Cardinality Constraints Research Articles

The sum of root-leaf distance interdiction problem with cardinality constraint by upgrading edges on trees

The sum of root-leaf distance interdiction problem with cardinality constraint by upgrading edges on trees

Leveraging enhanced egret swarm optimization algorithm and artificial intelligence-driven prompt strategies for portfolio selection

In the financial field, constructing efficient investment portfolios is a focal point of research, encompassing asset selection and optimization of asset allocation. With the advancements in Large Language Models (LLMs), generative Artificial Intelligence (AI) tools have showcased capabilities never seen before. However, the black-box nature of these tools renders their outputs difficult to interpret directly, often necessitating iterative fine-tuning to align with users’ expected outcomes. This study presents a structured prompt framework specifically designed for stock selection, aiming to provide direct and interpretable stock-selecting tools for investors of various levels. By creating representative scenarios and combining them into different cases for experimentation, we can explore how the construction of prompts influences the responses generated by generative AI tools. Additionally, this paper proposes a novel algorithm that combines the Nonlinear-Activated Beetle Antennae Search strategy with the Egret Swarm Optimization Algorithm (NBESOA) to address the Mean-Variance Portfolio Selection problem with Transaction Costs and Cardinality Constraints (MVPS-TCCC), utilizing real stock market data to construct portfolios based on generative AI tools recommendations. Simulation results indicate that, compared to other algorithms, NBESOA prefers optimizing portfolio configurations to achieve the highest Sharpe Ratio with the strictest constraints, bringing the outcomes closer to the portfolio’s efficient frontier.

An adapted Black Widow Optimization Algorithm for Financial Portfolio Optimization Problem with cardinalty and budget constraints

Financial Portfolio Optimization Problem (FPOP) is a cornerstone in quantitative investing and financial engineering, focusing on optimizing assets allocation to balance risk and expected return, a concept evolving since Harry Markowitz’s 1952 Mean-Variance model. This paper introduces a novel meta-heuristic approach based on the Black Widow Algorithm for Portfolio Optimization (BWAPO) to solve the FPOP. The new method addresses three versions of the portfolio optimization problems: the unconstrained version, the equality cardinality-constrained version, and the inequality cardinality-constrained version. New features are introduced for the BWAPO to adapt better to the problem, including (1) mating attraction and (2) differential evolution mutation strategy. The proposed BWAPO is evaluated against other metaheuristic approaches used in portfolio optimization from literature, and its performance demonstrates its effectiveness through comparative studies on benchmark datasets using multiple performance metrics, particularly in the unconstrained Mean-Variance portfolio optimization version. Additionally, when encountering cardinality constraint, the proposed approach yields competitive results, especially noticeable with smaller datasets. This leads to a focused examination of the outcomes arising from equality versus inequality cardinality constraints, intending to determine which constraint type is more effective in producing portfolios with higher returns. The paper also presents a comprehensive mathematical model that integrates real-world constraints such as transaction costs, transaction lots, and a dollar-denominated budget, in addition to cardinality and bounding constraints. The model assesses both equality/inequality cardinality constraint versions of the problem, revealing that the inequality constraint tends to offer a wider range of feasible solutions with increased return potential.

Discrete level-bundle method for mean-CVaR portfolio optimization with cardinality constraint

Discrete level-bundle method for mean-CVaR portfolio optimization with cardinality constraint

