Sorted-pareto dominance and qualitative notions of optimality

Pareto dominance is often used in decision making to compare decisions that have multiple preference values – however it can produce an unmanageably large number of Pareto optimal decisions. When preference value scales can be made commensurate, then the Sorted-Pareto relation produces a smaller, more manageable set of decisions that are still Pareto optimal. Sorted-Pareto relies only on qualitative or ordinal preference information, which can be easier to obtain than quantitative information. This leads to a partial order on the decisions, and in such partially-ordered settings, there can be many different natural notions of optimality. In this paper, we look at these natural notions of optimality, applied to the Sorted-Pareto and min-sum of weights case; the Sorted-Pareto ordering has a semantics in decision making under uncertainty, being consistent with any possible order-preserving function that maps an ordinal scale to a numerical one. We show that these optimality classes and the relationships between them provide a meaningful way to categorise optimal decisions for presenting to a decision maker

Sorted-pareto dominance: an extension to pareto dominance and its application in soft constraints

The Pareto dominance relation compares decisions with each other over multiple aspects, and any decision that is not dominated by another is called Pareto optimal, which is a desirable property in decision making. However, the Pareto dominance relation is not very discerning, and often leads to a large number of non-dominated or Pareto optimal decisions. By strengthening the relation, we can narrow down this nondominated set of decisions to a smaller set, e.g., for presenting a smaller number of more interesting decisions to a decision maker. In this paper, we look at a particular strengthening of the Pareto dominance called Sorted-Pareto dominance, giving some properties that characterise the relation, and giving a semantics in the context of decision making under uncertainty. We then examine the use of the relation in a Soft Constraints setting, and explore some algorithms for generating Sorted-Pareto optimal solutions to Soft Constraints problems

Computing possibly optimal solutions for multi-objective constraint optimisation with tradeoffs

Computing the set of optimal solutions for a multiobjective constraint optimisation problem can be computationally very challenging. Also, when solutions are only partially ordered, there can be a number of different natural notions of optimality, one of the most important being the notion of Possibly Optimal, i.e., optimal in at least one scenario compatible with the inter-objective tradeoffs. We develop an AND/OR Branch-and-Bound algorithm for computing the set of Possibly Optimal solutions, and compare variants of the algorithm experimentally

Minimality and comparison of sets of multi-attribute vectors

In a decision-making problem, there can be uncertainty regarding the user preferences. We assume a parameterised utility model, where in each scenario we have a utility function over alternatives, and where each scenario represents a possible user preference model consistent with the input preference information. With a set A of alternatives available to the decision maker, we can consider the associated utility function, expressing, for each scenario, the maximum utility among the alternatives. We consider two main problems: firstly, finding a minimal subset of A that is equivalent to it, i.e., that has the same utility function. Secondly, we consider how to compare A to another set of alternatives B, where A and B correspond to different initial decision choices. We derive mathematical results that allow different computational techniques for these two problems, using linear programming, and especially, using the extreme points of the epigraph of the utility function

Algorithms for Scheduling Problems

This edited book presents new results in the area of algorithm development for different types of scheduling problems. In eleven chapters, algorithms for single machine problems, flow-shop and job-shop scheduling problems (including their hybrid (flexible) variants), the resource-constrained project scheduling problem, scheduling problems in complex manufacturing systems and supply chains, and workflow scheduling problems are given. The chapters address such subjects as insertion heuristics for energy-efficient scheduling, the re-scheduling of train traffic in real time, control algorithms for short-term scheduling in manufacturing systems, bi-objective optimization of tortilla production, scheduling problems with uncertain (interval) processing times, workflow scheduling for digital signal processor (DSP) clusters, and many more

Planning urban pavement maintenance by a new interactive multiobjective optimization approach

Pavement maintenance is essential to prevent the deterioration of asset value and to satisfy the expectations of all stakeholders (objectives). However, the budgets are often insufficient to keep the road pavement at optimum levels. Therefore, a decision making process ought to be used for prioritizing different maintenance activities in order to achieve pre-defined goals by optimizing the use of the available budget. One of the biggest difficulties in multiobjective optimization method is the large number of the feasible solutions (Pareto optimal set or its approximation), which makes it hard for the Decision Maker to select the best solution.To support interaction with the decision maker for identifying the best combination of maintenance actions, this paper proposes a new methodology named Interactive Multiobjective Optimization-Dominance Rough Set Approach (IMO-DRSA), using a decision-rule preference model.The preference information, obtained by the Decision Maker (DM) during the course of the interaction, is processed using the Dominance-based Rough Set Approach in order to achieve a decision model expressed in terms of easily understandable if ....then ... decision rules. This approach makes possible an interaction between the analyst and the decision maker and helps the decision maker to classify maintenance options and allocate limited funds according to predefined objectives (quantitative or qualitative). An application of the proposed methodology to road pavements of an Italian urban sub-network is presented