Two meanings of “many”
Multiple objectives and multiple modes solve different decision problems. A serious architecture must preserve the distinction.
Many definitions of quality
A candidate is assessed on several criteria—cost, time, quality, risk, energy or fairness. The desired output is a set of non-dominated trade-offs.
one search space → many objective valuesMany structurally different solutions
Several permutations may have equal or near-equal objective value while representing different routes, schedules, assignments or operational strategies.
one quality region → many solution structuresWhat multi-objective COIN already changes
Single-objective COIN can rank candidates by one scalar fitness value. With several objectives, no single scalar ordering is neutral. Improving one criterion may worsen another. The dissertation therefore combines the COIN generator with non-dominated sorting and crowding distance inspired by NSGA-II.
Illustrative objective space. The highlighted candidates form a non-dominated trade-off boundary; none is universally best without a preference.
Non-dominated rank defines quality
Candidate A dominates B when A is no worse in every objective and better in at least one. The first front contains candidates not dominated by any other candidate. Subsequent fronts describe progressively weaker trade-off layers.
Crowding distance protects spread
Rank alone can concentrate selection around a small region of the Pareto front. Crowding distance favours candidates in less populated objective-space neighborhoods, helping the evidence set cover more trade-offs.
COIN then learns from the selected trade-offs
The better and worse groups become multi-objective evidence interfaces. Incidences in well-ranked, diversity-supporting candidates are rewarded. Incidences in weak candidates may be punished. The matrix is still an edge model, but its evidence now arrives from a set of compromises rather than a single ordering.
Multi-objective learning architecture
The shared matrix is not merely an average of elite solutions. Its negative update changes the geometry of the search: coincidences repeatedly shared by poor candidates lose probability, so the generator spends less effort reconstructing the same unproductive substructures. At the same time, distinct positive building blocks belonging to different high-quality modes can retain probability in H.
COIN supports diversity not by assigning one generator to each mode, but by pruning shared negative structure while allowing several useful structures to coexist in one generator.
How a shared COIN generator retains multimodality
Suppose two production schedules have similar cost and makespan but use different worker allocations. Or two routes have nearly identical distance but use different roads. These are distinct modes: operationally meaningful alternatives that may occupy similar positions in objective space.
The important mechanism is selective suppression. If poor candidates from several regions repeatedly contain the same negative coincidence, punishment reduces that shared negative building block in H. This prunes a common route into weak regions of the search space. The building blocks that distinguish Mode A from Mode B do not need to be erased merely because they differ; when they remain associated with strong candidates, both can retain probability.
Multimodality is therefore difficult, but it does not require splitting the original COIN generator. It depends on whether reward preserves the structures of several strong modes and punishment removes negative structures without indiscriminately destroying their alternatives.
How negative-space pruning supports several modes
COIN keeps one shared generator. Its multimodal capability depends on what the update removes and what it leaves available. The useful unit of reasoning is not a complete solution but the coincidence building blocks distributed across the population.
- Observe diverse strong candidates.
Different high-quality modes contribute different useful coincidences to the same H.
- Find recurring negative structure.
Poor candidates may differ globally while sharing local incidences that repeatedly lead toward weak regions.
- Punish shared negative building blocks.
Probability is removed from those incidences and returned to their alternatives, pruning common paths into low-quality space.
- Retain modal building blocks.
Useful coincidences belonging to different modes can remain probable when the evidence does not identify them as negative.
- Resample combinations.
The shared H continues generating candidates from the reduced search space while preserving several promising structural vocabularies.
- Repeat under population evidence.
Multimodality emerges from accumulated selective pressure rather than an explicit one-generator-per-mode partition.
The generator remains shared
The model is not split by mode. What changes is the probability landscape: negative correlations reduce access to repeatedly weak substructures, while the surviving positive structures can describe more than one basin of strong solutions.
The capability is empirical, not automatic
A shared H can retain several modes only when the representation and update distinguish their useful building blocks from the structures associated with poor candidates. Learning rate, population composition and better/worse selection therefore affect whether diversity survives.
How to evaluate both capabilities
| Question | Multi-objective evidence | Multimodal evidence |
|---|---|---|
| Quality | Hypervolume, epsilon indicator, generational distance | Peak ratio, success per mode, best quality within each niche |
| Diversity | Spread and coverage in objective space | Edge-set diversity, permutation distance, number of stable modes |
| Reliability | Front stability across seeds and budgets | Mode survival, rediscovery rate and collapse frequency |
| Efficiency | Evaluations and time to a useful front | Evaluations required to discover and retain each mode |
| Decision value | Coverage of stakeholder trade-offs | Operationally distinct alternatives after removing duplicates |
A strong experiment should compare positive-only learning with shared-generator COIN using reward and punishment. The central ablation is whether negative-space pruning in one H retains more modes, retains them longer and reaches them more reliably across random seeds.
Why decision-makers may need both
Schedule portfolios
Balance makespan, labour, energy and changeover while preserving different workforce or machine-allocation strategies.
Route alternatives
Trade distance, time, emissions and risk while preserving geographically distinct routes resilient to disruption.
Resource configurations
Balance access, waiting time and workload while retaining alternatives suitable for different demand scenarios.
Structurally distinct designs
Offer several high-quality configurations rather than minor variants of the same architecture.
The practical output is not “the algorithm found many answers.” It is a compact portfolio where each alternative represents a meaningful trade-off or operational mode. Redundant solutions should be removed; differences should be explained in language stakeholders can evaluate.
Capability boundary and research status
The architecture retains a representation boundary. H is a first-order pairwise model. Problems governed by higher-order blocks, long-range precedence or context-dependent interactions may require richer probabilistic structures or hybrid local search.