Solving the Probabilistic TSP with Ant Colony Optimization

In this paper, we describe new ways to apply Ant Colony Optimization (ACO) to the Probabilistic Traveling Salesperson Problem (PTSP). PTSP is a stochastic extension of the well known Traveling Salesperson Problem (TSP), where each customer will require a visit only with a certain probability. The goal is to find an a priori tour visiting all customers with minimum expected length, customers not requiring a visit simply being skipped in the tour.We show that ACO works well even when only an approximative evaluation function is used, which speeds up the algorithm, leaving more time for the actual construction. As we demonstrate, this idea can also be applied successfully to other state-of-the-art heuristics. Furthermore, we present new heuristic guidance schemes for ACO, better adapted to the PTSP than what has been used previously. We show that these modifications lead to significant improvements over the standard ACO algorithm, and that the resulting ACO is at least competitive to other state-of-the-art heuristics.     

Combined Discrete-event Simulation and Ant Colony Optimisation Approach for Selecting Optimal Screening Policies for Diabetic Retinopathy

In this paper we present the first application to a healthcare problem of discrete-event simulation (DES) embedded in an ant colony optimisation (ACO) model. We are concerned with choosing optimal screening policies for retinopathy, a sight-threatening complication of diabetes. The early signs of retinopathy can be detected by screening before the patient is aware of symptoms, and blindness prevented by laser treatment. In this paper we describe the methodology used to combine the purpose-written DES model with the ACO algorithm. We simulate the effects of different screening strategies on a population of diabetic patients, and compare them in terms of two objective functions: Min C/E, cost-effectiveness (minimum incremental cost per year of sight saved, compared with a no-screening baseline) and Max E, maximum effectiveness (years of sight saved). We describe how ACO is used to optimise these two objectives, and discuss the issues involved in optimising stochastic variables. We present results for a range of different assumptions and scenarios about the format of screening programmes, using realistic data, and make policy recommendations on the basis of our findings.     

Combining two pheromone structures for solving the car sequencing problem with Ant Colony Optimization

The car sequencing problem involves scheduling cars along an assembly line while satisfying capacity constraints. In this paper, we describe an Ant Colony Optimization (ACO) algorithm for solving this problem, and we introduce two different pheromone structures for this algorithm: the first pheromone structure aims at learning for “good” sequences of cars, whereas the second pheromone structure aims at learning for “critical” cars. We experimentally compare these two pheromone structures, that have complementary performances, and show that their combination allows ants to solve very quickly most instances.     

A study of ACO capabilities for solving the maximum clique problem

This paper investigates the capabilities of the Ant Colony Optimization (ACO) meta-heuristic for solving the maximum clique problem, the goal of which is to find a largest set of pairwise adjacent vertices in a graph. We propose and compare two different instantiations of a generic ACO algorithm for this problem. Basically, the generic ACO algorithm successively generates maximal cliques through the repeated addition of vertices into partial cliques, and uses “pheromone trails” as a greedy heuristic to choose, at each step, the next vertex to enter the clique. The two instantiations differ in the way pheromone trails are laid and exploited, i.e., on edges or on vertices of the graph. We illustrate the behavior of the two ACO instantiations on a representative benchmark instance and we study the impact of pheromone on the solution process. We consider two measures—the re-sampling and the dispersion ratio—for providing an insight into the performance at run time. We also study the benefit of integrating a local search procedure within the proposed ACO algorithm, and we show that this improves the solution process. Finally, we compare ACO performance with that of three other representative heuristic approaches, showing that the former obtains competitive results.     

Ant colony optimization and local search for bin packing and cutting stock problems

The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimization problems. Exact solution methods can only be used for very small instances, so for real-world problems, we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In the work presented here, we used an ant colony optimization (ACO) approach to solve both Bin Packing and Cutting Stock Problems. We present a pure ACO approach, as well as an ACO approach augmented with a simple but very effective local search algorithm. It is shown that the pure ACO approach can compete with existing evolutionary methods, whereas the hybrid approach can outperform the best-known hybrid evolutionary solution methods for certain problem classes. The hybrid ACO approach is also shown to require different parameter values from the pure ACO approach and to give a more robust performance across different problems with a single set of parameter values. The local search algorithm is also run with random restarts and shown to perform significantly worse than when combined with ACO.     

