Medium-sized Problems Research Articles

On Discrete Subproblems in Integer Optimal Control with Total Variation Regularization in Two Dimensions

We analyze integer linear programs that we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems with total variation regularization. We discuss NP-hardness of the discretized problems and the connection to graph-based problems. We show that the underlying polyhedron exhibits structural restrictions in its vertices with regard to which variables can attain fractional values at the same time. Based on this property, we derive cutting planes by employing a relation to shortest-path and minimum bisection problems. We propose a branching rule and a primal heuristic which improves previously found feasible points. We validate the proposed tools with a numerical benchmark in a standard integer programming solver. We observe a significant speedup for medium-sized problems. Our results give hints for scaling toward larger instances in the future. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by the Deutsche Forschungsgemeinschaft [Grant MA 10080/2-1]. 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.2024.0680 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0680 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Designing a new sustainable healthcare network considering the COVID-19 pandemic: Artificial intelligence-based solutions

The COVID-19 pandemic, which is still spreading its new mutations all around the world, is considered a healthcare challenge around the world. The best approach to forestall this pandemic is to avoid exposure to the virus. Therefore, medical protective equipment is essential for fighting this pandemic. This underlines the chief role of having a sustainable supply chain network (SCN) for producing and distributing personal protective equipment to avoid shortage and augmenting costs. The reality, however, is that the COVID-19 pandemic leads to many developments in countries and this study is another step for these purposes. This research developsa multi-period, multi-objective, multi-echelon, and multi-product medical protective equipment sustainable SCN considering the production, distribution, allocation, and inventory with “risk pooling” strategy effect with the aim of filling the existing gaps in health SCN research during the COVID-19 pandemic. By applying the risk pooling strategy, lower inventory levels or higher service levels can be achieved without increasing inventory costs. This model explores the possibility of lateral transshipments between distribution centers, as a way to increase the reliability of SCN performance. We model a new production, inventory, distribution, location, and allocation problem and consider four objectives for our suggested model (i) minimizing total SCN costs, (ii) minimizing environmental effects, (iii) minimizing social impacts, and (iv) maximizing the reliability of demand delivery. The proposedmodel simultaneously examines all three dimensions of sustainability (economic, environmental, and social) as well as the reliability of demand delivery. Considering all of these decisions and assumptions brings the studied problem closer to reality. We employ various algorithms for solving our developed model with different sizes: the improved version of the augmented ε-constraint (AUGMECON2) algorithm for small and medium-sized problems and two meta-heuristic algorithms, i.e., Multi-Objective Whale Optimization Algorithm (MOWOA) and Multi-Objective Variable Neighborhood Search (MOVNS) algorithm, for large-sized ones. The Taguchi approach is used to tune the parameters of meta-heuristic algorithms, and a comparison is performed using four evaluation metrics: Mean Ideal Distance (MID), Number of Pareto Solutions (NPS), Maximum Spread (MS), and Spread of Non-Dominance Solution (SNS). Proposed solving methods for the studied problem and making comparisons between them are another innovation of this study. A couple of numerical examples are provided to illustrate the applicability of the presented solution methods. Finally, sensitivity analysis for problem parameters is performed to validate our suggested model. Our study reveals the superiority of the MOWOA over the other algorithms.

Pricing heterogeneous products to heterogeneous customers who buy sequentially

This paper considers optimal pricing in a system with limited substitutable resources, such as certain goods or services. Prices for the different resources have to be set and then customers with heterogeneous preferences show up sequentially. Customers, of n types, select an item from the m available resources, depending on their valuations of the resources and the prices. The goal is to analyze this optimization problem, characterize a set of candidates to optimal solutions and provide methods for solving it. We prove that this problem is NP-hard to approximate within a factor O(n1-ε)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n^{1-\\varepsilon })$$\\end{document} for any fixed ε>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon >0$$\\end{document}. Another important contribution is to prove that, the space of prices (which in principle is a continuous domain in Rm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {R}}^m$$\\end{document}), can be reduced to a finite set of vectors of cardinality mm-2nm2m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m^{m-2}n^m2^m$$\\end{document}. For a deterministic version of the problem, where the customer types are known to the firm, we provide a mathematical program that chooses the best set of prices. We report extensive computational results showing the usefulness of our exact approach to solve medium size problems with up to 200 customers and different assortments of products and customer types. We then show how to approximate the stochastic model by a small number of solutions of deterministic scenarios solved using a mixed-integer linear program.

