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Power system operators are faced with the problem of unit commitment belonging to mixed integer programming, which becomes very complicated, as units become large-scale and highly constrained. Because unit commitment problem is a binary problem with commitment and de-commitment, a discrete/binary optimization algorithm with superior performance is required. This paper proposes a novel hybrid binary bat algorithm for unit commitment problem, which consists of two process. To begin with, the proposed binary bat algorithm is applied to determining the commitment schedule of unit commitment problem. Specifically, an improved crossover operator based on exponential-logic-modulo map is proposed to enhance the convergence and maintain the diversity of populations. To prevent the algorithm from falling into a local optimum, a local mutation strategy performs local perturbation. Chaotic map is responsible for updating some parameters to increase the performance of the proposed algorithm. Furthermore, Lambda-iteration method is adopted to solve economic load dispatch in continuous space. Constraint handling is performed using the heuristic constraint produce. The effectiveness of the proposed algorithm is verified by benchmark functions and test systems. Additionally, the simulation results are compared with other well-established heuristic and binary approaches. [ABSTRACT FROM AUTHOR]

In this paper, we study the knapsack problem with conflict pair constraints. After a thorough literature survey on the topic, our study focuses on the special case of bipartite conflict graphs. For complete bipartite (multipartite) conflict graphs, the problem is shown to be NP-hard but solvable in pseudo-polynomial time, and it admits an FPTAS. Extensions of these results to more general classes of graphs are also presented. Further, a class of integer programming models for the general knapsack problem with conflict pair constraints is presented, which generalizes and unifies the existing formulations. The strength of the LP relaxations of these formulations is analyzed, and we discuss different ways to tighten them. Experimental comparisons of these models are also presented to assess their relative strengths. This analysis disclosed various strong and weak points of different formulations of the problem and their relationships to different types of problem data. This information can be used in designing special purpose algorithms for KPCC involving a learning component. [ABSTRACT FROM AUTHOR]

Delay-sensitive task offloading in a device-to-device assisted mobile edge computing (D2D-MEC) system with energy harvesting devices is a critical challenge due to the dynamic load level at edge nodes and the variability in harvested energy. In this paper, we propose a joint dynamic task offloading and CPU frequency control scheme for delay-sensitive tasks in a D2D-MEC system, taking into account the intricacies of multi-slot tasks, characterized by diverse processing speeds and data transmission rates. Our methodology involves meticulous modeling of task arrival and service processes using queuing systems, coupled with the strategic utilization of D2D communication to alleviate edge server load and prevent network congestion effectively. Central to our solution is the formulation of average task delay optimization as a challenging nonlinear integer programming problem, requiring intelligent decision making regarding task offloading for each generated task at active mobile devices and CPU frequency adjustments at discrete time slots. To navigate the intricate landscape of the extensive discrete action space, we design an efficient multi-agent DRL learning algorithm named MAOC, which is based on MAPPO, to minimize the average task delay by dynamically determining task-offloading decisions and CPU frequencies. MAOC operates within a centralized training with decentralized execution (CTDE) framework, empowering individual mobile devices to make decisions autonomously based on their unique system states. Experimental results demonstrate its swift convergence and operational efficiency, and it outperforms other baseline algorithms. [ABSTRACT FROM AUTHOR]

The multi-objective integer programming problem often occurs in multi-criteria decision-making situations, where the decision variables are integers. In the present paper, we have discussed an algorithm for finding all efficient solutions of a multi-objective integer quadratic programming problem. The proposed algorithm is based on the aspect that efficient solutions of a multi-objective integer quadratic programming problem can be obtained by enumerating ranked solutions of an integer quadratic programming problem. For determining ranked solutions of an integer quadratic programming problem, we have constructed a related integer linear programming problem and from ranked solutions of this integer linear programming problem, ranked solutions of the original integer quadratic programming problem are generated. Theoretically, we have shown that the developed method generates the set of all efficient solutions in a finite number of steps, and numerically we have elaborated the working of our algorithm and compared our results with existing algorithms. Further, we have analyzed that the developed method is efficient for solving a multi-objective integer quadratic programming problem with a large number of constraints, variables and objectives. [ABSTRACT FROM AUTHOR]

