An efficient ant colony system based on receding horizon control for the aircraft arrival sequencing and scheduling problem

The aircraft arrival sequencing and scheduling (ASS) problem is a salient problem in air traffic control (ATC), which proves to be nondeterministic polynomial (NP) hard. This paper formulates the ASS problem in the form of a permutation problem and proposes a new solution framework that makes the first attempt at using an ant colony system (ACS) algorithm based on the receding horizon control (RHC) to solve it. The resultant RHC-improved ACS algorithm for the ASS problem (termed the RHC-ACS-ASS algorithm) is robust, effective, and efficient, not only due to that the ACS algorithm has a strong global search ability and has been proven to be suitable for these kinds of NP-hard problems but also due to that the RHC technique can divide the problem with receding time windows to reduce the computational burden and enhance the solution's quality. The RHC-ACS-ASS algorithm is extensively tested on the cases from the literatures and the cases randomly generated. Comprehensive investigations are also made for the evaluation of the influences of ACS and RHC parameters on the performance of the algorithm. Moreover, the proposed algorithm is further enhanced by using a two-opt exchange heuristic local search. Experimental results verify that the proposed RHC-ACS-ASS algorithm generally outperforms ordinary ACS without using the RHC technique and genetic algorithms (GAs) in solving the ASS problems and offers high robustness, effectiveness, and efficienc

An interacting replica approach applied to the traveling salesman problem

We present a physics inspired heuristic method for solving combinatorial optimization problems. Our approach is specifically motivated by the desire to avoid trapping in metastable local minima- a common occurrence in hard problems with multiple extrema. Our method involves (i) coupling otherwise independent simulations of a system ("replicas") via geometrical distances as well as (ii) probabilistic inference applied to the solutions found by individual replicas. The {\it ensemble} of replicas evolves as to maximize the inter-replica correlation while simultaneously minimize the local intra-replica cost function (e.g., the total path length in the Traveling Salesman Problem within each replica). We demonstrate how our method improves the performance of rudimentary local optimization schemes long applied to the NP hard Traveling Salesman Problem. In particular, we apply our method to the well-known "$k$-opt" algorithm and examine two particular cases- $k=2$ and $k=3$. With the aid of geometrical coupling alone, we are able to determine for the optimum tour length on systems up to $280$ cities (an order of magnitude larger than the largest systems typically solved by the bare $k=3$ opt). The probabilistic replica-based inference approach improves $k-opt$ even further and determines the optimal solution of a problem with $318$ cities and find tours whose total length is close to that of the optimal solutions for other systems with a larger number of cities.Comment: To appear in SAI 2016 conference proceedings 12 pages,17 figure

An Efficient Solution to Travelling Salesman Problem using Genetic Algorithm with Modified Crossover Operator

The traveling salesman problem (TSP) is a famous NP-hard problem in the area of combinatorial optimization. It is utilized to locate the shortest possible route that visits every city precisely once and comes back to the beginning point from a given set of cities and distance. This paper proposes an efficient and effective solution for solving such a query. A modified crossover method using Minimal Weight Variable, Order Selection Crossover operator, a modified mutation using local optimization and a modified selection method using KMST is proposed. The crossover operator (MWVOSX) chooses a particular order from multiple orders which have the minimum cost and takes the remaining from the other parent in backward and forward order. Then it creates two new offspring. Further, it selects the least weight new offspring from those two offspring. The efficiency of the proposed algorithm is compared to the classical genetic algorithm. Comparisons show that our proposed algorithm provides much efficient results than the existing classical genetic algorithm

Fuzzy Expert Ants to speed up big TSP Problems using ACS

Ant colony algorithms are a group of heuristic optimization algorithms that have been inspired by behavior of real ants foraging for food. In these algorithms some simple agents (i.e. ants), search the solution space for finding the suitable solution. Ant colony algorithms have many applications to computer science problems especially in optimization, such as machine drill optimization, and routing. This group of algorithms have some sensitive parameters controlling the behavior of agents, like relative pheromone importance on trail and pheromone decay coefficient. Convergence and efficiency of algorithms is highly related to these parameters. Optimal value of these parameters for a specific problem is determined through trial and error and does not obey any rule. Some approaches proposed to adapt parameter of these algorithms for better answer. The most important feature of the current adaptation algorithms are complication and time overhead. In this paper we have presented a simple and efficient approach based on fuzzy logic for optimizing ACS algorithm and by using different experiments efficiency of this proposed approach has been evaluated and we have shown that the presented concept is one of the most important reasons in success for parameter adapting algorithms

The Anglerfish algorithm: A derivation of randomized incremental construction technique for solving the traveling salesman problem

Combinatorial optimization focuses on arriving at a globally optimal solution given constraints, incomplete information and limited computational resources. The combination of possible solutions are rather vast and often overwhelms the limited computational power. Smart algorithms have been developed to address this issue. Each offers a more efficient way of traversing the search landscapes. Critics have called for a realignment in the bio-inspired metaheuristics field. We propose an algorithm that simplifies the search operation to only randomized population initialization following the Randomized Incremental Construction Technique, which essentially compartmentalizes optimization into smaller sub-units. This relieves the need of complex operators normally imposed on the current metaheuristics pool. The algorithm is more generic and adaptable to any optimization problems. Benchmarking is conducted using the traveling salesman problem. The results are comparable with the results of advanced metaheuristic algorithms. Hence, suggesting that arbitrary exploration is practicable as an operator to solve optimization problems. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature

An Improved Modular Hybrid Ant Colony Approach for Solving Traveling Salesman Problem

Our primary aim is to design a framework to solve the well knowntraveling salesman problem(TSP) using combined approach ofAnt Colony Optimization (ACO) and Genetic Algorithm (GA).Several solutions exists for the above problem using ACO or GAand even using a hybrid approach of ACO and GA. Ourframework gives the optimal solution for the above problem byusing the modular hybrid approach of ACO and GA along withheuristic approaches.We have incorporated GA, RemoveSharpand LocalOpt heuristic approaches in ACO module, hence eachiteration calls the GA and heuristics within ACO module whichresults in a higher amount of pheromone deposited in the optimalpath for global pheromone update. As a result the convergence isquicker and solution is optimal