Combinatorial Ant Optimization and the Flowshop Problem

Researchers have developed efficient techniques, meta-heuristics to solve many Combinatorial Optimization (CO) problems, e.g., Flow shop Scheduling Problem, Travelling Salesman Problem (TSP) since the early 60s of the last century. Ant Colony Optimization (ACO) and its variants were introduced by Dorigo et al. [DBS06] in the early 1990s which is a technique to solve CO problems. In this thesis, we used the ACO technique to find solutions to the classic Flow shop Scheduling Problem and proposed a novel method for solution improvement. Our solution is composed of two phases; in the first phase, we solved TSP using ACO technique which gave us an initial permutation or tour. We used the same trip as an initial solution for our problem and then improved it by using 2-opt exchanges which yielded in a promising result. Furthermore, we introduced another improvement technique which gave us a more promising result. We have compared our results with the best (optimal) and worst solution known till date. A comprehensive experimental study using existing dataset proves that our approach remarkably gives good results

A New Spatial Approach for Efficient Transformation of Equality - Generalized TSP to TSP

The Equality - Generalized Travelling Salesman Problem (E-GTSP) asks to find a Hamiltonian cycle visiting each group exactly once, where each group represents a type of visiting node. This can represent a range of combinatorial optimization problem of NP-hard type like planning, logistics, etc. Its solution requires transformation of E-GTSP to TSP before solving it using a given TSP solver. This paper presents 5 different search-algorithms for optimal transformation which considers spatial spread of nodes of each group. Algorithms are tested over 15 cities with different street-network’s fractal-dimension for 5 instances of group-counts each. It’s observed that the R-Search algorithm, which selects nodes from each group depending upon their radial separation with respect to the start-end point, is the optimal search criterion among all other algorithms with a mean length error of 8.8%. This study will help developers and researchers to answer complex routing problems from a spatial perspective

The 2-period balanced traveling salesman problem

In the 2-period Balanced Traveling Salesman Problem (2B-TSP), the customers must be visited over a period of two days: some must be visited daily, and the others on alternate days (even or odd days); moreover, the number of customers visited in every tour must be balancedâ, i.e. it must be the same or, alternatively, the difference between the maximum and the minimum number of visited customers must be less than a given threshold. The salesman's objective is to minimize the total distance travelled over the two tours. Although this problem may be viewed as a particular case of the Period Traveling Salesman Problem, in the 2-period Balanced TSP the assumptions allow for emphasizing on routing aspects, more than on the assignment of the customers to the various days of the period. The paper proposes two heuristic algorithms particularly suited for the case of Euclidean distances between the customers. Computational experiences and a comparison between the two algorithms are also given.

Exact/heuristic hybrids using rVNS and hyperheuristics for workforce scheduling

In this paper we study a complex real-world workforce scheduling problem. We propose a method of splitting the problem into smaller parts and solving each part using exhaustive search. These smaller parts comprise a combination of choosing a method to select a task to be scheduled and a method to allocate resources, including time, to the selected task. We use reduced Variable Neighbourhood Search (rVNS) and hyperheuristic approaches to decide which sub problems to tackle. The resulting methods are compared to local search and Genetic Algorithm approaches. Parallelisation is used to perform nearly one CPU-year of experiments. The results show that the new methods can produce results fitter than the Genetic Algorithm in less time and that they are far superior to any of their component techniques. The method used to split up the problem is generalisable and could be applied to a wide range of optimisation problems

A vehicle routing model with split delivery and stop nodes

In this work, a new variant of the Capacitated Vehicle Routing Problem (CVRP) is presented where the vehicles cannot perform any route leg longer than a given length L (although the routes can be longer). Thus, once a route leg length is close to L, the vehicle must go to a stop node to end the leg or return to the depot. We introduce this condition in a variation of the CVRP, the Split Delivery Vehicle Routing Problem, where multiple visits to a customer by different vehicles are allowed. We present two formulations for this problem which we call Split Delivery Vehicle Routing Problem with Stop Nodes: a vehicle flow formulation and a commodity flow formulation. Because of the complexity of this problem, a heuristic approach is developed. We compare its performance with and without the stop nodesSplit delivery vehicle routing problem, Stop node, Granular neighborhood, Tabu search

A study on exponential-size neighborhoods for the bin packing problem with conflicts

We propose an iterated local search based on several classes of local and large neighborhoods for the bin packing problem with conflicts. This problem, which combines the characteristics of both bin packing and vertex coloring, arises in various application contexts such as logistics and transportation, timetabling, and resource allocation for cloud computing. We introduce $O(1)$ evaluation procedures for classical local-search moves, polynomial variants of ejection chains and assignment neighborhoods, an adaptive set covering-based neighborhood, and finally a controlled use of 0-cost moves to further diversify the search. The overall method produces solutions of good quality on the classical benchmark instances and scales very well with an increase of problem size. Extensive computational experiments are conducted to measure the respective contribution of each proposed neighborhood. In particular, the 0-cost moves and the large neighborhood based on set covering contribute very significantly to the search. Several research perspectives are open in relation to possible hybridizations with other state-of-the-art mathematical programming heuristics for this problem.Comment: 26 pages, 8 figure