A Hybrid Metaheuristic for the Quadratic Assignment Problem

The quadratic assignment problem (QAP) is known to be NP-hard. We propose a hybrid metaheuristic called ANGEL to solve QAP. ANGEL combines the ant colony optimization (ACO), the genetic algorithm (GA) and a local search method (LS). There are two major phases in ANGEL, namely ACO phase and GA phase. Instead of starting from a population that consists of randomly generated chromosomes, GA has an initial population constructed by ACO in order to provide a good start. Pheromone acts as a feedback mechanism from GA phase to ACO phase. When GA phase reaches the termination criterion, control is transferred back to ACO phase. Then ACO utilizes pheromone updated by GA phase to explore solution space and produces a promising population for the next run of GA phase. The local search method is applied to improve the solutions obtained by ACO and GA. We also propose a new concept called the eugenic strategy intended to guide the genetic algorithm to evolve toward a better direction. We report the results of a comprehensive testing of ANGEL in solving QAP. Over a hundred instances of QAP benchmarks were tested and the results show that ANGEL is able to obtain the optimal solution with a high success rate of 90%. This work was supported in part by the National Science Council, R.O.C., under Contract NSC 91-2213-E-005-017.     

Ant Colony Optimisation for Machine Layout Problems

Flexible machine layout problems describe the dynamic arrangement of machines to optimise the trade-off between material handling and rearrangement costs under changing and uncertain production environments. A previous study used integer-programming techniques to solve heuristically reduced versions of the problem. As an alternative, this paper introduces an ant colony optimisation (ACO) algorithm to generate good solutions. Experimental results are presented, with ACO obtaining better solutions than the reduction heuristic.     

Concave minimum cost network flow problems solved with a colony of ants

In this work we address the Single-Source Uncapacitated Minimum Cost Network Flow Problem with concave cost functions. This problem is NP-Hard, therefore we propose a hybrid heuristic to solve it. Our goal is not only to apply an ant colony optimization (ACO) algorithm to such a problem, but also to provide an insight on the behaviour of the parameters in the performance of the algorithm. The performance of the ACO algorithm is improved with the hybridization of a local search (LS) procedure. The core ACO procedure is used to mainly deal with the exploration of the search space, while the LS is incorporated to further cope with the exploitation of the best solutions found. The method we have developed has proven to be very efficient while solving both small and large size problem instances. The problems we have used to test the algorithm were previously solved by other authors using other population based heuristics. Our algorithm was able to improve upon some of their results in terms of solution quality, proving that the HACO algorithm is a very good alternative approach to solve these problems. In addition, our algorithm is substantially faster at achieving these improved solutions. Furthermore, the magnitude of the reduction of the computational requirements grows with problem size.     

Solving the post enrolment course timetabling problem by ant colony optimization

In this work we present a new approach to tackle the problem of Post Enrolment Course Timetabling as specified for the International Timetabling Competition 2007 (ITC2007), competition track 2. The heuristic procedure is based on Ant Colony Optimization (ACO) where artificial ants successively construct solutions based on pheromones (stigmergy) and local information. The key feature of our algorithm is the use of two distinct but simplified pheromone matrices in order to improve convergence but still provide enough flexibility for effectively guiding the solution construction process. We show that by parallelizing the algorithm we can improve the solution quality significantly. We applied our algorithm to the instances used for the ITC2007. The results document that our approach is among the leading algorithms for this problem; in all cases the optimal solution could be found. Furthermore we discuss the characteristics of the instances where the algorithm performs especially well.     

A hybrid metaheuristic for the resource-constrained project scheduling problem

This study presents a hybrid metaheuristic ANGEL for the resource-constrained project scheduling problem (RCPSP). ANGEL combines ant colony optimization (ACO), genetic algorithm (GA) and local search strategy. The procedures of ANGEL are as follows. First, ACO searches the solution space and generates activity lists to provide the initial population for GA. Next, GA is executed and the pheromone set in ACO is updated when GA obtains a better solution. When GA terminates, ACO searches again by using a new pheromone set. ACO and GA search alternately and cooperatively in the solution space. This study also proposes an efficient local search procedure which is applied to yield a better solution when ACO or GA obtains a solution. A final search is applied upon the termination of ACO and GA. The experimental results of ANGEL on the standard sets of the project instances show that ANGEL is an effective method for solving the RCPSP.     

