New Heuristic Algorithms for Solving Single-Vehicle and Multi-Vehicle Generalized Traveling Salesman Problems (GTSP)

Among numerous NP-hard problems, the Traveling Salesman Problem (TSP) has been one of the most explored, yet unknown one. Even a minor modification changes the problem’s status, calling for a different solution. The Generalized Traveling Salesman Problem (GTSP)expands the TSP to a much more complicated form, replacing single nodes with a group or cluster of nodes, where the objective is to find a minimum-length tour containing exactly one node from each cluster. In this paper, a new heuristic method is presented for solving singlevehicle single-depot GTSP with the ability of controlling the search strategy from conservative to greedy and vice versa. A variant algorithm is then developed to accommodate the multi-vehicle single-depot condition, which is modified afterwards to accommodate the multi-vehicle multi-depot GTSP

Fitness landscape analysis of the simple assembly line balancing problem type 1

As the simple assembly line balancing problem type 1 (SALBP1) has been proven to be NP-hard, heuristic and metaheuristic approaches are widely used for solving middle to large instances. Nevertheless, the characteristics (fitness landscape) of the problem’s search space have not been studied so far and no rigorous justification for implementing various metaheuristic methods has been presented. Aiming to fill this gap in the literature, this study presents the first comprehensive and in-depth Fitness Landscape Analysis (FLA) study for SALBP1. The FLA was performed by generating a population of 1000 random solutions and improving them to local optimal solution, and then measuring various statistical indices such as average distance, gap, entropy, amplitude, length of the walk, autocorrelation, and fitness-distance among all solutions, to understand the complexity, structure, and topology of the solution space. We solved 83 benchmark problems with various cycle times taken from Scholl’s dataset which required 83000 local searches from initial to optimal solutions. The analysis showed that locally optimal assembly line balances in SALBP1 are distributed nearly uniformly in the landscape of the problem, and the small average difference between the amplitudes of the initial and optimal solutions implies that the landscape was almost plain. In addition, the large average gap between local and global solutions showed that global optimum solutions in SALBP1 are difficult to find, but the problem can be effectively solved using a single-solution-based metaheuristic to near-optimality. In addition to the FLA, a new mathematical formulation for the entropy (diversity) of solutions in the search space for SALBP1 is also presented in this paper

Designing Solvable Graphs for Multiple Moving Agents

Solvable Graphs (also known as Reachable Graphs) are types of graphs that any arrangement of a specified number of agents located on the graph’s vertices can be reached from any initial arrangement through agents’ moves along the graph’s edges, while avoiding deadlocks (interceptions). In this paper, the properties of Solvable Graphs are investigated, and a new concept in multi agent motion planning, called Minimal Solvable Graphs is introduced. Minimal Solvable Graphs are the smallest graphs among Solvable Graphs in terms of the number of vertices. Also, for the first time, the problem of deciding whether a graph is Solvable for m agents is answered, and a new algorithm is presented for making an existing graph solvable and lean for a given number of agents. Finally, through an industrial example, it is demonstrated that how the findings of this paper can be used in designing and reshaping transportation networks (e.g. railways, traffic roads, AGV routs, robotic workspaces, etc.) for multiple moving agents such as trains, vehicles, and robots

Solving the n-Queens Problem Using a Tuned Hybrid Imperialist Competitive Algorithm

Abstract: The n-queens problem is a classical combinatorial optimization problem which has been proved to be NP-har