Complex Combinatorial Optimization Problem Research Articles

Deep reinforcement learning for autonomous SideLink radio resource management in platoon-based C-V2X networks: An overview

Dynamic and autonomous SideLink (SL) Radio Resource Management (RRM) is essential for platoon-based cellular vehicular networks. However, this task is challenging due to several factors. These include the limited spectrum below 6 GHz, stringent vehicle-to-everything (V2X) communications requirements, uncertain and dynamic environments, limited vehicle sensing capabilities, and inherent distributed operation. These limitations often lead to resource collisions, data packet loss, and increased latency. Current standardized approaches in Long-Term Evolution-V2X (LTE-V2X) and New Radio-V2X (NR-V2X) rely on random resource selection, limiting their efficiency. Moreover, RRM is inherently a complex combinatorial optimization problem. It may involve conflicting objectives and constraints, making traditional approaches inadequate. Platoon-based communication necessitates careful resource allocation to support a diverse mix of communication types. These include safety-critical control messaging within platoons, less time-sensitive traffic management information between platoons, and even infotainment services like media streaming. Optimizing resource sharing inter- and intra- platoons is crucial to avoid excessive interference and ensure overall network performance. Deep Reinforcement Learning (DRL), combining Deep Learning (DL) and Reinforcement Learning (RL), has recently been investigated for network resource management. It offers a potential solution for these challenges. A DRL agent, represented by deep neural networks, interacts with the environment and learns optimal decision-making through trial and error. This paper overviews proposed DRL-based methods for autonomous SL RRM in single and multi-agent platoon-based C-V2X networks. It considers both intra- and inter-platoon communications with their specific requirements. We discuss the components of Markov Decision Processes (MDP) used to model the sequential decision-making of RRM. We then detail the DRL algorithms, training paradigms, and insights on the achieved results. Finally, we highlight challenges in existing works and suggest strategies for addressing them.

Applying the Simulated Annealing Algorithm to the Set Orienteering Problem with Mandatory Visits

This study addresses the set orienteering problem with mandatory visits (SOPMV), a variant of the team orienteering problem (SOP). In SOPMV, certain critical sets must be visited. The study began by formulating the mathematical model for SOPMV. To tackle the challenge of obtaining a feasible route within time constraints using the original MILP approach, a two-stage mixed-integer linear programming (MILP) model is proposed. Subsequently, a simulated annealing (SA) algorithm and a dynamic programming method were employed to identify the optimal route. The proposed SA algorithm was used to solve the SOP and was compared to other algorithms, demonstrating its effectiveness. The SA was then applied to solve the SOPMV problem. The results indicate that the solutions obtained using SA are superior and more efficient compared to those derived from the original MILP and the two-stage MILP. Additionally, the results reveal that the solution quality deteriorates as the ratio of the set of mandatory visits increases or the maximum allowable travel time decreases. This study represents the first attempt to integrate mandatory visits into SOP, thereby establishing a new research direction in this area. The potential impact of this research is significant, as it introduces new possibilities for addressing complex combinatorial optimization problems.

A dictionary-based Bayesian approach to optimizing left-turn restriction locations in grid networks

Left-turn movements at signalized intersections pose significant safety risks for the drivers and efficiency concerns for the traffic operations in urban networks. Restricting left-turn movements at selected locations has been shown to be effective at improving operational efficiency and mitigating safety concerns. However, determining optimal locations to restrict left-turns is a complex combinatorial optimization problem that is compounded by the lack of analytical forms for the objective function and constraints, as well as potential interdependencies between the decision variables. Following the common solution paradigm for this type of optimization problems, this paper presents a novel Bayesian approach that utilizes dictionary-based embeddings and is tailored for high-dimensional combinatorial (or even mixed) spaces. Simulation studies conducted using the Aimsun software under perfect or imperfect grid networks demonstrate that the presented method can consistently find promising left-turn restriction configurations that outperform the all-or-nothing strategies (to restrict all or none left-turn movements at all intersections), as well as the population based incremental learning algorithm. In addition, the presented method often does so with less simulation cost, thus showcasing its potential for efficient solution of more general traffic optimization problems.

Fit Entropy-Based Dynamic Communication Resource Slicing-Optimization Method in Smart Distribution Grids on the Medium-Low-Voltage Side.