Multiple Objective Hub Locations Problem for Medical Supply Chain Optimization (Solving Sample Problems in Large Sizes with MOPSO and NSGA II Algorithms)

Today, the problem of facility location planning is mainly from the long-term and strategic operational level of large private organizations. Based on the hub location model for the green supply chain of medical and pharmaceutical equipment, it is possible to investigate the current condition of the facilities and significantly improve the demand coverage by spending acceptable costs. Therefore, after presenting the mathematical model, validation was performed in small dimensions and then sensitivity analysis was performed on the main parameters of the model. Next, Bender's analysis algorithm was used to analyze the NP-hardness of the model. Finally, by comparing the model solving time without implementing the Benders decomposition algorithm and by using it, it is clear that in high-dimensional example problems, the Benders decomposition algorithm reaches the solution in much less time than the normal case, and according to the answers, the performance can be acceptable. In addition, to show the efficiency of the model, two meta-heuristic algorithms NSGAII and MOPSO were developed. Then, based on the analysis, it can be seen that the computational time increases exponentially with the increase in the size of the sample problems, which is a reason for the NP-Hard of the problem. However, the MOPSO algorithm is better than the NSGA II algorithm in terms of computational time up to medium size problems.

Assortment and promotion optimization in a retail chain

An examination of two areas of promotion and assortment planning in an environment is attempted in this paper. Sales promotion is a marketing strategy used by retailers to increase sales and profits by retaining customers and preventing them from switching to their competitors. Various products are available on the market that can substitute each other, so the best product assortment must be determined as well. In order to model the above subject, a nonlinear integer programming problem is proposed. Model solution involves rephrasing the problem as mixed integer linear programming. Small- and medium-sized problems can therefore be solved using MIP solver software. Firefly algorithms are designed to solve large-scale problems. According to the numerical results, determining the best product assortment for stores must also be done simultaneously with finding the optimal promotion. As a matter of fact, the promotion of the products significantly affects the assortment scenarios for the stores. Consequently, the selection of the promotional discount may result in large profit losses if the assortment planning is not taken into consideration. In order to assess the importance and sensitivity of the model parameters, a sensitivity analysis is conducted. The sensitivity analysis demonstrates that the model is able to respond to changes in market demand and competition, and provides an effective tool for chain stores to optimize their promotion and assortment strategies. To further validate the effectiveness of the model, a case study is conducted in Tehran, Iran. The results of the case study demonstrate the ability of the model to effectively optimize promotion and assortment strategies in real-world settings. Overall, the proposed model provides a valuable tool for chain stores to optimize their promotion and assortment strategies, and improve their market competitiveness.

Balancing and Scheduling of Sustainable Flexible Transfer Lines

In response to sustainability imperatives, manufacturers adapt production lines for enhanced energy efficiency. This study focuses on flexible transfer lines (FTL), which are renowned for flexibility and efficiency in mass-customized production. This study addresses the pivotal challenges of balancing and scheduling FTL, aiming to optimize cycle time and total energy cost. A novel mixed-integer linear programming model and a multi-objective optimization approach utilizing the epsilon-constraint method are introduced for solving small to medium-sized problems. The findings advance sustainable practices by exploring the impact of varying energy modes on FTL sustainability, offering manufacturers insights into energy-efficient production strategies.

Batch scheduling in a multi-purpose system with machine downtime and a multi-skilled workforce

The paper presents a discrete-time mixed-integer linear programming (MILP) model for a generalised flexible job-shop scheduling problem as represented by a state-task network. The problem is characterised by reentrant flow, sequence-dependent changeover time, machine downtime, and skilled labour requirements. Two preprocessing procedures are proposed to reduce the size of the MILP model, and represent a major contribution of the research. The procedures reduce the number of assignment variables by exploiting job precedence and workforce qualifications. Machine availability for each task is determined as a function of possible start and end times, given duration, and maintenance schedule. The overall objective is to maximise the number of scheduled tasks while minimising their total finish time. Computational experiments are conducted with real and randomly generated instances. The results show that optimal solutions can be obtained for medium-size problems within a reasonable amount of time, primarily due to the use of the preprocessing procedures.