Parallel fractional dominance MOEAs for feature subset selection in big data

In this paper, we solve the feature subset selection (FSS) problem with three objective functions namely, cardinality, area under receiver operating characteristic curve (AUC) and Matthews correlation coefficient (MCC) using novel multi-objective evolutionary algorithms (MOEAs). MOEAs often encounter poor convergence due to the increase in non-dominated solutions and getting entrapped in the local optima. This situation worsens when dealing with large, voluminous big and high-dimensional datasets. To address these challenges, we propose parallel, fractional dominance-based MOEAs for FSS under Spark. Further, to improve the exploitation of MOEAs, we introduce a novel batch opposition-based learning (BOP) along with a cardinality constraint on the opposite solution. Accordingly, we propose two variants, namely, BOP1 and BOP2. In BOP1, a single neighbour is randomly chosen in the opposite solution space, whereas in BOP2, a group of randomly chosen neighbours in the opposite solution space. In either case, the opposite solutions are evaluated to improve the exploitation capability of the underlying MOEAs. We observe that in terms of mean optimal objective function values and across all datasets, the proposed BOP2 variant of parallel fractional dominance-based algorithms emerges as the top performer in obtaining efficient solutions. Further, we introduce a novel metric, namely the ratio of hypervolume (HV) and inverted generated distance (IGD), HV/IGD, that combines both diversity and convergence. With respect to the mean HV/IGD computed over 20 runs and Formula 1 racing, the BOP1 variants of fractional dominance-based MOEAs outperformed other algorithms.

Cardinality Constraint Non-Uniform Sampling for Maximizing Reconstruction Accuracy of Time-Varying Signals

Cardinality Constraint Non-Uniform Sampling for Maximizing Reconstruction Accuracy of Time-Varying Signals

An accelerated deterministic algorithm for maximizing monotone submodular minus modular function with cardinality constraint

Submodular optimization not only covers some classical combinatorial optimization problems, but also has a wide range of applications in fields such as machine learning and artificial intelligence. For submodular maximization problems with constraints, some work has been done including the design of approximation algorithms, the measurement of approximation algorithms in terms of quality and efficiency, etc. In this paper, we consider the problem of maximizing a non-negative monotone submodular function minus a non-negative modular function with the cardinality constraint. This model has been applied to many scenarios, such as team formation problem, influence maximization problem, recommender systems problem, etc. We propose a threshold algorithm that achieve a (1/2−O(ε),2)-bicriteria approximation ratio and query complexity O(nlog⁡n). Our algorithm makes a small sacrifice in the approximation ratio but improves the best query complexity result of existing deterministic algorithms from O(n2) to O(nlog⁡n) in the worst case.

Robust Portfolio Mean-Variance Optimization for Capital Allocation in Stock Investment Using the Genetic Algorithm: A Systematic Literature Review

Traditional mean-variance (MV) models, considered effective in stable conditions, often prove inadequate in uncertain market scenarios. Therefore, there is a need for more robust and better portfolio optimization methods to handle the fluctuations and uncertainties in asset returns and covariances. This study aims to perform a Systematic Literature Review (SLR) on robust portfolio mean-variance (RPMV) in stock investment utilizing genetic algorithms (GAs). The SLR covered studies from 1995 to 2024, allowing a thorough analysis of the evolution and effectiveness of robust portfolio optimization methods over time. The method used to conduct the SLR followed the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines. The result of the SLR presented a novel strategy to combine robust optimization methods and a GA in order to enhance RPMV. The uncertainty parameters, cardinality constraints, optimization constraints, risk-aversion parameters, robust covariance estimators, relative and absolute robustness, and parameters adopted were unable to develop portfolios capable of maintaining performance despite market uncertainties. This led to the inclusion of GAs to solve the complex optimization problems associated with RPMV efficiently, as well as fine-tuning parameters to improve solution accuracy. In three papers, the empirical validation of the results was conducted using historical data from different global capital markets such as Hang Seng (Hong Kong), Data Analysis Expressions (DAX) 100 (Germany), the Financial Times Stock Exchange (FTSE) 100 (U.K.), S&P 100 (USA), Nikkei 225 (Japan), and the Indonesia Stock Exchange (IDX), and the results showed that the RPMV model optimized with a GA was more stable and provided higher returns compared with traditional MV models. Furthermore, the proposed method effectively mitigated market uncertainties, making it a valuable tool for investors aiming to optimize portfolios under uncertain conditions. The implications of this study relate to handling uncertainty in asset returns, dynamic portfolio parameters, and the effectiveness of GAs in solving portfolio optimization problems under uncertainty, providing near-optimal solutions with relatively lower computational time.