With the rapid development of new energy and smart technology, the demand for inter-device communication in medium-low-voltage smart distribution grids has sharply increased, leading to a surge in the variety and quantity of communication services. To meet the needs of diverse and massive communication services, deploying service function chains to flexibly combine virtual resources has become crucial. This paper proposes an optimization method based on fit entropy and network utility to address the limited communication network resources in medium-low-voltage smart distribution grids. This was conducted by modeling the distribution grid as a three-domain model consisting of a service domain, a logical domain, and a physical domain and transforming it into a hierarchical bipartite hypergraph-matching problem, which is a complex combinatorial optimization problem. This paper introduces two matching optimization algorithms: "business domain-logic domain-physical domain integration" and "service domain-logic domain, logic domain-physical domain two-stage", which effectively address this problem based on fit entropy and utility. The simulation results demonstrate that these algorithms significantly improve service success rates and resource utilization, enhancing overall network utility.

Learning to Allocate Time-Bound and Dynamic Tasks to Multiple Robots Using Covariant Attention Neural Networks

Abstract In various applications of multi-robotics in disaster response, warehouse management, and manufacturing, tasks that are known a priori and tasks added during run time need to be assigned efficiently and without conflicts to robots in the team. This multi-robot task allocation (MRTA) process presents itself as a combinatorial optimization (CO) problem that is usually challenging to be solved in meaningful timescales using typical (mixed)integer (non)linear programming tools. Building on a growing body of work in using graph reinforcement learning to learn search heuristics for such complex CO problems, this paper presents a new graph neural network architecture called the covariant attention mechanism (CAM). CAM can not only generalize but also scale to larger problems than that encountered in training, and handle dynamic tasks. This architecture combines the concept of covariant compositional networks used here to embed the local structures in task graphs, with a context module that encodes the robots’ states. The encoded information is passed onto a decoder designed using multi-head attention mechanism. When applied to a class of MRTA problems with time deadlines, robot ferry range constraints, and multi-trip settings, CAM surpasses a state-of-the-art graph learning approach based on the attention mechanism, as well as a feasible random-walk baseline across various generalizability and scalability tests. Performance of CAM is also found to be at par with a high-performing non-learning baseline called BiG-MRTA, while noting up to a 70-fold improvement in decision-making efficiency over this baseline.

Enhancing the performance of coherent Ising machines in the large-noise regime with a fifth-order nonlinearity

Coherent Ising machines (CIMs), leveraging the bistable physical properties of coherent light to emulate Ising spins, exhibit great potential as hardware accelerators for tackling complex combinatorial optimization problems. Recent advances have demonstrated that the performance of CIMs can be enhanced either by incorporating large random noise or higher-order nonlinearities, yet their combined effects on CIM performance remain mainly unexplored. In this work, we develop a numerical CIM model that utilizes a tunable fifth-order polynomial nonlinear dynamic function under large noise levels, which has the potential to be implemented in all-optical platforms. We propose a normal form of a CIM model that allows for both supercritical and subcritical pitchfork bifurcation operational regimes, with fifth-order nonlinearity and tunable hyperparameters to control the Ising spin dynamics. In the benchmark studies, we simulate various sets of MaxCut problems using our fifth-order polynomial CIM model. The results show a significant performance improvement, achieving an average of 59.5% improvement in median time-to-solution (TTS) and an average of 6 times improvement in median success rate (SR) for dense Maxcut problems in the BiqMac library, compared to the commonly used third-order polynomial CIM model with low noise. The fifth-order polynomial CIM model in the large-noise regime also shows better performance trends as the problem size scales up. These findings reveal the enhancements on the computational performance of Ising machines in the large-nose regime from fifth-order nonlinearity, showing important implications for both simulation and hardware perspectives.

