Max-min Ant Colony Optimization Research Articles

Optimization of Green Vehicle Paths Considering the Impact of Carbon Emissions: A Case Study of Municipal Solid Waste Collection and Transportation

In recent years, the waste produced as a result of the production and consumption activities of urban residents has led to significant environmental degradation and resource wastage. This paper focuses on the research object of municipal solid waste (MSW) collection and transportation based on the concept of “sustainable development and green economy”. Firstly, this study examines the current state of urban domestic garbage collection and transportation. It analyzes the following challenges and deficiencies of the existing collection and transportation system: (1) the operating efficiency of garbage collection vehicles is low, resulting in a significant accumulation of waste on the roadside and within the community; (2) the vehicle collection and transportation routes are fixed, and there are empty vehicles running; (3) the amount of garbage on a route exceeds the vehicle’s loading capacity, which requires the vehicle to perform a second round of collection and transportation. To enhance the efficiency of urban garbage collection and transportation and minimize the collection and transportation costs, we are investigating the problem of optimizing the path for green vehicles. To comprehensively optimize the fixed cost, variable cost, and carbon emission cost incurred during vehicle operation, a vehicle routing model with time windows is established, taking into account vehicle load constraints. Carbon emission coefficient and carbon tax parameters are introduced into the model and the “fuel-carbon emission” conversion method is used to measure the carbon cost of enterprises. An improved ant colony optimization (ACO) method is proposed: (1) the introduction of a vehicle load factor improves the ant state transfer method; (2) the updated pheromone method is improved, and additional pheromone is added to both the feasible path and the path with the minimum objective function; (3) the max–min ACO algorithm is introduced to address the issue of premature convergence of the algorithm; (4) the embedding of a 2-opt algorithm further prevents the ACO algorithm from falling into the local optimum. Finally, the calculation results based on the example data demonstrate that the algorithm has a significant advantage over the genetic algorithm (GA) and particle swarm optimization (PSO) algorithm. The total transportation distance determined by this algorithm is shorter than that of the GA and PSO methods, and the total cost of the scheme is 1.66% and 1.89% lower than that determined by GA and PSO, respectively. Compared to the data from the actual case, the number of vehicles required in the operation of this algorithm and model is reduced by three. Additionally, the total cost, fixed cost, and carbon emission cost incurred by the vehicles during operation were reduced by 31.2%, 60%, and 25.3% respectively. The results of this study help the station to collect and distribute waste efficiently, while also achieving the goals of energy saving, consumption reduction, and emission reduction.

Convergence Analysis of Path Planning of Multi-UAVs Using Max-Min Ant Colony Optimization Approach.

Unmanned Aerial Vehicles (UAVs) seem to be the most efficient way of achieving the intended aerial tasks, according to recent improvements. Various researchers from across the world have studied a variety of UAV formations and path planning methodologies. However, when unexpected obstacles arise during a collective flight, path planning might get complicated. The study needs to employ hybrid algorithms of bio-inspired computations to address path planning issues with more stability and speed. In this article, two hybrid models of Ant Colony Optimization were compared with respect to convergence time, i.e., the Max-Min Ant Colony Optimization approach in conjunction with the Differential Evolution and Cauchy mutation operators. Each algorithm was run on a UAV and traveled a predetermined path to evaluate its approach. In terms of the route taken and convergence time, the simulation results suggest that the MMACO-DE technique outperforms the MMACO-CM approach.

The Method of Transport Logistics Problem Solving by the MAX-MIN ACO Algorithm

The article provides a detailed analysis of the well-known mathematical methods that are used in solving transport logistics problems of various types. Their advantages and disadvantages are determined. The article proposes to use the methods of swarm intelligence to find the optimal route, taking into account all forbidden zones. The problem of transport logistics was solved by the ant colony optimization algorithm on a control example. The results of work of the method were analyzed. The main disadvantages are established. It is proposed to use a modification of the ant colony algorithm - the Max-Min ant colony optimization algorithm. The effectiveness of the method for solving the problem of transport logistics by the algorithm of max-min optimization of an ant colony was tested on a control example. An experimental calculation of the optimal route of traffic from the starting point to the final point is given taking into account the forbidden zones.

