portfolio with high return and low risk precisely in the Singapore stock market, which is one of the top performances in Asia. The proposed system uses the novel assessment indicator trend ratio to simultaneously consider the portfolio return and risk and then uses the global-best guided quantum-inspired tabu search algorithm with quantum-NOT gate (GNQTS) to search for the near-optimal solution. The decision-making system also includes 13 sliding windows to retain the freshest data and identify the suitable investment period. According to the experimental results, the system consisting of evolutionary computation can perform robust and rational decisions to efficiently construct a stable uptrend portfolio with the highest trend ratio in the Singapore stock market.

Metaheuristics are crucial for solving complex optimization problems effectively in many fields. With the recent increased interest in explainable artificial intelligence (XAI), the issue of how metaheuristics interact with XAI has attracted much attention. Most metaheuristics have stochastic search processes, and the jaguar algorithm (JA) is a unique algorithm that has exact search paths. JA shows potential abilities both in exploration and exploitation, but still faces limitations. Therefore, this study proposes a new metaheuristic based on JA and invents precision hunting behavior (PH-JA), which inherits the concept of JA and significantly strengthens its search efficiency. PH-JA improves the solution quality by adaptively detecting the current environment’s trends during movement and precisely hunting prey. Then, PH-JA makes the best of the historical information to reduce the computational cost. PH-JA is an explainable metaheuristic and has systematic operational procedures in that each movement is performed according to the present situation rather than random elements. Therefore, the path to a solution is interpretable and can return the same result with the same input. The experimental results demonstrated the superiority of PH-JA, which is better than other classical and state-of-the-art metaheuristics in terms of solution quality and evaluation costs.

Selecting the best combination of stocks with low risk and high return simultaneously is a significant challenge for investors. The Sharpe ratio is a common way to evaluate the performance of portfolios. However, the Sharp ratio has some defects such as that portfolios in uptrend will be calculated as high risk. Therefore, trend ratio on linear regression is proposed to find the portfolio that has a stable uptrend. Since the linear regression just roughly represents the portfolio trend and cannot be approached precisely, this paper proposes the quadratic regression trend to define the portfolio trend more accurately. In addition, the trend ratio on quadratic regression can signify the change of magnitude slowing down or speeding up in an uptrend or downtrend direction to help this model predict the future trend more precisely. This paper uses the adaptive quantum-inspired tabu search with not gate (ANQTS) to search the best portfolio and employs the 2-phase sliding window to consider more investment situations. The experiment results show that the proposed portfolio optimization model has better performance than the Sharp ratio and trend ratio on linear regression.

When investing in the stock market, investors first encounter the stock selection problem. Therefore, how to select a potential combination of stocks is a problem worth investigate. One commonly-used risk indicator is the Sharpe ratio. However, it defies the logic of investors because even an uptrend portfolio has a high risk. Thus, this paper proposes a strategy to improve the Sharpe ration denoted the trend ratio where the daily expected return is the slope of the trend line and the risk is the difference between the trend line and the fund standardization. Moreover, we propose doing normal trading and short selling simultaneously to increase the profit and spread the risk. We use the trend ratio to find a stable uptrend portfolio for normal trading and a stable downtrend portfolio for short selling. As there is no limitation to the amount of stocks in a portfolio, and because MPT's computation complexity grows exponentially when the number of stocks increases, we utilize the Quantum-inspired Tabu Search algorithm improved by the quantum-not-gate (GNQTS), to find an optimal portfolio in a large solution space. Besides, we use the sliding window to overcome the over-fitting problem. In addition of using the nearest time period as the training period, we use the same time period from the last year as the training period and tested it in the same period in current year, as some stocks have an economic cycle. Using the trend ratio while doing normal trading and short selling, with the GNQTS and sliding window, the experiment results show a promising result in which the risk is spread effectively and the profit is maximized.

In the stock selection problem, the Sharpe ratio is one of the commonly used indicators, but it tends to identify the portfolio with a flat trend as the best one. This paper uses the trend ratio to access the portfolio with a stable upward trend. By the portfolio trend line with initial funds, the trend ratio can simultaneously consider the daily expected return, daily risk and fairly compare with the different portfolios and different investment periods lengths. In addition to the access indicator, this paper provides diversified investments such as time deposit, buying round lots or buying odd lots. Different situation suits different investment method. Therefore, this paper applies the 2-phase investment sliding windows to avoid the overfitting problem and chooses the best investment method by multiple training using Global-best Guided Quantum-inspired Tabu Search with Not Gate (GNQTS) to find the best portfolio effectively and efficiently. Furthermore, the experimental results show that the proposed method can find the well-performing portfolio with higher return and lower risk in both the training and testing periods.

Jaguar algorithm (JA) has excellent performance in solving optimization problems. Different from traditional metaheuristic algorithms, JA has great abilities both in exploitation and exploration. Therefore, JA can find the best solution more quickly and efficiently. However, JA has some defects. JA considers only one dimension at a time, therefore it requires more evaluations. Moreover, JA does not adjust its step according to the distance of prey. To solve these problems, this study proposes the multi-dimensional jaguar algorithm (MJA) can consider multiple dimensions simultaneously and hunt all preys at the same time. MJA includes the adaptive step, which is adjusted according to the level of the solution. In this way, MJA can adapt its step in every dimension and can rush to its prey more accurately, which allows it to find the local optimal solution more efficiently than traditional JA. Furthermore, MJA uses information from multiple territories to jump diagonally to find the global optimum more accurately and efficiently. MJA, therefore, has stronger search ability than traditional JA. The self-analysis and experiments of this study show that the performance of MJA is better than traditional JA and other metaheuristic algorithms.