Many-objective optimization refers to the problems containing large number of objectives, typically more than four. Non-dominance is an inadequate strategy for convergence Pareto front such problems, as almost all solutions in population become non-dominated, resulting loss pressure. However, some it may be possible generate using only a few rendering rest objectives redundant. Such reducible manageable relevant which can optimized conventional multiobjective evolutionary algorithms (MOEAs)....

We present a family of tests for detecting initialization bias in the mean simulation output series using hypothesis testing framework. The null is that does not change throughout run. alternative specifies general transient function. are asymptotically optimal based on cumulative sums deviations about sample mean. A particular test this applied to variety models. requires very modest computation and appears be both robust powerful.

Many-objective optimization problems (MaOPs) contain four or more conflicting objectives to be optimized. A number of efficient decomposition-based evolutionary algorithms have been developed in the recent years solve them. However, computationally expensive MaOPs scarcely investigated. Typically, surrogate-assisted methods used literature tackle problems, but such studies largely focused on with 1-3 objectives. In this paper, we present an approach called hybrid many-objective algorithm...

Multiobjective optimization problems with more than three objectives are commonly referred to as many-objective (MaOPs). Development of algorithms solve MaOPs has garnered significant research attention in recent years. "Decomposition" is a adopted approach toward this aim, wherein the problem divided into set simpler subproblems guided by reference vectors. The vectors often predefined and distributed uniformly objective space. Use such uniform distribution shown commendable performance on...

A number of real-world problems involve extremization multiple conflicting objectives, referred to as multiobjective optimization problems. Multiobjective evolutionary algorithms (MOEAs) have been widely adopted obtain Pareto front (PF) approximation for such An indispensable step in development and evaluation MOEAs is benchmarking, which involves comparisons with peer using performance metrics, hypervolume (HV) inverted generational distance (IGD). However, the de-facto practice use final...

Bilevel optimization refers to a hierarchical problem in which needs be performed at two nested levels, namely the upper level and lower level. The aim is identify optimum of problem, subject optimality corresponding problem. Several problems from domain engineering, logistics, economics, transportation have inherent structure requires them modeled as bilevel problems. usually inordinate amount function evaluations since search conducted for evaluating each solution. are especially high when...

Robust design optimization aims to find solutions that are competent and reliable under given uncertainties. While such uncertainties can emerge from a number of sources (imprecise variable values, errors in performance estimates, varying environmental conditions, etc.), this paper focuses on problems where emanate variables. In commercial designs, being is often more practical value than globally best (but unreliable). poses three key challenges: 1) appropriate formulation the problem ; 2)...

The field of many-objective optimization has grown out infancy and a number contemporary algorithms can deliver well converged diverse sets solutions close to the Pareto optimal front. Concurrently, studies in cognitive science have highlighted pitfalls imprecise decision-making presence large alternatives. Thus, for effective decision-making, it is important devise methods identify handful (7 ± 2) from potentially set tradeoff solutions. Existing measures such as reflex/bend angle, expected...

Bilevel optimization, as the name reflects, deals with optimization at two interconnected hierarchical levels. The aim is to identify optimum of an upper-level leader problem, subject optimality a lower-level follower problem. Several problems from domain engineering, logistics, economics, and transportation have inherent nested structure which requires them be modeled bilevel problems. Increasing size complexity such has prompted active theoretical practical interest in design efficient...

A number of population based optimization algorithms have been proposed in recent years to solve unconstrained and constrained single multi-objective problems. Most such inherently prefer a feasible solution over an infeasible one during the course search, which translates approaching constraint boundary from side search space. Previous studies [1], [2] already demonstrated benefits explicitly maintaining fraction solutions Infeasiblity Driven Evolutionary Algorithm (IDEA) for multiobjective...

In engineering design optimization, evaluation of a single solution (design) often requires running one or more computationally expensive simulations. Surrogate assisted optimization (SAO) approaches have long been used for solving such problems, in which approximations/surrogates are lieu simulations during the course search. Existing SAO use same type approximation model to represent all objectives and constraints regions search space. The selection surrogate over another is nontrivial an...

Constrained optimization problems (COPs) are frequently encountered in real-world design applications. For some COPs, the evaluation of objective(s) and/or constraint(s) may involve significant computational/temporal/financial cost. Such referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">expensive</i> COPs (ECOPs). Surrogate modeling has been widely used conjunction with methods for such problems, wherein search is partially...