A Perturbed Self-organizing Multiobjective Evolutionary Algorithm to solve Multiobjective TSP

Travelling Salesman Problem (TSP) is a very important NP-Hard problem getting focused more on these days. Having improvement on TSP, right now consider the multi-objective TSP (MOTSP), broadened occurrence of travelling salesman problem. Since TSP is NP-hard issue MOTSP is additionally a NP-hard issue. There are a lot of algorithms and methods to solve the MOTSP among which Multiobjective evolutionary algorithm based on decomposition is appropriate to solve it nowadays. This work presents a new algorithm which combines the Data Perturbation, Self-Organizing Map (SOM) and MOEA/D to solve the problem of MOTSP, named Perturbed Self-Organizing multiobjective Evolutionary Algorithm (P-SMEA). In P-SMEA Self-Organizing Map (SOM) is used extract neighborhood relationship information and with MOEA/D subproblems are generated and solved simultaneously to obtain the optimal solution. Data Perturbation is applied to avoid the local optima. So by using the P-SMEA, MOTSP can be handled efficiently. The experimental results show that P-SMEA outperforms MOEA/D and SMEA on a set of test instances

Hybridization of Decomposition and Local Search for Multiobjective Optimization

Combining ideas from evolutionary algorithms, decomposition approaches, and Pareto local search, this paper suggests a simple yet efficient memetic algorithm for combinatorial multiobjective optimization problems: memetic algorithm based on decomposition (MOMAD). It decomposes a combinatorial multiobjective problem into a number of single objective optimization problems using an aggregation method. MOMAD evolves three populations: 1) population PLfor recording the current solution to each subproblem; 2) population PPfor storing starting solutions for Pareto local search; and 3) an external population PEfor maintaining all the nondominated solutions found so far during the search. A problem-specific single objective heuristic can be applied to these subproblems to initialize the three populations. At each generation, a Pareto local search method is first applied to search a neighborhood of each solution in PPto update PLand PE. Then a single objective local search is applied to each perturbed solution in PLfor improving PLand PE, and reinitializing PP. The procedure is repeated until a stopping condition is met. MOMAD provides a generic hybrid multiobjective algorithmic framework in which problem specific knowledge, well developed single objective local search and heuristics and Pareto local search methods can be hybridized. It is a population based iterative method and thus an anytime algorithm. Extensive experiments have been conducted in this paper to study MOMAD and compare it with some other state-of-the-art algorithms on the multiobjective traveling salesman problem and the multiobjective knapsack problem. The experimental results show that our proposed algorithm outperforms or performs similarly to the best so far heuristics on these two problems

Robustness of Mission Plans for Unmanned Aircraft.

This thesis studies the robustness of optimal mission plans for unmanned aircraft. Mission planning typically involves tactical planning and path planning. Tactical planning refers to task scheduling and in multi aircraft scenarios also includes establishing a communication topology. Path planning refers to computing a feasible and collision-free trajectory. For a prototypical mission planning problem, the traveling salesman problem on a weighted graph, the robustness of an optimal tour is analyzed with respect to changes to the edge costs. Specifically, the stability region of an optimal tour is obtained, i.e., the set of all edge cost perturbations for which that tour is optimal. The exact stability region of solutions to variants of the traveling salesman problems is obtained from a linear programming relaxation of an auxiliary problem. Edge cost tolerances and edge criticalities are derived from the stability region. For Euclidean traveling salesman problems, robustness with respect to perturbations to vertex locations is considered and safe radii and vertex criticalities are introduced. For weighted-sum multi-objective problems, stability regions with respect to changes in the objectives, weights, and simultaneous changes are given. Most critical weight perturbations are derived. Computing exact stability regions is intractable for large instances. Therefore, tractable approximations are desirable. The stability region of solutions to relaxations of the traveling salesman problem give under approximations and sets of tours give over approximations. The application of these results to the two-neighborhood and the minimum 1-tree relaxation are discussed. Bounds on edge cost tolerances and approximate criticalities are obtainable likewise. A minimum spanning tree is an optimal communication topology for minimizing the cumulative transmission power in multi aircraft missions. The stability region of a minimum spanning tree is given and tolerances, stability balls, and criticalities are derived. This analysis is extended to Euclidean minimum spanning trees. This thesis aims at enabling increased mission performance by providing means of assessing the robustness and optimality of a mission and methods for identifying critical elements. Examples of the application to mission planning in contested environments, cargo aircraft mission planning, multi-objective mission planning, and planning optimal communication topologies for teams of unmanned aircraft are given.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120837/1/mniendo_1.pd

A hybrid CFGTSA based approach for scheduling problem: a case study of an automobile industry

In the global competitive world swift, reliable and cost effective production subject to uncertain situations, through an appropriate management of the available resources, has turned out to be the necessity for surviving in the market. This inspired the development of the more efficient and robust methods to counteract the existing complexities prevailing in the market. The present paper proposes a hybrid CFGTSA algorithm inheriting the salient features of GA, TS, SA, and chaotic theory to solve the complex scheduling problems commonly faced by most of the manufacturing industries. The proposed CFGTSA algorithm has been tested on a scheduling problem of an automobile industry, and its efficacy has been shown by comparing the results with GA, SA, TS, GTS, and hybrid TSA algorithms

Stability measure for a generalized assembly line balancing problem

AbstractA generalized formulation for assembly line balancing problem (GALBP) is considered, where several workplaces are associated with each workstation. Thus, all tasks assigned to the same workstation have to be partitioned into blocks: each block regroups all tasks to be performed at the same workplace. The product items visit all workplaces sequentially, therefore, all blocks are proceeded in a sequential way. However, the tasks grouped into the same block are executed simultaneously. As a consequence, the execution of a block takes only the time of its longest task. This parallel execution modifies the manner to take into account the cycle time constraint. Precedence and exclusion constraints also exist for workstations and their workplaces. The objective is to assign all given tasks to workstations and workplaces while minimizing the line cost estimated as a weighted sum of the number of workstations and workplaces. The goal of this article is to propose a stability measure for feasible and optimal solutions of this problem with regard to possible variations of the processing time of certain tasks. A heuristic procedure providing a compromise between the objective function and the suggested stability measure is developed and evaluated on benchmark data sets

Efficiently Constructing Convex Approximation Sets in Multiobjective Optimization Problems

Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the approximation set up to a multiplicative factor in each component, a convex approximation set only requires this multiplicative approximation to be achieved by some convex combination of finitely many images of solutions in the set. This makes convex approximation sets efficiently computable for a wide range of multiobjective problems - even for many problems for which (classic) approximations sets are hard to compute. In this article, we propose a polynomial-time algorithm to compute convex approximation sets that builds upon an exact or approximate algorithm for the weighted sum scalarization and is, therefore, applicable to a large variety of multiobjective optimization problems. The provided convex approximation quality is arbitrarily close to the approximation quality of the underlying algorithm for the weighted sum scalarization. In essence, our algorithm can be interpreted as an approximate variant of the dual variant of Benson's Outer Approximation Algorithm. Thus, in contrast to existing convex approximation algorithms from the literature, information on solutions obtained during the approximation process is utilized to significantly reduce both the practical running time and the cardinality of the returned solution sets while still guaranteeing the same worst-case approximation quality. We underpin these advantages by the first comparison of all existing convex approximation algorithms on several instances of the triobjective knapsack problem and the triobjective symmetric metric traveling salesman problem