A Multi-Colony Social Learning Approach for the Self-Organization of a Swarm of UAVs

This research offers an improved method for the self-organization of a swarm of UAVs based on a social learning approach. To start, we use three different colonies and three best members i.e., unmanned aerial vehicles (UAVs) randomly placed in the colonies. This study uses max-min ant colony optimization (MMACO) in conjunction with social learning mechanism to plan the optimized path for an individual colony. Hereinafter, the multi-agent system (MAS) chooses the most optimal UAV as the leader of each colony and the remaining UAVs as agents, which helps to organize the randomly positioned UAVs into three different formations. Afterward, the algorithm synchronizes and connects the three colonies into a swarm and controls it using dynamic leader selection. The major contribution of this study is to hybridize two different approaches to produce a more optimized, efficient, and effective strategy. The results verify that the proposed algorithm completes the given objectives. This study also compares the designed method with the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) to prove that our method offers better convergence and reaches the target using a shorter route than NSGA-II.

Efficiently solving the thief orienteering problem with a max–min ant colony optimization approach

We tackle the thief orienteering problem (ThOP), an academic multi-component problem that combines two classical combinatorial problems, namely the Knapsack Problem and the Orienteering Problem. In the ThOP, a thief has a time limit to steal items that distributed in a given set of cities. While traveling, the thief collects items by storing them in their knapsack, which in turn reduces the travel speed. The thief has as the objective to maximize the total profit of the stolen items. In this article, we present an approach that combines swarm-intelligence with a randomized packing heuristic. Our solution approach outperforms existing works on almost all the 432 benchmarking instances, with significant improvements.

A Comparative Performance Analysis of Computational Intelligence Techniques to Solve the Asymmetric Travelling Salesman Problem.

This paper presents a comparative performance analysis of some metaheuristics such as the African Buffalo Optimization algorithm (ABO), Improved Extremal Optimization (IEO), Model-Induced Max-Min Ant Colony Optimization (MIMM-ACO), Max-Min Ant System (MMAS), Cooperative Genetic Ant System (CGAS), and the heuristic, Randomized Insertion Algorithm (RAI) to solve the asymmetric Travelling Salesman Problem (ATSP). Quite unlike the symmetric Travelling Salesman Problem, there is a paucity of research studies on the asymmetric counterpart. This is quite disturbing because most real-life applications are actually asymmetric in nature. These six algorithms were chosen for their performance comparison because they have posted some of the best results in literature and they employ different search schemes in attempting solutions to the ATSP. The comparative algorithms in this study employ different techniques in their search for solutions to ATSP: the African Buffalo Optimization employs the modified Karp–Steele mechanism, Model-Induced Max-Min Ant Colony Optimization (MIMM-ACO) employs the path construction with patching technique, Cooperative Genetic Ant System uses natural selection and ordering; Randomized Insertion Algorithm uses the random insertion approach, and the Improved Extremal Optimization uses the grid search strategy. After a number of experiments on the popular but difficult 15 out of the 19 ATSP instances in TSPLIB, the results show that the African Buffalo Optimization algorithm slightly outperformed the other algorithms in obtaining the optimal results and at a much faster speed.

Determination of critical slip surface and safety factor of slope using the vector sum numerical manifold method and MAX-MIN ant colony optimization algorithm

The numerical manifold method (NMM) has been used to solve geotechnical problems with valuable results. In this paper, a numerical model based on the NMM is proposed to investigate two primary concerns in slope stability analyses, i.e., critical slip surface (CSS) determination and safety factor (Fs) calculation. In our proposed numerical model, the optimization algorithm of MAX-MIN ant colony (MMACOA), which is considered to be an algorithm with the best performance for such optimization problems, will be used to determine CSS. In the process of determining the CSS, the trial safety factor for a trial slip surface is calculated with the vector sum method (VSM) according to the stress field produced by an NMM analysis. Accuracy of the numerical model is validated with three typical examples. The numerical model has great potential in the evaluation of stability of real slopes.