Runtime Analysis of Quality Diversity Algorithms

AbstractQuality diversity (QD) is a branch of evolutionary computation that gained increasing interest in recent years. The Map-Elites QD approach defines a feature space, i.e., a partition of the search space, and stores the best solution for each cell of this space. We study a simple QD algorithm in the context of pseudo-Boolean optimisation on the “number of ones” feature space, where the ith cell stores the best solution amongst those with a number of ones in $$[(i-1)k, ik-1]$$ [ ( i - 1 ) k , i k - 1 ] . Here k is a granularity parameter $$1 \le k \le n+1$$ 1 ≤ k ≤ n + 1 . We give a tight bound on the expected time until all cells are covered for arbitrary fitness functions and for all k and analyse the expected optimisation time of QD on OneMax and other problems whose structure aligns favourably with the feature space. On combinatorial problems we show that QD finds a $${(1-1/e)}$$ ( 1 - 1 / e ) -approximation when maximising any monotone sub-modular function with a single uniform cardinality constraint efficiently. Defining the feature space as the number of connected components of an edge-weighted graph, we show that QD finds a minimum spanning forest in expected polynomial time. We further consider QD’s performance on classes of transformed functions in which the feature space is not well aligned with the problem. The asymptotic performance is unaffected by transformations on easy functions like OneMax. Applying a worst-case transformation to a deceptive problem increases the expected optimisation time from $$O(n^2 \log n)$$ O ( n 2 log n ) to an exponential time. However, QD is still faster than a (1+1) EA by an exponential factor.

A Collaborative Neurodynamic Optimization Approach to Distributed Chiller Loading.

In this article, we present a collaborative neurodynamic optimization approach to distributed chiller loading in the presence of nonconvex power consumption functions and binary variables associated with cardinality constraints. We formulate a cardinality-constrained distributed optimization problem with nonconvex objective functions and discrete feasible regions, based on an augmented Lagrangian function. To overcome the difficulty caused by the nonconvexity in the formulated distributed optimization problem, we develop a collaborative neurodynamic optimization method based on multiple coupled recurrent neural networks reinitialized repeatedly using a meta-heuristic rule. We elaborate on experimental results based on two multi-chiller systems with the parameters from the chiller manufacturers to demonstrate the efficacy of the proposed approach in comparison to several baselines.

Index tracking via reparameterizable subset sampling in neural networks

Index tracking aims at replicating the benchmark index performance by constructing a tracking portfolio consisting of partial component stocks of the index. This is an NP-hard question because of the cardinality constraint which limits the number of component stocks in the tracking portfolios. This paper proposes a new method to solve this problem in an end-to-end way by using a continuous subset sampling relaxation which can provide differentiable gradients calculation in neural networks. The proposed approach is tested with the FTSE-100 index data and the S&P100 index data, and compared with widely used index tracking methods, such as the forward and backward selection and optimization solvers. According to the empirical results, our proposed approach achieves the best tracking performance for different evaluation criteria.

Should Only Popular Products Be Stocked? Warehouse Assortment Selection for E-Commerce Companies

Problem definition: This paper studies the single-warehouse assortment selection problem that aims to minimize the order fulfillment cost under the cardinality constraint. We propose two fulfillment-related cost functions corresponding to spillover fulfillment and order splitting. This problem includes the fill rate maximization problem as a special case. We show that although the objective function is submodular for a broad class of cost functions, the fill rate maximization problem with the largest order size being two is NP-hard. Methodology/results: To make the problem tractable to solve, we formulate the general warehouse assortment problem under the two types of cost functions as mixed integer linear programs (MILPs). We also provide a dynamic programming algorithm to solve the problem in polynomial time if orders are nonoverlapping. Furthermore, we propose a simple heuristic called the marginal choice indexing (MCI) policy that allows the warehouse to store the most popular products. This policy is easy to compute, and hence, it is scalable to large-size problems. Although the performance of MCI can be arbitrarily bad in some extreme scenarios, we find a general condition under which it is optimal. This condition is satisfied by many multi-purchase choice models. Managerial implications: Through extensive numerical experiments on a real-world data set from RiRiShun Logistics, we find that the MCI policy is surprisingly near optimal in all the settings we tested. Simply applying the MCI policy, the fill rate is estimated to improve by 9.18% on average compared with the current practice for the local transfer centers on the training data set. More surprisingly, the MCI policy outperforms the MILP optimal solution in 14 of 25 cases on the test data set, illustrating its robustness against demand fluctuations. History: This paper has been accepted as part of the 2021 M&SOM Data-Driven Research Challenge. Funding: This work was supported by the Singapore Ministry of Education (MoE) Tier 1 [Grant 23-0619-P0001]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/msom.2022.0428 .