A Knowledge-Guided Competitive Co-Evolutionary Algorithm for Feature Selection

In real-world applications, feature selection is crucial for enhancing the performance of data science and machine learning models. Typically, feature selection is a complex combinatorial optimization problem and a multi-objective optimization problem. Its primary goals are to reduce the dimensionality of the dataset and enhance the performance of machine learning algorithms. The selection of features in high-dimensional datasets is challenging due to the intricate relationships between features, which pose significant challenges to the performance and computational efficiency of algorithms. This paper introduces a Knowledge-Guided Competitive Co-Evolutionary Algorithm (KCCEA) for feature selection, especially for high-dimensional features. In the proposed algorithm, we make improvements to the foundational dominance-based multi-objective evolutionary algorithm in two aspects. First, the use of feature correlation as knowledge to guide evolution enhances the search speed and quality of traditional multi-objective evolutionary algorithm solutions. Second, a dynamically allocated competitive–cooperative evolutionary mechanism is proposed, integrating the improved knowledge-guided evolution with traditional evolutionary algorithms, further enhancing the search efficiency and diversity of solutions. Through rigorous empirical testing on various datasets, the KCCEA demonstrates superior performance compared to basic multi-objective evolutionary algorithms, providing effective solutions to multi-objective feature selection problems while enhancing the interpretability and effectiveness of prediction models.

Agile earth observation satellite constellations scheduling for large area target imaging using heuristic search

Demand for imaging of large area targets by space-based assets such as constellations of Earth Observation Satellites (EOS) is on the rise for different applications. The area targets coverage cannot be achieved by a single satellite in a single observation opportunity, as the region for imaging spreads wider than the coverage swaths of imaging sensors. Hence, the imaging satellites are scheduled in a cooperative way to achieve maximum coverage of the area in a given planning time horizon. The scheduling algorithms also aim to maximize or minimize some specific objectives of interest while simultaneously complying with all resource constraints for an efficient use of precious space resources. As the current generation satellites are highly agile, there are many ways of choosing an imaging location in the target area for each single observation opportunity of a satellite. Even though the possible imaging region in continuous space is discretized into a finite number of strips for each observation, the huge combinatorial search space formed with all satellites’ imaging opportunities makes the problem intractable. Thus, the area target imaging scheduling is a complex combinatorial NP-hard optimization problem. Many exact and heuristic methods were evolved to provide a solution to this scheduling problem. Even though the exact methods solve the problem to optimality, they are limited to smaller problem instances because of the high computational complexities involved in those methods. More focus is seen in the literature on heuristic approaches as they guarantee scheduling performance with feasible solutions within an acceptable computational complexity. This paper presents our efficient heuristic approach proposed for the scheduling problem for imaging a large area target using a constellation of multiple satellites. Our approach is an extension of a widely used greedy approach in combination with insights from dynamic programming. In this paper, first we addressed the scheduling problem by describing it in detail and formulating it into a non-linear integer programming problem, considering the multi-objectives of achieving maximum coverage and minimum imaging resolution. The solution to the problem comprises two phases, namely the area decomposition phase and the scheduling phase. In the area decomposition phase, the area target is divided into strips dynamically for each observation opportunity of a satellite. Then exact observation period of each strip is computed using a simplified semi-analytical computational method. In the scheduling phase, we applied our heuristic search strategy, namely Forward and Backward Heuristic Search (FBHS) to obtain a near optimal solution within an acceptable computational time. Through the extensive simulations conducted under various scenarios, the effectiveness of the proposed method is verified in comparison with the baseline greedy approach.

AquaNutriOpt: Optimizing nutrients for controlling harmful algal blooms in Python—A case study of Lake Okeechobee

We present AquaNutriOpt, a user-friendly Python package designed to tackle a complex combinatorial optimization problem aimed at optimizing nutrient management for the control of harmful algal blooms. This optimization process involves the identification of optimal Best Management Practices (BMPs) and Treatment Technologies (TTs). AquaNutriOpt is constructed based on a novel integer programming model, which we present in this paper. The package can accommodate various user inputs, automatically transforming them into an optimization model, and then solving it using a free solver. To demonstrate AquaNutriOpt’s efficacy, we conduct a series of experiments on two watersheds around Lake Okeechobee in Florida, USA. These experiments illustrate that the optimal BMPs/TTs obtained by AquaNutriOpt can significantly reduce Phosphorus loads into the lake across various budget scenarios. We validate the results by running simulations with the process-based Watershed Assessment Model (WAM), confirming that the estimated percentage reductions closely align with the reports from WAM.