Metaheuristics for scheduling jobs with incompatible families on parallel batching machines

In this paper, we discuss the scheduling of jobs with incompatible families on parallel batching machines. The performance measure is total weighted tardiness. This research is motivated by a scheduling problem found in the diffusion and oxidation areas of semiconductor wafer fabrication where the machines can be modelled as parallel batch processors. Given that this scheduling problem is NP-hard, we suggest an ant colony optimization (ACO) and a variable neighbourhood search (VNS) approach. Both metaheuristics are hybridized with a decomposition heuristic and a local search scheme. We compare the performance of the two algorithms with that of a genetic algorithm (GA) based on extensive computational experiments. The VNS approach outperforms the ACO and GA approach with respect to time and solution quality.     

An improved approach to attribute reduction with ant colony optimization

Attribute reduction problem (ARP) in rough set theory (RST) is an NPhard one, which is difficult to be solved via traditionally analytical methods. In this paper, we propose an improved approach to ARP based on ant colony optimization (ACO) algorithm, named the improved ant colony optimization (IACO). In IACO, a new state transition probability formula and a new pheromone traps updating formula are developed in view of the differences between a traveling salesman problem and ARP. The experimental results demonstrate that IACO outperforms classical ACO as well as particle swarm optimization used for attribute reduction.     

部分联合运输策略下的物流车辆路径优化问题研究

论文分析了物流车辆路径优化问题的特点,提出了企业自营物流和第三方物流协同运输的部分联合运输策略。根据客户需求节点的特点进行了节点分类,建立了以车辆调用成本、车辆运输成本、第三方物流运输成本之和最小为目标的整数线性规划模型。根据部分联合运输策略下各类客户需求点运输方式特点,构造了一种新的变维数矩阵编码结构,并对传统算法中概率选择操作方式进行修改,提出了一种新的智能优化算法并与枚举法和遗传算法的运算结果进行了算法性能对比分析。结果显示,本文提出的逆选择操作蚁群算法具有较快的运算速度和较高的稳定性,是求解此类问题的一种有效算法。     

Analytical and stochastic modelling techniques

In mining supply chains, large combinatorial optimization problems arise. These are NP-hard and typically require a large number of computing resources to solve them. In particular, the run-time overheads can become increasingly prohibitive with increasing problem sizes. Parallel methods provide a way to manage such run-time issues by utilising several processors in independent or shared memory architectures. However it is not obvious how to adapt serial optimisation algorithms to perform best in a parallel environment. Here, we consider a resource constrained scheduling problem which is motivated in mining supply chains and present two popular meta-heuristics, ant colony optimization (ACO) and simulated annealing and investigate how best to parallelize these methods on a shared memory architecture consisting of several cores. ACO’s solution construction framework is inherently parallel allowing a relatively straightforward parallel implementation. However, for best performance, ACO needs an element of local search. This significantly complicates the paralellization. Several alternative schemes for parallel ACO with elements of local search are considered and evaluated empirically. We find that ACO with local search is the most effective single-threaded algorithm. The best parallel implementation can obtain similar quality results to the serial method in significantly less elapsed time.     

A novel ant colony optimization approach for on-line scheduling and due date determination

This paper aims to develop an on-line Ant Colony Optimization (ACO) framework, where jobs arrive over time, and at any time we lack knowledge concerning future jobs. A due date is determined upon job arrival, and jobs are sequenced on the machine to optimize the sum of weighted lead times with all due dates met. We propose that each ant is associated with a sequence of waiting jobs with quoted due dates. This waiting sequence is constantly updated over time (whenever a job is selected to be processed or a new job arrives). The on-line schedule is constructed by selecting the first job in the waiting list of the “best” ant to process (along with its due date) as the machine becomes available. However, for the ant where this job is not the first one in the list, processing it pushes back the waiting jobs positioned before it. If such push back results in a due date violation, this ant will be eliminated. Further, our ACO framework does not include the iterative procedure due to the characteristics of the on-line problem; this is one difference from the traditional ACO framework besides ant elimination. The computational testing on generated instances shows that our ACO algorithm outperforms an existing effective on-line algorithm in the literature. Also, with local search incorporated using the EDD (Earliest Due Date) rule, improvements can be obtained in both computational outcome and time.     

