Bat Algorithm for Multi-objective Optimisation

Engineering optimization is typically multiobjective and multidisciplinary with complex constraints, and the solution of such complex problems requires efficient optimization algorithms. Recently, Xin-She Yang proposed a bat-inspired algorithm for solving nonlinear, global optimisation problems. In this paper, we extend this algorithm to solve multiobjective optimisation problems. The proposed multiobjective bat algorithm (MOBA) is first validated against a subset of test functions, and then applied to solve multiobjective design problems such as welded beam design. Simulation results suggest that the proposed algorithm works efficiently.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1004.417

Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives

The properties of local optimal solutions in multi-objective combinatorial optimization problems are crucial for the effectiveness of local search algorithms, particularly when these algorithms are based on Pareto dominance. Such local search algorithms typically return a set of mutually nondominated Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper investigates two aspects of PLO-sets by means of experiments with Pareto local search (PLS). First, we examine the impact of several problem characteristics on the properties of PLO-sets for multi-objective NK-landscapes with correlated objectives. In particular, we report that either increasing the number of objectives or decreasing the correlation between objectives leads to an exponential increment on the size of PLO-sets, whereas the variable correlation has only a minor effect. Second, we study the running time and the quality reached when using bounding archiving methods to limit the size of the archive handled by PLS, and thus, the maximum size of the PLO-set found. We argue that there is a clear relationship between the running time of PLS and the difficulty of a problem instance.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII, Ljubljana : Slovenia (2014

Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives

The properties of local optimal solutions in multi-objective combinatorial optimization problems are crucial for the effectiveness of local search algorithms, particularly when these algorithms are based on Pareto dominance. Such local search algorithms typically return a set of mutually nondominated Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper investigates two aspects of PLO-sets by means of experiments with Pareto local search (PLS). First, we examine the impact of several problem characteristics on the properties of PLO-sets for multi-objective NK-landscapes with correlated objectives. In particular, we report that either increasing the number of objectives or decreasing the correlation between objectives leads to an exponential increment on the size of PLO-sets, whereas the variable correlation has only a minor effect. Second, we study the running time and the quality reached when using bounding archiving methods to limit the size of the archive handled by PLS, and thus, the maximum size of the PLO-set found. We argue that there is a clear relationship between the running time of PLS and the difficulty of a problem instance.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII, Ljubljana : Slovenia (2014

Using Stochastic Dominance in Multi-Objective Optimizers for Aerospace Design Under Uncertainty

In optimization under uncertainty for aerospace design, statistical moments of the quan- tity of interest are often treated as separate objectives and are traded off in a multi-objective optimization formulation. However, in many design problems the trade-off between sta- tistical moments can be large and the Pareto front representing this trade-off can include designs with undesirable behavior, such as being robust but being guaranteed to give a worse performance than another design. When a simulation of a system is computation- ally expensive, obtaining the full Pareto front is unfeasible and so spending optimization time obtaining such undesirable designs wastes time that could be spent obtaining more desirable alternatives. As a remedy, we propose an optimization formulation that can use multiple dominance criteria to avoid generating potentially inferior designs. We consider various orders of stochastic dominance as criteria to use alongside statistical moment based Pareto dominance, and illustrate how this gives rise to improved designs using a limited computational budget in an acoustic horn design problem and a transonic airfoil design problem.EPSRC DTA grant, grant number EP/L504920/