Multicriteria ranking using weights which minimize the score range

Various schemes have been proposed for generating a set of non-subjective weights when aggregating multiple criteria for the purposes of ranking or selecting alternatives. The maximin approach chooses the weights which maximise the lowest score (assuming there is an upper bound to scores). This is equivalent to finding the weights which minimize the maximum deviation, or range, between the worst and best scores (minimax). At first glance this seems to be an equitable way of apportioning weight, and the Rawlsian theory of justice has been cited in its support.We draw a distinction between using the maximin rule for the purpose of assessing performance, and using it for allocating resources amongst the alternatives. We demonstrate that it has a number of drawbacks which make it inappropriate for the assessment of performance. Specifically, it is tantamount to allowing the worst performers to decide the worth of the criteria so as to maximise their overall score. Furthermore, when making a selection from a list of alternatives, the final choice is highly sensitive to the removal or inclusion of alternatives whose performance is so poor that they are clearly irrelevant to the choice at hand

Control of substrate access to the active site in methane monooxygenase

Methanotrophs consume methane as their major carbon source and have an essential role in the global carbon cycle by limiting escape of this greenhouse gas to the atmosphere. These bacteria oxidize methane to methanol by soluble and particulate methane monooxygenases (MMOs). Soluble MMO contains three protein components, a 251-kilodalton hydroxylase (MMOH), a 38.6-kilodalton reductase (MMOR), and a 15.9-kilodalton regulatory protein (MMOB), required to couple electron consumption with substrate hydroxylation at the catalytic diiron centre of MMOH. Until now, the role of MMOB has remained ambiguous owing to a lack of atomic-level information about the MMOH–MMOB (hereafter termed H–B) complex. Here we remedy this deficiency by providing a crystal structure of H–B, which reveals the manner by which MMOB controls the conformation of residues in MMOH crucial for substrate access to the active site. MMOB docks at the α[subscript 2]β[subscript 2] interface of α[subscript 2]β[subscript 2]γ[subscript 2] MMOH, and triggers simultaneous conformational changes in the α-subunit that modulate oxygen and methane access as well as proton delivery to the diiron centre. Without such careful control by MMOB of these substrate routes to the diiron active site, the enzyme operates as an NADH oxidase rather than a monooxygenase. Biological catalysis involving small substrates is often accomplished in nature by large proteins and protein complexes. The structure presented in this work provides an elegant example of this principle.National Institute of General Medical Sciences (U.S.) (Grant GM 32114

A combined approach for analysing heuristic algorithms

When developing optimisation algorithms, the focus often lies on obtaining an algorithm that is able to outperform other existing algorithms for some performance measure. It is not common practice to question the reasons for possible performance differences observed. These types of questions relate to evaluating the impact of the various heuristic parameters and often remain unanswered. In this paper, the focus is on gaining insight in the behaviour of a heuristic algorithm by investigating how the various elements operating within the algorithm correlate with performance, obtaining indications of which combinations work well and which do not, and how all these effects are influenced by the specific problem instance the algorithm is solving. We consider two approaches for analysing algorithm parameters and components—functional analysis of variance and multilevel regression analysis—and study the benefits of using both approaches jointly. We present the results of a combined methodology that is able to provide more insights than when the two approaches are used separately. The illustrative case studies in this paper analyse a large neighbourhood search algorithm applied to the vehicle routing problem with time windows and an iterated local search algorithm for the unrelated parallel machine scheduling problem with sequence-dependent setup times.PostprintPeer reviewe

Lawson criterion for ignition exceeded in an inertial fusion experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion

Valid Inequalities and Projecting the Multicommodity Extended Formulation for Incapacitated Fixed Charge Network Flow Problems

Multicommodity extended formulations of single source uncapacitated fixed charge network flow problems have significantly sharper linear programming relaxations than the standard flow formulations. However the tradeoff is the introduction of many new constraints and variables to accomodate a sink-oriented flow disaggregation. In this paper we introduce a new family of dicut collection inequalities and show that they completely describe the projection of the multicommodity formulation onto the original variables. A simple subclass is seen to include a variety of known inequalities for particular models, and combinatorial separation is examined for some special cases

Gainfree Leontief Substitution Flow Problems

Leontief substitution systems have been studied by economists and operations researchers for many rears. We show how such linear systems are naturally viewed as Leontief substitution flow problems on directed hypergraphs, and that important solution properties follow from structural characteristics of the hypergraphs. We give a strongly polynomial, non-simplex algorithm for Leontief substitution flow problems that satisfy a gainfree property leading to acyclic extreme solutions. Integrality conditions follow easily from this algorithm. Another structural property, support disjoint reachability, leads to necessary and sufficient conditions for extreme solutions to be binary. In a survey of applications, we show how the Leontief flow paradigm links polyhedral combinatorics, expert systems, mixed integer model formulation, and some problems in graph optimization

Linear-time Algorithms for the 2-connected Steiner Subgraph Problem On Special Classes of Graphs

The 2-connected Steiner subgraph problem is that of finding a minimum-weight 2-connected subgraph that spans a subset of distinguished vertices. This paper presents linear-time algorithms for solving the 2-connected Steiner subgraph problem on two special classes of graphs, W4-free graphs and Halin graphs. Although different in detail, the algorithms adopt a common strategy exploiting known decompositions. As a special case, the algorithms also solve the Traveling Salesman Problem on W4-free graphs and Halin graphs