Improving problem formulation and human interaction

Optimisation problems have traditionally been formulated as single objective and solved with the use of gradient- based or direct search methods. Most practical real-world problems involve multiple, often conflicting objectives, and also highly complex search spaces. Competing goals and objectives necessarily give rise to a set of compromise options and solutions.

To counteract some of these difficulties, multiple-criteria decision-making (MCDM), which is a sub-discipline of operations research and which explicitly considers multiple criteria in decision-making environments, is brought together with evolutionary multi-objective optimisation (EMO). Evolutionary algorithms possess several characteristics that are desirable for this kind of problem, helping to direct the decision-maker to regions of preferred solutions.

In the literature there are three main types of decision-maker interventions reflecting ‘how’ and ‘when’ to express or articulate EMO preferences with respect to the individual criteria:

  • A priori preference articulation: Denotes the process of introducing and incorporating the preferences before the search process
  • A posteriori preference articulation: Denotes the process of introducing and incorporating the preferences at the end of the search process
  • Progressive preference articulation: Denotes the process of introducing, incorporating, and modifying the preferences in an interactive and progressive way at any time during the search process

Given equally adequate solvers, with the equal ability to identify promising solution areas in the search space, the decision-maker is seen as having the capability to control the optimisation process by focusing on criteria thresholds to extract viable solutions. This approach has been useful, however it involves mostly unidirectional workflows with the assumption of known and definable problems with known and definable constraints. The challenge in these circumstances is posed as one of interpreting and deciding upon trade-offs and when and how to best express them.

In practice there are few, if any, real occasions when there is not feedback between the problem definition and solution requirements, and this is especially true when dealing with dynamic multi-criteria dimensionality. The solver of choice plays an important role and is required to efficiently evaluate the solution space under consideration. However, this is only one element in a more challenging process. For example, wider interaction, which optimises methods and scope for thinking about the problem, is also required. In essence, the potential solution space to be searched is not just the conceived landscape, but also those yet to be conceived. And, conventionally, while little heed is paid to these hidden opportunities and threats lurking elsewhere, they represent a chance to identify superior solutions. Problem re-formulations and bi-directional workflows can be used to bring forward richer problem formulations. The search then is realised as not just for optimal or robust solutions in the given landscape, but for the best solution in all conceivable landscapes—a significantly different opportunity. What is discovered during the search of solution spaces affects the understanding of the problem. This establishes a learning link that can bring new landscapes into the analysis that will likely contain better solutions. Metaphorically, why continue to look for diamonds in the dust when the dust tells us there may be richer pickings elsewhere?

In contemporary optimisation techniques, there is little if any mention of bringing together the problem, domain, expert, solutions, preferences, and an open discovery process into one unifying framework. By providing a means for users to engage more easily, collaboratively, and intuitively with their business and modelling knowledge and with heuristic insights, richer discussions can be brought forward and previously hidden or obscured solutions can be revealed.

In attempting to shift towards a problem-centric perspective in the optimisation processes, an open discussion of problems and objectives, as well as an interactive exploration of all alternatives, is necessary. This approach will provide a better understanding of the problem and reveal the impact of selecting one alternative solution over another. With improved human interaction, usually best applied through visual exploration techniques, more real- world experience can be brought to the situation, enabling more appropriate solutions for the business.



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