Discrete-continuous model for facility location problem with capacity-cost relation constraints

The facility location problem (FLP) involves optimally locating a set of facilities that must satisfy the demands of a group of customers distributed in a planar area. Traditionally, various FLP models have been applied to find new facilities by considering already-existing facilities, and choosing new locations among a given set of discrete candidates. These are unreasonable because a limited set of candidates may not include the optimal locations. In this study, we developed a mathematical model based on mixed-integer linear programming (MILP) for FLP. In this model, the locations of existing facilities are known and categorized as discrete. On the other hand, the locations of new facilities to be found are categorized as continuous and discrete. In addition, the optimal number of new facilities is determined by a judgment formula. The cost of facilities is also considered, including fixed opening costs and variable capacity-related costs. To make the model closer to reality, the entire area is divided into several zones with varying costs. We developed a greedy multiphase location method for the proposed MILP (MPL-MILP) that efficiently determines the exact locations of new facilities in a stepwise manner. For large-scale problems, we developed a two-variable-based dynamic iterative partial optimization (TVB-DIPO) to obtain near-optimal solutions within a given time limit. Computational experiments were conducted to test the performance of the proposed MPL-MILP and TVB-DIPO. The results indicate that MPL-MILP is suitable for small- and medium-sized problems with exact solutions, while TVB-DIPO is more suitable for large-scale problems with higher solution efficiencies.

A Huff-like location model with quality adjustment and/or closing of existing facilities

The problem of an expanding chain in a given area is considered. It may locate a new facility, vary the quality of its existing facilities, close some of them, or a combination of all these possibilities, whatever is the best to maximize its profit, given a budget for the expansion. A new competitive location and design model is proposed that allows all these possibilities. The resulting model is a difficult to solve MINLP problem. A branch-and-bound method based on interval analysis is proposed to cope with it. The method can solve medium-size problems in a reasonable amount of CPU time. An ad-hoc heuristic and a hybrid method that usually find a near-optimal solution in a fraction of time of the exact method are also proposed. Some computational studies are presented to show the performance of the algorithms.

An Estimation of Distribution Algorithm for Permutation Flow-Shop Scheduling Problem

Estimation of distribution algorithms (EDAs) is a subset of evolutionary algorithms widely used in various optimization problems, known for their favorable results. Each generation of EDAs builds a probabilistic model to represent the most promising individuals, and the next generation is created by sampling from this model. The primary challenge in designing such algorithms lies in effectively constructing the probabilistic model. The mutual exclusivity constraint imposes an additional challenge for EDAs to approach permutation-based problems. In this study, we propose a new EDA called Position-Guided Sampling Estimation of Distribution Algorithm (PGS-EDA) specifically designed for permutation-based problems. Unlike conventional approaches, our algorithm focuses on the positions rather than the elements during the sampling phase. We evaluate the performance of our algorithm on the Permutation Flow-shop Scheduling Problem (PFSP). The experiments conducted on various sizes of Taillard instances provide evidence of the effectiveness of our algorithm in addressing the PFSP, particularly for small and medium-sized problems. The comparison results with other EDAs designed to handle permutation problems demonstrate that our PSG-EDA algorithm consistently achieves the lowest Average Relative Percentage Deviation (ARPD) values in 19 out of the 30 instances of sizes 20 and 50 used in the study. These findings validate the superior performance of our algorithm in terms of minimizing the makespan criterion of the PFSP.

The power of typed affine decision structures: a case study

AbstractTADS are a novel, concise white-box representation of neural networks. In this paper, we apply TADS to the problem of neural network verification, using them to generate either proofs or concise error characterizations for desirable neural network properties. In a case study, we consider the robustness of neural networks to adversarial attacks, i.e., small changes to an input that drastically change a neural networks perception, and show that TADS can be used to provide precise diagnostics on how and where robustness errors a occur. We achieve these results by introducing Precondition Projection, a technique that yields a TADS describing network behavior precisely on a given subset of its input space, and combining it with PCA, a traditional, well-understood dimensionality reduction technique. We show that PCA is easily compatible with TADS. All analyses can be implemented in a straightforward fashion using the rich algebraic properties of TADS, demonstrating the utility of the TADS framework for neural network explainability and verification. While TADS do not yet scale as efficiently as state-of-the-art neural network verifiers, we show that, using PCA-based simplifications, they can still scale to medium-sized problems and yield concise explanations for potential errors that can be used for other purposes such as debugging a network or generating new training samples.