Fully CMOS‐Based p‐Bits with a Bistable Resistor for Probabilistic Computing

AbstractProbabilistic computing can solve complex combinatorial optimization problems more efficiently than conventional deterministic computing. A probabilistic bit (p‐bit) with an n‐p‐n bistable resistor (biristor) is demonstrated for probabilistic computing. It is fabricated on an 8‐inch wafer with complementary metal–oxide–semiconductor (CMOS) compatible technologies. Its stochastic behavior of threshold switching, which is based on the phenomenon of a single transistor latch, provides output with a Boltzmann distribution. The p‐bit is composed of a biristor, a serial resistor, and a comparator. The output probability of the biristor‐based p‐bits shows a sigmoidal relationship with the input voltage, showing typical p‐bit characteristics. Invertible Boolean logic operations with p‐bits are demonstrated, and weighted maximum Boolean satisfiability problems are solved with high energy efficiency and accuracy. The biristor‐based p‐bits with perfect CMOS compatibility show sufficient device stability, demonstrating the possibility of large‐scale integration with a p‐bit array for complex optimization solvers.

Formulation of the airport collaborative gate allocation problem and the Bee Colony Optimization solution approach

This article formulates the Collaborative Gate Allocation (CGA) problem as a novel concept to reduce aircraft gate-waiting time and to increase aircraft gate utilization. The proposed CGA concept assumes voluntary collaboration and negotiation among airlines and airport operators, enabling them to share real-time information on gate-utilization and gate-sharing. The proposed policy is especially applicable to U.S. airports, as an alternative to exclusive or preferential gate-sharing practices, at terminal buildings that accommodate a large number of smaller airlines during periods of high congestion and delays caused by high traffic demands, bad weather conditions, or any ad hoc situations. The CGA problem belongs to the class of complex combinatorial optimization problems, whose optimal solution is difficult to discover. This article develops a Swarm Intelligence-based model for the CGA problem. Our approach to solving the CGA problem is based on the Bee Colony Optimization (BCO) metaheuristic. The BCO algorithm belongs to the class of population-based algorithms. This technique uses a similarity between the way in which bees in nature look for nectar, and the way in which optimization algorithms search for an optimum solution to a combinatorial optimization problem. Numerical experiments are performed using Denver International Airport as a real-world case study. We show that the proposed CGA problem can be efficiently solved by our BCO algorithm, and that applications of the CGA concept can significantly reduce gate delays.

Meta-Learning-Based Deep Reinforcement Learning for Multiobjective Optimization Problems.

Deep reinforcement learning (DRL) has recently shown its success in tackling complex combinatorial optimization problems. When these problems are extended to multiobjective ones, it becomes difficult for the existing DRL approaches to flexibly and efficiently deal with multiple subproblems determined by the weight decomposition of objectives. This article proposes a concise meta-learning-based DRL approach. It first trains a meta-model by meta-learning. The meta-model is fine-tuned with a few update steps to derive submodels for the corresponding subproblems. The Pareto front is then built accordingly. Compared with other learning-based methods, our method can greatly shorten the training time of multiple submodels. Due to the rapid and excellent adaptability of the meta-model, more submodels can be derived so as to increase the quality and diversity of the found solutions. The computational experiments on multiobjective traveling salesman problems and multiobjective vehicle routing problems with time windows demonstrate the superiority of our method over most of the learning-based and iteration-based approaches.

Modelling the forest harvesting tour problem

In a globalized market, forest management plans play an important role in the sustainability of forest enterprises. Several optimization processes have therefore been developed to support decision-making in forestry operations. However, important issues remain to be addressed, such as planning the allocation of harvesting areas and scheduling the harvesting teams that are contracted for these purposes. Harvesting schedules include different time scales and natural constraints, so that finding optimal or even good quality ones constitutes a highly complex combinatorial optimization problem. Efficient planning of harvesting operations can significantly reduce the costs associated with logistics and improve the economic performance of companies in the sector. In Uruguay, almost 75\% of total forest harvesting operations for pulp production are carried out by contractor companies, so they are an important player in the supply chain. This study aims to optimize the allocation and routing of the harvesting equipment of forest contractors, which must be located at the sites to be harvested during the year. Numerical experiments over a case study based on realistic data have shown that realistic-sized instances can be resolved by standard mathematical programming software in a reasonable time. The mathematical programming model can also be useful to evaluate potential gains in joint planning by several contractors with respect to the costs incurred by separate planning; as illustrated also with numerical examples over the same case study. This model can be used to support annual forest harvest scheduling and equipment allocation for corporate contractors, leading to better quality plans and improvement opportunities.