An Efficient Scenario Reduction Method for Problems with Higher Moment Coherent Risk Measures

In this paper, we present an efficient scenario reduction method for optimization problems whose objective function is the higher moment coherent risk (HMCR) measures. Compared with existing approaches, our method places greater emphasis on the characteristics of optimization problems. Because the value of HMCR measures only depends on a small subset of scenarios that correspond to high cost or loss, our approach is based mostly on the concept of ineffective scenarios previously proposed in the literature, which entails identifying the scenarios whose removal from the problem results in no change of the optimal value. We test our method on a simple portfolio optimization problem with only nine risky assets and a realistic one with 50 risky assets and cardinality constraints. Results show that our scenario reduction method can yield a more accurate optimal solution and optimal value, along with a smaller reduced-scenario set. Even at the same reduction level, our method continues to outperform the existing scenario reduction methods. Interestingly, the portfolio produced by our method is also more diversified than others. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the National Natural Science Foundation of China [Grants 71720107002 and U1901223]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0375 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0375 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Robust radiotherapy planning with spatially-based uncertainty sets

Radiotherapy treatment planning is a challenging large-scale optimization problem plagued by uncertainty. Following the robust optimization methodology, we propose a novel, spatially based uncertainty set for robust modeling of radiotherapy planning, producing solutions that are immune to unexpected changes in biological conditions. Our proposed uncertainty set realistically captures biological radiosensitivity patterns that are observed using recent advances in imaging, while its parameters can be personalized for individual patients. We exploit the structure of this set to devise a compact reformulation of the robust model. We develop a row-generation scheme to solve real, large-scale instances of the robust model. This method is then extended to a relaxation-based scheme for enforcing challenging, yet clinically important, dose–volume cardinality constraints. The computational performance of our algorithms, as well as the quality and robustness of the computed treatment plans, are demonstrated on simulated and real imaging data. Based on accepted performance measures, such as minimal target dose and homogeneity, these examples demonstrate that the spatially robust model achieves almost the same performance as the nominal model in the nominal scenario, and otherwise, the spatial model outperforms both the nominal and the box-uncertainty models.

Assortment Optimization: An Annotated Reading Assortment

Which varieties or brands of a product should a retailer stock on its shelf? Carrying a large variety caters to more customers' needs, but could cannibalize the sales of high-end brands and also cause an inventory nightmare. Assortment optimization aims to formalize these tradeoffs, with the basic problem being as follows. There is a universe of brands j ∈ U , each with a market-accepted price r j . For any S ⊆ U , a function ϕ ( j, S ) indicates the probability that a representative customer from the population would purchase j when given the choice from assortment S , under the market prices. The optimization problem is to maximize the average revenue per customer, i.e. [EQUATION] (1) possibly with constraints on S due to shelf size. Assortment optimization started out by showing how to efficiently find the optimal S from the exponentially many possibilities, under well-established parametric forms for the function ϕ that are called ( discrete) choice models. Since then, the literature has developed choice models of its own that are specialized for assortment optimization. The basic problem has also been extended, and connected with topics such as online algorithms, machine learning, and mechanism design that are mainstream in the Economics and Computation community, with a vast horizon for future directions. This is an annotated reading list about assortment optimization, that aims to provide broad coverage while facing a "cardinality constraint" on the number of papers in the assortment.