A two-echelon location routing problem considering sustainability and hybrid open and closed routes under uncertainty

Location-routing is an extremely important problem in supply chain management. In the location-routing problem, decisions are made about the location of facilities such as distribution centers as well as the set of vehicle routes. Today, organizations seek to reduce the transportation cost by outsourcing leading to a particular kind of transportation problems known as open routing. However, the increasing attention to environment have led to paying more attention to environmental issues and reducing the environmental impacts of logistics activities. To this end, in this paper, both open and closed routes were simultaneously addressed by developing a multi-objective mixed integer linear programming model that included three economic, environmental, and social responsibility aspects. The three objective functions of the proposed model encompass the minimization of total costs and greenhouse gas emissions, and the maximization of employment rate and economic development. Also, in this study, a different type of routing was considered in each echelon. A small-sized problem instance was solved using the Augmented Epsilon Constraint (AEC) method with the CPLEX Optimizer Solver for the validation of the proposed model. Moreover, the sensitivity analysis was performed to investigate the effect of changing main parameters on the values of the objective function. Due to the NP-Hardness of the problem, two efficient metaheuristic algorithms of Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Stochastic Fractal Search (MOSFS) were exploited to solve the medium and large size problems. The performance of the algorithms was compared on the basis of six different well-known indexes of Time, MID, RAS, Diversity, Spacing, and SNS. According to the obtained results, the performance of the MOSFS algorithm was %20, %9, %11.22, %10.03, and %19.06 higher than the performance of the NSGA-II on the basis of SNS, RAS, MID, Diversity, and Time indexes, respectively. On the other hand, the NSGA-II performance was %6.3 higher than the MOSFS performance in terms of Spacing index.

Accelerated linear algebra compiler for computationally efficient numerical models: Success and potential area of improvement.

The recent dramatic progress in machine learning is partially attributed to the availability of high-performant computers and development tools. The accelerated linear algebra (XLA) compiler is one such tool that automatically optimises array operations (mostly fusion to reduce memory operations) and compiles the optimised operations into high-performant programs specific to target computing platforms. Like machine-learning models, numerical models are often expressed in array operations, and thus their performance can be boosted by XLA. This study is the first of its kind to examine the efficiency of XLA for numerical models, and the efficiency is examined stringently by comparing its performance with that of optimal implementations. Two shared-memory computing platforms are examined-the CPU platform and the GPU platform. To obtain optimal implementations, the computing speed and its optimisation are rigorously studied by considering different workloads and the corresponding computer performance. Two simple equations are found to faithfully modell the computing speed of numerical models with very few easily-measureable parameters. Regarding operation optimisation within XLA, results show that models expressed in low-level operations (e.g., slice, concatenation, and arithmetic operations) are successfully fused while high-level operations (e.g., convolution and roll) are not. Regarding compilation within XLA, results show that for the CPU platform of certain computers and certain simple numerical models on the GPU platform, XLA achieves high efficiency (> 80%) for large problems and acceptable efficiency (10%~80%) for medium-size problems-the gap is from the overhead cost of Python. Unsatisfactory performance is found for the CPU platform of other computers (operations are compiled in a non-optimal way) and for high-dimensional complex models for the GPU platform, where each GPU thread in XLA handles 4 (single precision) or 2 (double precision) output elements-hoping to exploit the high-performant instructions that can read/write 4 or 2 floating-point numbers with one instruction. However, these instructions are rarely used in the generated code for complex models and performance is negatively affected. Therefore, flags should be added to control the compilation for these non-optimal scenarios.

A Branch-and-Bound Algorithm for the Bi-Objective Quay Crane Scheduling Problem Based on Efficiency and Energy

Motivated by the call of the International Maritime Organization to meet the emission targets of 2030, this study considers two important practical aspects of quay crane scheduling: efficiency and energy consumption. More precisely, we introduce the bi-objective quay crane scheduling problem where the objective is to minimize the vessel’s completion time and the crane’s energy consumption. This is done by formulating a bi-objective mixed-integer programming model. A branch-and-bound algorithm was developed as the exact solution approach to find the full set of Pareto-optimal solutions. We consider (i) various lower bounds for both objectives, (ii) specific upper bounds, (iii) additional branching criteria, and (iv) fathoming criteria to detect Pareto-optimal solutions. Numerical experiments on benchmark instances show that the branch-and-bound algorithm can efficiently solve small- and medium-sized problems.

