Contribution-Based Cooperative Co-Evolution for Nonseparable Large-Scale Problems With Overlapping Subcomponents

A Review of Population-Based Metaheuristics for Large-Scale Black-Box Global Optimization—Part II

“…Due to non-exclusive nature of the groups, this algorithm takes, to some extent, the overlapping nature of the problem into account. Jia et al [133] use variable interaction analysis to identify the underlying components of the objective function and their shared variables. They then use a contribution-based mechanism to promote components with a higher contribution towards improving the objective function and assign the shared variables the components with large contributions.…”

“…CCFR2 [146] improves upon CCFR by averaging the improvements per function evaluations to account for unequal subpopulations. CCFR2 [146] and some other algorithms [133,142] exponentially decay the effect of historical contributions. Ren et al [147] define the contribution as a function of both δ (t) k and the standard deviation across all components.…”

“…Ren et al [147] define the contribution as a function of both δ (t) k and the standard deviation across all components. Some authors suggested various normalization of δ (t) k [118,133,142,148,149] as the contribution of a component.…”

“…Shen et al [142] use a roulette-wheel selection mechanism based on the contributions. Jia et al [133] optimize all the components whose contribution is more than half the best contribution. Although not specifically designed to address the imbalance problem, overlapped CC [124] replicates influential decision variables in more than one component, which has the effect of optimizing influential variables more often.…”

“…Components in the first front as determined by non-dominated sorting CCFR [145] Weighted average of two most recent contributions (normalized) Equalize contributions then round-robin with stagnation detection CBCCO [133] Weighted average of all previous contributions Round-robin followed by all components with contributions higher than half of the best ICRA [142] Weighted average of all previous contributions Probabilistic roulette-wheel based on the contribution F3C [149] Most recent normalized contribution Round-robin followed by fuzzy rule-based allocation based on contribution and diversity these problems have two or more conflicting objectives causing them to have multiple trade-off solutions known as the Paretooptimal solutions. Scalability of multiobjective problems can be studied in either the objective space [157] or the decision space.…”