In this paper, we introduce the Steiner Bi-objective Shortest Path Problem. This problem is defined on a directed graph G=(V,A), with subset T?V of terminals. Arcs are labeled travel time and cost. The goal to find complete set efficient paths between every pair nodes in T. motivation behind stems from data preprocessing for vehicle routing problems. We propose solution method based labeling ap...

The most important issue in multi-objective optimization problems is to determine the Pareto points along the Pareto frontier. If the optimization problem involves multiple conflicting objectives, the results obtained from the Pareto-optimality will have the trade-off solutions that shaping the Pareto frontier. Each of these solutions lies at the boundary of the Pareto frontier, such that the i...

Some recent works in machine learning and computer vision involve the solution of a bilevel optimization problem. Here the solution of a parameterized lower-level problem binds variables that appear in the objective of an upper-level problem. The lower-level problem typically appears as an argmin or argmax optimization problem. Many techniques have been proposed to solve bi-level optimization p...

hub covering problem (hlp) is a very popular areas of research for its wide ranges of applications in different service or manufacturing industries. this paper considers a bi-objective hub covering location problem with congestion. the objectives minimize the total transportation cost and the total waiting time for all hobs, respectively. the resulted multi-objective decision-making problem is ...

The difficulty to solve multiple objective combinatorial optimization problems with traditional techniques has urged researchers to look for alternative, better performing approaches for them. Recently, several algorithms have been proposed which are based on the Ant Colony Optimization metaheuristic. In this contribution, the existing algorithms of this kind are reviewed and a proposal of a ta...

....... The fast and elitist non-dominated sorting genetic algorithm (NSGA-II) contains a mechanism to sort individuals in a multi-objective optimization problem into non-dominated fronts, based on their performance in each optimization variable. When dealing with a bi-objective problem it is possible to carry-out the non-dominated sorting more efficiently, using the new sorting method presente...

Distribution centers (DCs) play important role in maintaining the uninterrupted flow of goods and materials between the manufacturers and their customers.This paper proposes a mathematical model as the bi-objective capacitated multi-vehicle allocation of customers to distribution centers. An evolutionary algorithm named non-dominated sorting ant colony optimization (NSACO) is used as the optimi...