An approximation algorithm for K-best enumeration of minimal connected edge dominating sets with cardinality constraints

K-best enumeration, which asks to output k-best solutions without duplication, is a helpful tool in data analysis for many fields. In such fields, graphs typically represent data. Thus subgraph enumeration has been paid much attention to such fields. However, k-best enumeration tends to be intractable since, in many cases, finding one optimum solution is NP-hard. To overcome this difficulty, we combine k-best enumeration with a concept of enumeration algorithms called approximation enumeration algorithms. As a main result, we propose a 4-approximation algorithm for minimal connected edge dominating sets which outputs k minimal solutions with cardinality at most 4⋅OPT‾, where OPT‾ is the cardinality of a minimum solution which is not outputted by the algorithm. Our proposed algorithm runs in O(nm2Δ) delay, where n, m, Δ are the number of vertices, the number of edges, and the maximum degree of an input graph.

A cost-effective seed selection model for multi-constraint influence maximization in social networks

The Influence Maximization (IM) problem aims to maximize the diffusion of information or adoption of products among users within a social network by identifying and activating a set of initial users. It is not unrealistic to have a higher activation cost for more influential users in real-life applications. However, existing works on IM focus solely on finding the most influential users as the seed set, without considering either the activation costs of individual nodes and the total budget or the size of the seed set. This oversight may lead to infeasible solutions, particularly from financial and managerial perspectives, respectively. To address these issues, we propose a more realistic and generalized formulation called Multi-Constraint Influence Maximization (MCIM) to achieve a cost-effective solution under both budgetary and cardinality constraints. The MCIM model allows for variable-length solutions, necessitating the exclusion of seed nodes from the influence spread estimation. Consequently, unlike existing IM formulations, the spread function under the MCIM model is no longer monotonic but submodular. As it has also been proven to be an NP-hard problem, we propose a Simple Additive Weighting (SAW)-assisted Differential Evolution (DE) algorithm for solving large-size real-world IM problems. Experimental results on four datasets demonstrate the effectiveness of the proposed formulation and algorithm in finding optimal and cost-effective solutions.

Supervised Feature Selection via Collaborative Neurodynamic Optimization.

As a crucial part of machine learning and pattern recognition, feature selection aims at selecting a subset of the most informative features from the set of all available features. In this article, supervised feature selection is at first formulated as a mixed-integer optimization problem with an objective function of weighted feature redundancy and relevancy subject to a cardinality constraint on the number of selected features. It is equivalently reformulated as a bound-constrained mixed-integer optimization problem by augmenting the objective function with a penalty function for realizing the cardinality constraint. With additional bilinear and linear equality constraints for realizing the integrality constraints, it is further reformulated as a bound-constrained biconvex optimization problem with two more penalty terms. Two collaborative neurodynamic optimization (CNO) approaches are proposed for solving the formulated and reformulated feature selection problems. One of the proposed CNO approaches uses a population of discrete-time recurrent neural networks (RNNs), and the other use a pair of continuous-time projection networks operating concurrently on two timescales. Experimental results on 13 benchmark datasets are elaborated to substantiate the superiority of the CNO approaches to several mainstream methods in terms of average classification accuracy with three commonly used classifiers.

Differentially private submodular maximization with a cardinality constraint over the integer lattice

Differentially private submodular maximization with a cardinality constraint over the integer lattice

A Fuzzy Portfolio Model With Cardinality Constraints Based on Differential Evolution Algorithms

Uncertain information in the securities market exhibits fuzziness. In this article, expected returns and liquidity are considered as trapezoidal fuzzy numbers. The possibility mean and mean absolute deviation of expected returns represent the returns and risks of securities assets, while the possibility mean of expected turnover represents the liquidity of securities assets. Taking into account practical constraints such as cardinality and transaction costs, this article establishes a fuzzy portfolio model with cardinality constraints and solves it using the differential evolution algorithm. Finally, using fuzzy c-means clustering algorithm, 12 stocks are selected as empirical samples to provide numerical calculation examples. At the same time, fuzzy c-means clustering algorithm is used to cluster the stock yield data and analyse the stock data comprehensively and accurately, which provides a reference for establishing an effective portfolio.