The Set Orienteering Problem is a generalization of the popular Orienteering Problem, where customers are grouped into mutually exclusive clusters, and the profit of each cluster is collected by visiting at least one customer in the respective cluster. For this NP-hard problem, we develop a novel heuristic algorithm rooted in the memetic search framework. This algorithm incorporates a pre-processing phase to accelerate the search, an inherit-mutate-repair crossover operator for generating high-quality offspring solutions, and a local search that integrates strategic oscillation to adaptively explore both feasible and infeasible regions of the search space. Other innovative features of our method include a fast tri-individual population, a solution-based tabu strategy based on hashing techniques, and an adaptive mutation operator. Extensive experimental results on two sets of 496 large benchmark instances demonstrate the strong competitiveness of the proposed approach in comparison to state-of-the-art heuristics documented in the literature. Specifically, for the 192 large original benchmark instances, the proposed algorithm outperforms the current best-known solutions for 27 instances, while matching all other established results. For the 304 new larger benchmark instances, the proposed algorithm improves the best-known solutions for 138 instances. Further experiments are carried out to provide deeper insights into the performance of the algorithm by analyzing its primary elements.
This paper develops a sensitivity computation framework for distributionally robust optimization (DRO) models with event-wise ambiguity set, quantifying how the worst-case loss responds to perturbations of the ambiguity-set parameters, including mean bounds, dispersion radii, and scenario probabilities. This framework covers many commonly-used loss functions and dispersion measures and therefore accommodates extensive well-studied DRO applications in the operations management community such as portfolio optimization and chance-constrained program. We first exploit the decomposable structure of the event-wise ambiguity set and derive a scenario-wise dual reformulation of the worst-case loss. We then establish the compactness of the optimal dual solution set for two common loss functions. Leveraging this dual reformulation together with the compactness of the optimal dual set, we next derive directional derivative of the worst-case loss and derive its computationally tractable formula, obtained by solving a small convex optimization subproblem. To achieve meaningful comparisons across heterogeneous parameters, we introduce scenario-wise and globally averaged normalized sensitivity indices that convert the directional derivatives into dimensionless, elasticity-like measures. Furthermore, we establish a rigorous first-order expansion of the worst-case loss under arbitrary parameter perturbations. Finally, we validate the practical efficacy of our framework through extensive numerical experiments on a redundancy allocation problem, demonstrating how the sensitivity map identifies critical ambiguity-set parameters, and how the choice of dispersion measure affects robustness to data outliers.
Robotic Mobile Fulfillment Systems (RMFS) are essential to the logistics frameworks within contemporary e-commerce warehouses. These systems involve three primary aspects of decision-making: rack-to-AGV assignment, AGV path planning, and conflict mediation for multiple AGVs. While substantial research has been dedicated to these elements in isolation, comprehensive integrated studies addressing the problem holistically are still relatively few. This study introduces a co-optimization problem for task assignment and global path planning for multiple AGVs in RMFS, effectively integrating dispatching, conflict-free routing, and scheduling of these vehicles. We formulate this problem as a mixed-integer linear programming (MILP) model, aimed at minimizing the total operational time of AGVs and the maximum picking completion time. Given that the problem is NP-hard, efficiently solving the MILP model for realistic-scale instances presents significant challenges. To address this issue, we developed a two-echelon K-Means and an enhanced conflict-based search algorithm. This approach allocates racks to AGVs using the K-Means algorithm while planning conflict-free paths for AGVs through an enhanced conflict-based search method. Furthermore, we rigorously analyze key structural properties of the problem, revealing several theoretically grounded properties embedded within the algorithm’s logic. To ensure high-quality lower bounds, we propose a relaxation model that does not involve planning paths for AGVs. Our experimental results indicate that: (i) our algorithm achieves solutions with minimal optimality gaps compared to the high-quality lower bounds developed; (ii) it outperforms existing benchmark algorithms in terms of solution quality and demonstrates superior computational efficiency; and (iii) the proposed properties significantly enhance the algorithm’s performance. In conclusion, this paper presents a robust and tailored approach to RMFS, providing valuable managerial insights to empower warehouse operators in their decision-making processes.
The concept of fairness in optimization models has opened up a wide range of practical applications, ranging from the equitable access to services in location, to team formation problems in human resources. Recently, the concept of fairness has found applications in the important area of maximizing diversity, giving rise to the Fair Max-Min Diversity (FMMD) problem which incorporates group fairness constraints. In this paper, we target this novel variant of the well-known Max-Min Diversity Problem (MMDP) that constitutes a challenge for today’s solvers.We explore two metaheuristic paradigms to develop new solution methods for the FMMD problem: Greedy Randomized Adaptive Search Procedure (GRASP) and Probabilistic Tabu Search (PTS). A computational study reveals that incorporating memory mechanisms makes PTS particularly effective in solving FMMD instances. To further enhance performance, we propose an advanced version of PTS that integrates memory-based perturbation and strategic oscillation mechanisms. Extensive computational experiments demonstrate that our advanced PTS consistently outperforms basic metaheuristics on all problems and achieves significantly superior performance relative to the exact approaches for larger problems. Additional analysis highlights the contributions of each proposed component, offering insights into the design of efficient methods for diversity optimization under fairness constraints.