Cooperative Path Planning of Multiple UAVs by using Max–Min Ant Colony Optimization along with Cauchy Mutant Operator

In a dynamic environment with wind forces and tornadoes, eliminating fluctuations and noise is critical to get the optimal results. Avoiding collision and simultaneous arrival of multiple unmanned aerial vehicles (multi-UAVs) is also a great problem. This paper addresses the cooperative path planning of multi-UAVs with in a dynamic environment. To deal with the aforementioned issues, we combine the maximum–minimum ant colony optimization (MMACO) and Cauchy Mutant (CM) operators to make a bio-inspired optimization algorithm. Our proposed algorithm eliminates the limitations of classical ant colony optimization (ACO) and MMACO, which has the issues of the slow convergence speed and a chance of falling into local optimum. This paper chooses the CM operator to enhance the MMACO algorithm by comparing and examining the varying tendency of fitness function of the local optimum position and the global optimum position when taking care of multi-UAVs path planning problems. It also makes sure that the algorithm picks the shortest route possible while avoiding collision. Additionally, the proposed method is more effective and efficient when compared to the classic MMACO. Finally, the simulation experiment results are performed under the dynamic environment containing wind forces and tornadoes.

Searching for critical slip surfaces of slopes using stress fields by numerical manifold method

This study first reviews the numerical manifold method (NMM) which possesses some advantages over the traditional limit equilibrium methods (LEMs) in calculating the factors of safety (Fs) of the slopes. Then, with regard to a trial slip surface (TSS), associated stress fields reproduced by NMM as well as the enhanced limit equilibrium method are combined to compute Fs. In order to search for the potential critical slip surface (CSS), the MAX-MIN ant colony optimization algorithm (MMACOA), one of the best performing algorithms for some optimization problems, is adopted. Procedures to obtain Fs in conjunction with the potential CSS are described. Finally, the proposed numerical model and traditional methods are compared with stability analysis of three typical slopes. The numerical results show that Fs and CSSs of the slopes can be accurately calculated with the proposed model.

Improving ant colony optimization algorithm with epsilon greedy and Levy flight

Ant colony optimization (ACO) algorithm is a meta-heuristic and reinforcement learning algorithm, which has been widely applied to solve various optimization problems. The key to improving the performance of ACO is to effectively resolve the exploration/exploitation dilemma. Epsilon greedy is an important and widely applied policy-based exploration method in reinforcement learning and has also been employed to improve ACO algorithms as the pseudo-stochastic mechanism. Levy flight is based on Levy distribution and helps to balance searching space and speed for global optimization. Taking advantage of both epsilon greedy and Levy flight, a greedy–Levy ACO incorporating these two approaches is proposed to solve complicated combinatorial optimization problems. Specifically, it is implemented on the top of max–min ACO to solve the traveling salesman problem (TSP) problems. According to the computational experiments using standard TSPLIB instances, greedy–Levy ACO outperforms max–min ACO and other latest TSP solvers, which demonstrates the effectiveness of the proposed methodology.

A Novel Ant Colony Optimization Algorithm With Levy Flight

Ant Colony Optimization (ACO) is a widely applied meta-heuristic algorithm. Little researches focused on the candidate selection mechanism, which was developed based on the simple uniform distribution. This paper employs the Levy flight mechanism based on Levy distribution to the candidate selection process and takes advantage of Levy flight that not only guarantees the search speed but also extends the searching space to improve the performance of ACO. Levy ACO incorporating with Levy flight developed on the top of Max-min ACO. According to the computational experiments, the performance of Levy ACO is significantly better than the original Max-min ACO and some latest Traveling Salesman Problem (TSP) solvers.