Designing a sustainable bioethanol supply chain network: A combination of machine learning and meta-heuristic algorithms

Bioethanol demands have increased during the last decade due to unexpected events worldwide. It is among the renewable energy sources that are utilized to replace fossil-fuel-based energy. Designing an efficient, Sustainable Bioethanol Supply Chain Network (SBSCN) is a critical task for the government and communities to manage the bioethanol demands appropriately. The contribution of this study is threefold. First, this study project the demand using three popular machine learning methods, including Random Forest (RF), Extreme Gradient Boosting (XGBoost), and Ensemble Learning (Adaboost) methods, to find the best one to be utilized as an input to the proposed mathematical to find optimal values for strategic, planning, and tactical decision variables. Second, the unemployment rate is considered an important parameter of the model to maximize the social effects. Third, since the proposed model of this study is NP-hard, to solve the problem, the CPLEX solver is applied for small size and two meta-heuristic algorithms, including Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-Objective Invasive Weed Optimization (MOIWO) are considered for medium and large size problems to find Pareto optimal solutions. Due to the sensitivity of two meta-heuristics algorithms, the Taguchi method, such as Max Spread (MS) and Mean Ideal Distance (MID), is utilized to control the parameters of those two applied algorithms. Since North Dakota (ND) is among the states with the most potential to produce bioethanol due to its vast land area, including marginal cropland and Conservation Research Program (CRP), the proposed model has been evaluated and validated based on the ND case study. The results show that the MOIWO algorithm outperforms NSGA-II based on the proposed model and the case study of this paper. Also, this algorithm is more reliable in terms of solution quality to tackle the problem. Finally, some research directions are discussed for future studies, and managerial insights are provided. • Bioethanol consumption experienced an increasing due to unexpected worldwide event. • Utilizing machine learning approaches to estimate the bioethanol demand in N.D. • Designing sustainable bioethanol supply chain by two meta-heuristic algorithms. • Optimal locations of biorefinery, pre-processing, distribution, and demand centers. • Gradual replacement of liquid fossil fuels with bioethanol to reduce air pollutions.

Robust permutation flow shop total weighted completion time problem: Solution and application to the oil and gas industry

This work proposes exact solution approaches for the m-machine robust permutation flow shop problem, where operation processing times are uncertain and vary in a given interval. Following the concept of budgeted uncertainty, the objective is to obtain a robust scheduling that minimizes the total weighted completion time of the restricted worst-case scenario, in which only a subset of operation processing times will deviate to worst-case values. We develop several robust counterpart formulations, which can be used to derive optimal solutions for medium-sized problem instances by using a Column-and-Constraint Generation algorithm. The efficacy of the solution methods is validated through experiments on three sets of randomly-generated instances. Finally, a case study for the maintenance schedule of Brazilian oil platforms is presented.

Scheduling Large-Size Identical Parallel Machines with Single Server Using a Novel Heuristic-Guided Genetic Algorithm (DAS/GA) Approach

Parallel Machine Scheduling (PMS) is a well-known problem in modern manufacturing. It is an optimization problem aiming to schedule n jobs using m machines while fulfilling certain practical requirements, such as total tardiness. Traditional approaches, e.g., mix integer programming and Genetic Algorithm (GA), usually fail, particularly in large-size PMS problems, due to computational time and/or memory burden and the large searching space required, respectively. This work aims to overcome such challenges by proposing a heuristic-based GA (DAS/GA). Specifically, a large-scale PMS problem with n independent jobs and m identical machines with a single server is studied. Individual heuristic algorithms (DAS) and GA are used as benchmarks to verify the performance of the proposed combined DAS/GA on 18 benchmark problems established to cover small, medium, and large PMS problems concerning standard performance metrics from the literature and a new metric proposed in this work (standardized overall total tardiness). Computational experiments showed that the heuristic part (DAS-h) of the proposed algorithm significantly enhanced the performance of the GA for large-size problems. The results indicated that the proposed algorithm should only be used for large-scale PMS problems because DAS-h trapped GA in a region of local optima, limiting its capabilities in small- and mainly medium-sized problems.