This article investigates a static on-demand transportation problem in which users are picked up and dropped off at existing bus stops. Specifically, the selection of bus stops for each request, along with the bus routes, is simultaneously determined by the booking system using an optimization algorithm. We focus on service quality by lexicographically minimizing request travel time (including both walking time and time spent on the bus) and total route length. We introduce a matheuristic algorithm based on small and large neighborhood search, incorporating state-of-the-art operators and a set covering component. The algorithm is tested on a new set of instances, based on real data from New York City, which we propose as a future benchmark. On our New York City instances, this algorithm outperforms prior approaches by finding feasible solutions for all instances and reducing user ride time by more than 5%; it also performs well on related benchmark problems. Additionally, we discuss implementation details for decision-makers and practitioners.
Generalized Linear Models (GLMs) are a key tool in Explainable Machine Learning, since they provide an easy-to-understand explanation of their coefficients and the impact of the different features in predictions. However, not all accurate GLMs may be equally appealing due to presence of secondary objectives such as sparsity or other measurement costs. For this reason, several methods have been proposed in the literature to address the multiobjective problem of joint optimization of accuracy and other secondary criteria, sparsity being the most popular objective if explainability is pursued.In this work we explore how different GLMs with good accuracy can be. We consider a biobjective P-Dispersion Problem, in which P models are sought jointly maximizing an overall accuracy measure as well as a dispersion measure.Several metrics are used to measure dispersion, such as a function of the distance between their parameters or the set of features used to predict. Moreover, different scenarios for the feasible region are considered, e.g., whether the P models are to be chosen from, or added to, a list of pre-selected GLMs. All these variants are expressed as biobjective nonlinear mixed-integer optimization problems. Numerical tests are also presented, showing the effectiveness and the relevance of the proposed methodology.
The k-clustering minimum biclique completion problem (k-CMBCP) is a challenging combinatorial optimization problem with important applications in areas such as multicast network design and supply chain management. Given a bipartite graph G=(U,V,E), the k-CMBCP aims to partition U into k disjoint clusters Ui, and each cluster Vi⊆V contains all vertices in V that are adjacent to at least one vertex in Ui. For each bipartite cluster (Ui,Vi), the induced subgraph is completed into a biclique by adding edges as needed. The objective is to minimize the total number of edges added across all clusters. This study proposes a frequent pattern mining-based hybrid evolutionary algorithm (FPMHEA) to effectively address the k-CMBCP by exploiting structural information inherent in the problem graphs. The FPMHEA features a frequent pattern-based population initialization to generate high-quality and diverse initial solutions, a frequent pattern-guided crossover operator to strengthen search guidance during recombination, and an attribute-based tabu search with fast incremental evaluation for efficient local optimization. Extensive computational experiments on three widely used benchmark sets of 63 instances demonstrate that FPMHEA is highly competitive in both solution quality and computational efficiency compared with several state-of-the-art algorithms. Specifically, it improves the best-known upper bounds in literature for 44 instances and fails to match the best-known results on only 4 cases within short running times. Additional analysis further confirms the substantial contributions of the main algorithmic components to the overall performance of FPMHEA.
The set covering problem (SCP) is one of the classical combinatorial optimization problems with various applications. In recent years, many algorithms have been proposed for solving SCP, especially local search algorithms have shown outstanding performance in solving ability. In this work, we develop an efficient local search algorithm named FastSC for SCP. First, we propose an improved configuration checking strategy to prevent the search from revisiting previously explored solutions. Second, we propose an adaptive subset selection strategy that dynamically adjusts the selection mode based on instance properties. Third, we implement a perturbation mechanism to help the algorithm escape local optima and explore promising solution spaces. Four, we present a new search mode that incorporates a gap line below the best-found solution to divide the search space into two parts and guide the algorithm toward a high-quality solution by adjusting the gap line. Experimental results show that FastSC is highly competitive with existing state-of-the-art algorithms, and particularly exhibits a distinct advantage on most challenging instances.