Improved energy efficient WSN using ACO based HSA for optimal cluster head selection

In recent era, increased consumption of energy in the wireless sensor network (WSN) is considered as a critical issue. The main constraints associated with these networks is the lower transmission range, reduced battery power and reduced memory requirement. There are very few designs that concentrates on designing newer routing protocol that considers these parameters for optimal selection of routes to reduce the energy consumption. With such aim, the proposed method designs a new routing protocol with optimal parameter selection. In addition, the study considers faster transmission of packets without losing the data accuracy. The network is divided into clusters, where the cluster center (center of the circle) is assumed to have minimum density in its own cluster. A path based clustering using Ant Colony Optimization (ACO) is used for this purpose. Here, the minimum density cluster is selected using Harmonic Search Algorithm (HSA). The ACO combined with HSA finds the optimal cluster head with minimum routing path with reduced energy consumption. The validation of the proposed method is carried out against ACO-Fuzzy, max-min ACO, mACO and ACO in terms of various performance metrics. The result shows that the proposed method achieves higher network throughput, maximum network lifetime and reduced consumption of energy than other methods.

A MULTIOBJECTIVE APPROACH FOR REAL TIME TASK ASSIGNMENT PROBLEM IN HETEROGENEOUS MULTIPROCESSORS

Effective assignment of real-time tasks in heterogeneous multi-processor systems to achieve high performance is said to be an NP-hard problem. This paper addresses the problem of real-time task assignment in heterogeneous multiprocessor systems with the goal of maximizing the number of task assigned and decreasing the energy consumption. A heuristic-based Multi-objective Hybrid Max-Min Ant Colony Optimization algorithm (MOHMMAS) on the heterogeneous multiprocessor system is proposed to analyze the tradeoffs between resource utilization of all assigned tasks and cumulative energy consumption. Also, we have constructed pareto fronts to illustrate different task allocations, which can cause a heterogeneous multiprocessor system to consume significantly different amounts of energy. The proposed algorithm has been implemented and evaluated using randomly generated problem instances.It was found that the proposed algorithm outperforms the Multi-objective ACO (MO-ACO) in terms of number of the tasks assigned and cumulative energy consumption of all assigned tasks.

Estimation of incomplete values in heterogeneous attribute large datasets using discretized Bayesian max–min ant colony optimization

The size of datasets is becoming larger nowadays and missing values in such datasets pose serious threat to data analysts. Although various techniques have been developed by researchers to handle missing values in different kinds of datasets, there is not much effort to deal with the missing values in mixed attributes in large datasets. This paper has proposed novel strategies for dealing with this issue. The significant attributes (covariates) required for imputation are first selected using gain ratio measure to decrease the computational complexity. Since analysis of continuous attributes in imputation process is complex, they are first discretized using a novel methodology called Bayesian classifier-based discretization. Then, missing values in them are imputed using Bayesian max–min ant colony optimization algorithm which hybridizes ACO with Bayesian principles. The local search technique is also introduced in ACO implementation to improve its exploitative capability. The proposed methodology is implemented in real datasets with different missing rates ranging from 5 to 50% and from the experimental results, it is observed that the proposed discretization and imputation algorithms produce better results than the existing methods.

Energy Optimization for Train Operation Based on an Improved Ant Colony Optimization Methodology

More and more lines are using the Communication Based Train Control (CBTC) systems in urban rail transit. Trains are operated by tracking a pre-determined target speed curve in the CBTC system, so one of the most effective ways of reducing energy consumption is to fully understand the optimum curves that should prevail under varying operating conditions. Additionally, target speed curves need to be calculated with optimum real-time performance in order to cope with changed interstation planning running time. Therefore, this paper proposes a fast and effective algorithm for optimization, based on a two-stage method to find the optimal curve using a max-min ant colony optimization system, using approximate calculations of a discrete combination optimization model. The first stage unequally discretizes the line based on static gradient and speed limit in low-density and it could conduct a comprehensive search for viable energy saving target speed curves. The second stage unequally discretizes the line based on first stage discretion results, it makes full use of first-stage optimization information as pheromone, quickly optimizing the results to satisfy real-time demands. The algorithm is improved through consideration of the experience of train drivers. Finally, the paper presents some examples based on the operation data of Beijing Changping Subway Line, which is using CBTC system. The simulation results show that the proposed approach presents good energy-efficient and real-time performance.

