A Toolkit for Generating Scalable Stochastic Multiobjective Test Problems

Abstract

Real-world optimization problems typically include uncertainties over various aspects of the problem formulation. Some existing algorithms are designed to cope with stochastic multiobjective optimization problems, but in order to benchmark them, a proper framework still needs to be established. This paper presents a novel toolkit that generates scalable, stochastic, multiobjective optimization problems. A stochastic problem is generated by transforming the objective vectors of a given deterministic test problem into random vectors. All random objective vectors are bounded by the feasible objective space, defined by the deterministic problem. Therefore, the global solution for the deterministic problem can also serve as a reference for the stochastic problem. A simple parametric distribution for the random objective vector is defined in a radial coordinate system, allowing for direct control over the dual challenges of convergence towards the true Pareto front and diversity across the front. An example for a stochastic test problem, generated by the toolkit, is provided.

Multi-objective biased randomised iterated greedy for robust permutation flow shop scheduling problem under disturbances

“…The discretised decreasing triangular distribution is preferred for its practicality where it provides good results and also it does not have relatively straight forward parameters to set. The asymmetric discretised decreasing triangular distribution can be generally defended as follows (Salomon, Purshouse, Giaghiozis, and Fleming, 2016):…”

sParEGO – A Hybrid Optimization Algorithm for Expensive Uncertain Multi-objective Optimization Problems

“…This simulates the effect that stochasticity can have when approaching the Paretooptimal Front (PF). The second problem, namely P2, is characterised by having a more smooth landscape with no local minima surrounding the global optimum, and stochasticity is added by the toolkit from [10].…”

“…The effect of these parameters is shown in Figure 2, in that: the density of hills around the optimum increases with an increase in d as shown in Figure 2(a), and; the proximity of local minima from the value zero decreases with an increase in e as shown in Figure 2(b). The toolkit from [10] is used here to transform the objective vectors of WFG4 into random vectors. The parameters have been chosen to ensure that uncertainty increases towards more optimal regions.…”

Active Robust Optimization: Optimizing for Robustness of Changeable Products

“…A general description for the stochastic features in uncertain MOPs can be found in the studies of Goh et al (2010) and Salomon et al (2016b). Goh et al (2010) have developed a generic method that can transform any deterministic MOP into a stochastic one by injecting a parametric configurable noise function to various parts of the problem formulation.…”

“…Goh et al (2010) have developed a generic method that can transform any deterministic MOP into a stochastic one by injecting a parametric configurable noise function to various parts of the problem formulation. Salomon et al (2016b) have presented a toolkit to generate uncertain MOPs that allows for direct control over the stochastic properties of the problem.…”