Investigating a citrus fruit supply chain network considering CO2 emissions using meta-heuristic algorithms

AbstractAccording to the increasing carbon dioxide released through vehicles and the shortage of water resources, decision-makers decided to combine the environmental and economic effects in the Agri-Food Supply Chain Network (AFSCN) in developing countries. This paper focuses on the citrus fruit supply chain network. The novelty of this study is the proposal of a mathematical model for a three-echelon AFSCN considering simultaneously CO2 emissions, coefficient water, and time window. Additionally, a bi-objective mixed-integer non-linear programming is formulated for production–distribution-inventory-allocation problem. The model seeks to minimise the total cost and CO+ emission simultaneously. To solve the multi-objective model in this paper, the Augmented Epsilon-constraint method is utilised for small- and medium-sized problems. The Augmented Epsilon-constraint method is not able to solve large-scale problems due to its high computational time. This method is a well-known approach to dealing with multi-objective problems. It allows for producing a set of Pareto solutions for multi-objective problems. Multi-Objective Ant Colony Optimisation, fast Pareto genetic algorithm, non-dominated sorting genetic algorithm II, and multi-objective simulated annealing are used to solve the model. Then, a hybrid meta-heuristic algorithm called Hybrid multi-objective Ant Colony Optimisation with multi-objective Simulated Annealing (HACO-SA) is developed to solve the model. In the HACO-SA algorithm, an initial temperature and temperature reduction rate is utilised to ensure a faster convergence rate and to optimise the ability of exploitation and exploration as input data of the SA algorithm. The computational results show the superiority of the Augmented Epsilon-constraint method in small-sized problems, while HACO-SA indicates that is better than the suggested original algorithms in the medium- and large-sized problems.

A binary tree seed algorithm with selection-based local search mechanism for huge-sized optimization problems

Tree seed algorithm (TSA) is a recently proposed metaheuristic algorithm for solving continuous optimization problems. In order to use TSA in binary optimization problems, the SimLogicTSA method was developed by adding logic gates and Jaccard’s similarity measure to this algorithm by Cinar and Kiran. Although SimLogicTSA is generally successful in small, medium, and large size problems, it has not been successful in the huge-sized problems by stucking into local minima. To overcome this problem, a new local search mechanism called enhanced local search module (ELSM) is proposed and the SimLogicTSA-ELSM algorithm is suggested by implementing the ELSM mechanism to the original SimLogicTSA algorithm. The proposed ELSM mechanism consists of a swap operator and logic-based gates. To analyze the contribution of the ELSM mechanism to the algorithm, firstly, the original SimLogicTSA and SimLogicTSA-ELSM algorithms were compared on the Cap and M* problem sets. The obtained results showed that the proposed algorithm produced more successful results than the original SimLogicTSA. Then, the proposed SimLogicTSA-ELSM is compared with many state-of-art algorithms in the literature by using different performance metrics on Cap and M* problem sets. The results show that SimLogicTSA-ELSM outperforms the compared algorithms in nearly all cases. Especially, the performance of the SimLogicTSA-ELSM stands out in huge-sized problems.

A prediction model for ranking branch-and-bound procedures for the resource-constrained project scheduling problem

The branch-and-bound (B&B) procedure is one of the most widely used techniques to get optimal solutions for the resource-constrained project scheduling problem (RCPSP). Recently, various components from the literature have been assembled by Coelho and Vanhoucke (2018) into a unified search algorithm using the best performing lower bounds, branching schemes, search strategies, and dominance rules. However, due to the high computational time, this procedure is only suitable to solve small to medium-sized problems. Moreover, despite its relatively good performance, not much is known about which components perform best, and how these components should be combined into a procedure to maximize chances to solve the problem. This paper introduces a structured prediction approach to rank various combinations of components (configurations) of the integrated B&B procedure. More specifically, two regression methods are used to map project indicators to a full ranking of configurations. The objective is to provide preference information about the quality of different configurations to obtain the best possible solution. Using such models, the ranking of all configurations can be predicted, and these predictions are then used to get the best possible solution for a new project with known network and resource values. A computational experiment is conducted to verify the performance of this novel approach. Furthermore, the models are tested for 48 different configurations, and their robustness is investigated on datasets with different numbers of activities. The results show that the two models are very competitive, and both can generate significantly better results than any single-best configuration.