Construction dust is a primary source of urban particulate matter pollution, posing a significant threat to public health and the urban environment. Based on the fugitive emission characteristics of construction dust, this study proposes a novel control method. Unlike existing research that relies on changing activity execution modes to reduce environmental impact, the core of this method lies in leveraging dynamic variations of meteorological conditions to mitigate construction dust pollution solely by optimizing activity execution times. Building on this, the study introduces a novel Resource-Constrained Project Scheduling Problem with Construction Dust Emission Reduction (RCPSP-CDER). By introducing a piecewise linear function to characterize the time-varying attributes of the meteorology-driven dust emission factor, a bi-objective optimization model for project duration and dust emissions is established. Two complementary solution approaches are developed: an ε-constraint Constraint Programming exact method (ε C-CP) and an NSGA-II metaheuristic. The high-rise building case study reveals that significant reductions in construction dust emissions can be achieved through scheduling optimization, even under resource constraints and with no extension to project duration or increase in cost. Sensitivity analysis reveals the impact of meteorological conditions and resource capacity on the emission reduction potential. Computational experiments on PSPLIB benchmark instances across four scales show that ε C-CP attains solution quality comparable to NSGA-II on small-scale instances and recovers the exact Pareto front on a subset of them, thereby serving as a reliable benchmark; on medium- and large-scale instances, NSGA-II consistently outperforms ε C-CP in both Pareto front quality and computational efficiency. This study provides project managers with a robust quantitative decision-making tool to achieve dust reduction targets under practical engineering constraints.
The end-to-end prediction and optimization paradigm based on Smart “Predict, then Optimize” (SPO) method provides a new approach for portfolio selection. In this paper, we study the end-to-end portfolio selection by leveraging deep learning in the SPO framework. We consider several deep learning models including two linear models, two recurrent neural network models, and two transformer-based models for financial time series forecasting, and incorporate them in the SPO loss functions in the mean–variance models. We train the end-to-end models using the Adam algorithm based on the specific structure of the SPO+ function to directly obtain the optimal portfolio weights. We compare via the real test the end-to-end paradigm with the two-stage prediction and optimization paradigm that uses the conventional Mean Squared Error (MSE) loss function, and illustrate the competitiveness of the former. Our tests also suggest that the iTransformer model appears to hold some superiority among the various deep learning models in this end-to-end portfolio selection practice.
Competitive pressure and economic growth have driven firms to diversify their production locations to access customer and raw material markets. The resulting production networks require coordinated planning across multiple factories, leading to distributed scheduling problems. In industrial production networks, processing at certain machines requires specialized and costly tools that are only available at a subset of factories, thereby inducing factory-eligibility constraints. Despite their practical relevance, such constraints have been largely overlooked in the scheduling literature over the past 15 years. We address this gap by extending the distributed permutation flowshop scheduling problem to incorporate eligibility constraints arising from tool availability, evolving dynamically through tool transfers between factories. To support on-time delivery while accounting for geographically dispersed factories, the model incorporates factory-dependent due dates and minimizes total tardiness. Accordingly, we develop three solution approaches: a novel network-flow-based mixed-integer programming model, a constraint programming formulation, and a tailored Iterated Greedy algorithm that reduces total tardiness by an average of 7.7% compared to the constraint programming approach for large instances. Computational experiments further show that tool transfers reduce total tardiness by 21.67% on average compared with static tool allocation. A sensitivity analysis confirms that tool transfers remain beneficial across varying tool redundancy levels and geographic network configurations.
The Simple Assembly Line Balancing Problem (SALBP) is a fundamental optimization challenge in the production and manufacturing domain. In this paper, we address a recently introduced variant, the Simple Assembly Line Balancing Problem with Power Peak Minimization (SALB3PM), which aims to minimize electricity consumption peaks. Despite the growing attention to this problem, existing approaches have yet to fully exploit the potential of logic-based methods. This work introduces exact solution approaches based on Satisfiability (SAT) and Maximum Satisfiability (MaxSAT) formulations to tackle SALB3PM efficiently. A experimental study was carried out on a benchmark set of 300 instances derived from the literature, considering state-of-the-art solvers across multiple paradigms, including SAT, MaxSAT, Integer Linear Programming (ILP), Constraint Programming (CP) and Pseudo-Boolean Optimization (PBO). The results clearly show that the proposed satisfiability-based methods outperform integer linear formulations. In this sense, the strategies introduced in this paper offer promising perspectives for extension to other SALBP variants.
Curriculum-Based Course Timetabling (CB-CTT) is a well-established benchmark problem in educational timetabling, with numerous real and synthetic datasets. Despite its long history of algorithmic developments, designing search methods that work effectively across diverse datasets under time limits remains challenging.In this paper, we focus on local search and, after a thorough analysis of all neighborhood structures reported in the literature, we propose an improved Simulated Annealing (SA) algorithm driven by an extended version of the classic LectureMove neighborhood, called LectureKick, that allows flexible lecture relocation while preserving feasibility. The neighborhood is further enriched with several sampling biases specifically designed to address the soft constraints of CB-CTT, while the overall behavior of the SA is regulated by a cut-off mechanism embedded in the cooling schedule.The method involves numerous parameters, both for the SA schedule and for the neighborhood biases, which are rigorously tuned on a large artificial dataset. The final algorithm is subsequently evaluated on the available benchmarks, including the “standard” ITC 2007 comp dataset, under the original competition timeout conditions.The results show that our approach clearly outperforms all previously proposed local search methods and is competitive with the best methods reported for CB-CTT overall, while improving upon them on several instances.