Surface Reconstruction by Voronoi Filtering

We give a simple combinatorial algorithm that computes a piecewise-linear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled surfaces, where density depends on a local feature size function, the output is topologically valid and convergent (both pointwise and in surface normals) to the original surface. We briefly describe an implementation of the algorithm and show example outputs. Received August 25, 1998, and in revised form March 31, 1999.     

A new solution algorithm for improving performance of ant colony optimization

This study proposes an improved solution algorithm using ant colony optimization (ACO) for finding global optimum for any given test functions. The procedure of the ACO algorithms simulates the decision-making processes of ant colonies as they forage for food and is similar to other artificial intelligent techniques such as Tabu search, Simulated Annealing and Genetic Algorithms. ACO algorithms can be used as a tool for optimizing continuous and discrete mathematical functions. The proposed algorithm is based on each ant searches only around the best solution of the previous iteration with β. The proposed algorithm is called as ACORSES, an abbreviation of ACO Reduced SEarch Space. β is proposed for improving ACO’s solution performance to reach global optimum fairly quickly. The ACORSES is tested on fourteen mathematical test functions taken from literature and encouraging results were obtained. The performance of ACORSES is compared with other optimization methods. The results showed that the ACORSES performs better than other optimization algorithms, available in literature in terms of minimum values of objective functions and number of iterations.     

An Ant Colony Algorithm for the Capacitated Vehicle Routing

The Vehicle Routing Problem (VRP) requires the determination of an optimal set of routes for a set of vehicles to serve a set of customers. We deal here with the Capacitated Vehicle Routing Problem (CVRP) where there is a maximum weight or volume that each vehicle can load. We developed an Ant Colony algorithm (ACO) for the CVRP based on the metaheuristic technique introduced by Colorni, Dorigo and Maniezzo. We present preliminary results that show that ant algorithms are competitive with other metaheuristics for solving CVRP.     

Autonomous localization based energy saving mechanism in indoor MANETs using ACO

The biggest challenge in MANETs is to find most efficient routing due to the changing topology and energy constrained battery operated computing devices. It has been found that Ant Colony Optimization (ACO) is a special kind of optimization technique having characterization of Swarm Intelligence (SI) which is highly suitable for finding the adaptive routing for such a type of volatile network. The proposed ACO routing algorithm uses position information and energy parameters as a routing metric to improve the performance and lifetime of network. Typical routing protocols have fixed transmission power irrespective of the distance between the nodes. Considering limiting factors, like small size, limited computational power and energy source, the proposed solution excludes use of GPS for identifying the distance between nodes for indoor MANETs. The distance between nodes can be determined by using Received Signal Strength Indicator (RSSI) measurements. Thus, an intelligent ACO routing algorithm with location information and energy metric is developed to adaptively adjust the transmission power and distribute the load to avoid critical nodes. Proposed Autonomous Localization based Eligible Energetic Path_with_Ant Colony Optimization (ALEEP_with_ACO) algorithm ensures that nodes in the network are not drained out of the energy beyond their threshold, as the load is shared with other nodes, when the energy of a node in the shortest path has reached its threshold. Hence, the total energy expenditure is reduced, thus prolonging the lifetime of network devices and the network. We simulated our proposal and compared it with the classical approach of AODV and other biological routing approaches. The results achieved show that ALEEP_with_ACO presents the best Packet Delivery Ratio (PDR), throughput and less packet drop specially under high mobility scenarios.     

Applying Ant System for solving Unequal Area Facility Layout Problems

Ant Colony Optimization (ACO) is a young metaheuristic algorithm which has shown promising results in solving many optimization problems. To date, a formal ACO-based metaheuristic has not been applied for solving Unequal Area Facility Layout Problems (UA-FLPs). This paper proposes an Ant System (AS) (one of the ACO variants) to solve them. As a discrete optimization algorithm, the proposed algorithm uses slicing tree representation to easily represent the problems without too restricting the solution space. It uses several types of local search to improve its search performance. It is then tested using several case problems with different size and setting. Overall, the proposed algorithm shows encouraging results in solving UA-FLPs.