Deep Reinforcement Learning Based Optimization Algorithm for Permutation Flow-Shop Scheduling

As a new analogy paradigm of human learning process, reinforcement learning (RL) has become an emerging topic in computational intelligence (CI). The synergy between the RL and CI is an emerging way to develop efficient solution algorithms for solving complex combinatorial optimization (CO) problems like machine scheduling problem. In this paper, we proposed an efficient optimization algorithm based on Deep RL for solving permutation flow-shop scheduling problem (PFSP) to minimize the maximum completion time. Firstly, a new deep neural network (PFSPNet) is designed for the PFSP to achieve the end-to-end output without limitation of problem sizes. Secondly, an actor-critic method of RL is used to train the PFSPNet without depending on the collection of high-quality labelled data. Thirdly, an improvement strategy is designed to refine the solution provided by the PFSPNet. Simulation results and statistical comparison show that the proposed optimization algorithm based on deep RL can obtain better results than the existing heuristics in similar computational time for solving the PFSP.

A Cooperative Scatter Search With Reinforcement Learning Mechanism for the Distributed Permutation Flowshop Scheduling Problem With Sequence-Dependent Setup Times

The integration of reinforcement learning technology into meta-heuristic algorithms to address complex combinatorial optimization problems has attracted much attention in recent years. A cooperative scatter search with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -learning mechanism (QCSS) is proposed for solving the DPFSP-SDST. In the diversification generation method, two effective heuristic algorithms are designed to construct an initial population with high quality and diversity. In the improved method, eight domain knowledge-guided perturbation operators are combined with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -learning to balance the exploration and exploitation capabilities of the QCSS algorithm. The reference set <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(\mathrm{RefSet})$</tex-math> </inline-formula> is divided into two subpopulations, and adaptive competition is adopted between the subpopulations to enhance search efficiency. In addition, a restart mechanism is proposed in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm{RefSet}$</tex-math> </inline-formula> update phase to ensure the diversity of solutions. The performance of the QCSS algorithm is verified on the benchmark set, and the experimental results demonstrate the robustness and effectiveness of the QCSS algorithm.

Automated Design of Metaheuristics Using Reinforcement Learning Within a Novel General Search Framework

Metaheuristic algorithms have been investigated intensively to address highly complex combinatorial optimisation problems. However, most metaheuristic algorithms have been designed manually by researchers of different expertise without a consistent framework to support effective algorithm design. This paper proposes a general search framework to formulate in a unified way a range of different metaheuristics. This framework defines generic algorithmic components, including selection heuristics and evolution operators. The unified general search framework aims to serve as the basis of analysing algorithmic components for automated algorithm design. With the established new general search framework, two reinforcement learning based methods, deep Q-network based and proximal policy optimisation based methods, have been developed to automatically design a new general population-based algorithm. The proposed reinforcement learning based methods are able to intelligently select and combine appropriate algorithmic components during different stages of the optimisation process. The effectiveness and generalization of the proposed reinforcement learning based methods are validated comprehensively across different benchmark instances of the capacitated vehicle routing problem with time windows. This study contributes to making a key step towards automated algorithm design with a general framework supporting fundamental analysis by effective machine learning.

Q-learning driven multi-population memetic algorithm for distributed three-stage assembly hybrid flow shop scheduling with flexible preventive maintenance

The distributed assembly flow shop scheduling (DAFS) problem has received much attention in the last decade, and a variety of metaheuristic algorithms have been developed to achieve the high-quality solution. However, there are still some limitations. On the one hand, these studies usually ignore the machine deterioration, maintenance, transportation as well as the flexibility of flow shops. On the other hand, metaheuristic algorithms are prone to fall into local optimality and are unstable in solving complex combinatorial optimization problems. Therefore, a multi-population memetic algorithm (MPMA) with Q-learning (MPMA-QL) is developed to address a distributed assembly hybrid flow shop scheduling problem with flexible preventive maintenance (DAHFSP-FPM). Specifically, a mixed integer linear programming (MILP) model targeted at the minimal makespan is first established, followed by an effective flexible maintenance strategy to simplify the model. To efficiently solve the model, MPMA is developed and Q-learning is used to achieve an adaptive individual assignment for each subpopulation to improve the performance of MPMA. Finally, two state-of-the-art metaheuristics and their Q-learning-based improvements are selected as rivals of the developed MPMA and MPMA-QL. A series of numerical studies are carried out along with a real-life case of a furniture manufacturing company, to demonstrate that MPMA-QL can provide better solutions on the studied DAHFSP-FPM..