A graph is said to be two connected if between every pair of nodes there are at least two node-disjoint paths. Given weights on the edges of the graph, the two connected subgraph problem is to find a two connected spanning subgraph of G whose weight is minimum. This problem has many applications in telecommunications. In this paper we consider a new variant of this problem with additional disjunctive constraints (called also conflict constraints) related to the survivability of telecommunication networks. This can be called the Disjunctive Two-Connected Subgraph Problem (DTCSP). First, we give an extended formulation for the problem whose variables are the cycles of the graph. Then, we use a column generation algorithm to solve its linear relaxation, and further show that the pricing reduces to finding a specific cycle in the graph which can be formulated as an integer programming problem. We also describe several valid inequalities for the polytope. Moreover, we study the related separation problems and devise separation routines for these inequalities. Using this, we devise a Branch-and-Cut-and-Price algorithm for the problem along with an extensive experimental study. [ABSTRACT FROM AUTHOR]

Multi-objective programming problem often contains numerous efficient solutions, which confuses the decision-maker. To assist in selecting the most desirable solution, optimizing a function over the efficient set becomes crucial. In this paper, we present a novel method for optimizing a general quadratic function over the efficient set of a multi-objective integer linear programming problem. To solve this problem, a ranking approach and efficiency test is utilized. The proposed methodology obtains a globally optimal solution by systematically scanning ranked solutions of an integer quadratic programming problem until the efficiency condition is satisfied. For generating ranked solutions, we construct a related integer linear programming problem. Then, ranked solutions of the integer linear programming problem are used for enumerating ranked solutions of the integer quadratic programming problem. The convergence of our algorithm is established theoretically, and its steps are illustrated using a numerical example. Aparticular case of the proposed method for optimizing a linear function over the efficient set of a multi-objective integer linear programming problem is also discussed. Further, extensive computational results demonstrate the effectiveness of our method for solving problems with large number of constraints, variables, and objective functions. Moreover, comparative analysis shows that the developed algorithm came out to be computationally more efficient as compared to the existing state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

• We have carefully proofread the whole manuscript to fix minor typos. • Each algorithm has been correctly labeled as "Algorithm" • The experimental results and their corresponding explanations have been updated. This paper addresses a new multi-commodity unpaired pickup and delivery vehicle routing problem in which each vehicle is allowed to visit each customer more than once for both pickup and delivery of each commodity. It is a complex variant of the classical capacitated vehicle routing problem and comes from resource transfer among different plants in a distributed manufacturing environment. Notably, the pairing decisions of pickup and delivery for each commodity and the routing decisions among customers are interdependent, and they need to be made simultaneously and collaboratively. Firstly, a mixed integer programming model is developed, and then new valid inequalities are derived to improve the linear programming relaxation. Afterwards, a branch-and-cut algorithm is proposed by exploring different branching strategies and tailored separation algorithms. Computational results based on real-case instances from an automobile manufacturing company demonstrate that the costs are considerably reduced by considering the multiple visits compared to the single visit of each customer. In addition, our proposed branch-and-cut algorithm outperforms a manual solution method adopted by the company in practice and two solution methods in the literature. Furthermore, two adaptations of our branch-and-cut algorithm also perform better than two state-of-the-art algorithms in solving two closely-related problems in terms of solution quality and computation time. Sensitivity analyses with respect to vehicle capacity, vehicle duration, and vehicle speed are conducted to derive several valuable managerial insights. [ABSTRACT FROM AUTHOR]

Because of the COVID-19 pandemic, Chinese hospitals are increasing their efforts to control the number of patients to decrease cross-infection risks. In this paper, we investigate the flexible physician scheduling problem for emergency departments (EDs), considering the constraint of the maximum number of emergency patients in one time period. We model the ED service system as a time-varying queue with returns and formulate the physician scheduling problem as a mixed-integer programming model. To solve the scheduling problem effectively, we design a learning-based two-stage optimization algorithm. In the first stage, we solve the physician staffing problem, in which two effective acceleration strategies based on machine learning models are developed. In the second stage, we propose a branch-and-price algorithm to determine the physician scheduling plan. Numerical experiments based on real-life data show that the proposed two-stage algorithm can effectively solve our flexible physician scheduling problem, and the scheduling plan obtained by the proposed two-stage algorithm can significantly improve the physician schedule without involving more physicians. [ABSTRACT FROM AUTHOR]