An integrated ant colony optimization algorithm to solve job allocating and tool scheduling problem

In this article, max–min ant colony optimization algorithm is proposed to determine how to allocate jobs and schedule tools with the objective of minimizing the makespan of processing plans in flexible manufacturing system. To expand the application range of max–min ant colony optimization algorithm, tool movement policy is selected as the running mode of flexible manufacturing system, which assumes that tools are shared among work centers and each operation is allowed to be machined by different kinds of tools. In the process of converting this scheduling problem into traveling salesman problem, disjunctive graph is modified to possess more than one path between each neighbor node. Besides providing practical methods of initializing pheromone, selecting node and calculating pheromone increment, max–min ant colony optimization algorithm employs the pheromone updating rule in max–min ant system to limit pheromone amount in a range, of which the upper and lower boundaries are updated after each iteration by formulations involving the current optimal makespan, the average number of optional tools and parameters. Finally, different sizes of processing plans are randomly generated, through which max–min ant colony optimization algorithm is proved effectively to tackle early stagnation and local convergence and thus obtains better solution than ant colony optimization algorithm and bidirectional convergence ant colony optimization algorithm.

Local container drayage problem with tractor and trailer operating in separable mode

In recent years, the Local Container Drayage Problem (LCDP) has received lots of studies in research as part of container transportation. This paper examines the LCDP under a special operation mode in which tractors and trailers can be separated, i.e., tractors can be assigned to a new task at another location while trailers are waiting for packing or unpacking. The problem is formulated as a vehicle routing and scheduling problem with temporal constraints. The resulting formulation can be used to solve small-scale problems. For large-scale problems, we develop a max–min Ant colony optimization algorithm to reduce the computation time. Numerical experiments with randomly generated instances are performed to demonstrate the performance of the algorithm.

A model induced max-min ant colony optimization for asymmetric traveling salesman problem

A large number of hybrid metaheuristics for asymmetric traveling salesman problem (ATSP) have been proposed in the past decades which produced better solutions by exploiting the complementary chara...

Task coalition formation and self‐adjustment in the wireless sensor networks

SUMMARYCoalition is an essential mechanism in the multi‐agent systems in the research of task‐oriented area. Self‐interested agents coordinate their behaviors in a coalition to pursue a common goal and obtain payoffs. We propose the clustering‐based coalition formation and self‐adjustment mechanisms for tasks in the wireless sensor network. Before coalition formation, the management center clusters attributes of sensors to reduce the scale of searching space during coalition formation. And then an improved MAX–MIN ant colony optimization algorithm is adopted to resolve the problem of coalition formation. If a coalition member fails to fulfill a task, it can sponsor a negotiation with some noncoalition nodes to execute coalition self‐repairing autonomously. The stimulus‐response mechanism of wasp colony is introduced to determine the probability of response to the task invitation to avoid consuming extra energy. Simulation results show that our model efficiently reduces energy consumption and network traffic, decreases the number of dead nodes, and prolongs the lifetime of the networks. Copyright © 2012 John Wiley & Sons, Ltd.

A model induced max-min ant colony optimization for asymmetric traveling salesman problem

A large number of hybrid metaheuristics for asymmetric traveling salesman problem (ATSP) have been proposed in the past decades which produced better solutions by exploiting the complementary characteristics of different optimization strategies. However, most of the hybridizations are criticized due to lacking of sufficient analytical basis. In this paper, a model induced max-min ant colony optimization (MIMM-ACO) is proposed to bridge the gap between hybridizations and theoretical analysis. The proposed method exploits analytical knowledge from both the ATSP model and the dynamics of ACO guiding the behavior of ants which forms the theoretical basis for the hybridization. The contribution of this paper mainly includes three supporting propositions that lead to two improvements in comparison with classical max-min ACO optimization (MM-ACO): (1) Adjusted transition probabilities are developed by replacing the static biased weighting factors with the dynamic ones which are determined by the partial solution that ant has constructed. As a byproduct, nonoptimal arcs will be indentified and excluded from further consideration based on the dual information derived from solving the associated assignment problem (AP). (2) A terminal condition is determined analytically based on the state of pheromone matrix structure rather than intuitively as in most traditional hybrid metaheuristics. Apart from the theoretical analysis, we experimentally show that the proposed algorithm exhibits more powerful searching ability than classical MM-ACO and outperforms state of art hybrid metaheuristics.