Minimizing tardiness and makespan for distributed heterogeneous unrelated parallel machine scheduling by knowledge and Pareto-based memetic algorithm

This work aims to deal with the distributed heterogeneous unrelated parallel machine scheduling problem (DHUPMSP) with minimizing total tardiness (TDD) and makespan. To solve this complex combinatorial optimization problem, this work proposed a knowledge and Pareto-based memetic algorithm (KPMA) which contains the following features: 1) four heuristic rules are designed including the shortest processing time rule, the minimum factory workload rule, the minimum machine finish time rule, and the earliest due date rule. Meanwhile, a hybrid heuristic initialization is developed to construct a population with great convergence and diversity; 2) four problem feature-based heuristic neighborhood structures are designed to increase the success rate of local search; and 3) a simple elite strategy is developed to enhance the usage of historical elite solutions. Finally, to evaluate the performance of KMPA, it is compared to five state-of-art and run on 20 instances with different scales. The results of numerical experiments show that the proposed hybrid heuristic initialization can efficiently save computation resources to improve the initialized convergence. In addition, the knowledge-based neighborhood structures can vastly accelerate exploration. Moreover, the elite strategy can efficiently improve the diversity of the final non-dominated solutions set. The proposed KPMA has better performance than the state-of-art and has a strong ability to solve DHUPMSP.

Generation of Nonlinear Substitutions by Simulated Annealing Algorithm

The problem of nonlinear substitution generation (S-boxes) is investigated in many related works in symmetric key cryptography. In particular, the strength of symmetric ciphers to linear cryptanalysis is directly related to the nonlinearity of substitution. In addition to being highly nonlinear, S-boxes must be random, i.e., must not contain hidden mathematical constructs that facilitate algebraic cryptanalysis. The generation of such substitutions is a complex combinatorial optimization problem. Probabilistic algorithms are used to solve it, for instance the simulated annealing algorithm, which is well-fitted to a discrete search space. We propose a new cost function based on Walsh–Hadamard spectrum computation, and investigate the search efficiency of S-boxes using a simulated annealing algorithm. For this purpose, we conduct numerous experiments with different input parameters: initial temperature, cooling coefficient, number of internal and external loops. As the results of the research show, applying the new cost function allows for the rapid generation of nonlinear substitutions. To find 8-bit bijective S-boxes with nonlinearity 104, we need about 83,000 iterations. At the same time, the probability of finding the target result is 100%.

A Multistep Iterative Ranking Learning Method for Optimal Project Portfolio Planning of Smart Grid

Optimal project portfolio planning is a typical nonconvex, multiobjective, highly constrained, multitemporal coupling, and combinatorial optimization problem. This paper proposes a novel multistep iterative ranking learning method (MIRL) to solve this complex combinatorial optimization problem from massive infrastructure projects of smart grid. The optimal project portfolio planning problem of power grid is formulated as the optimization process of massive project priority sorting with an improved knapsack model. The proposed method dynamically optimizes the best infrastructure project combination for each round to maximize the economic, social, and security benefits without exceeding the annual investment limit. A pairwise-based ranking learning algorithm is used to mine the priority sorting law from massive historical combination data of power grid to initialize candidate project portfolio. In order to approach the optimal portfolio planning solution with the constraint satisfactions of project construction duration and electric load supplies, a heuristic greedy strategy is designed to search the solution dynamically for selecting the project having highest construction benefits iteratively. The effectiveness of the proposed method is proved by experiments with real-world project data of Hunan power grid in China, and experimental results show that the proposed MIRL can outperform other methods on investment efficiency, calculation time, and rationality of project construction period schedule.