Are Individual Differences in Performance on Perceptual and Cognitive Optimization Problems Determined by General Intelligence?

Studies of human problem solving have traditionally used deterministic tasks that require the execution of a systematic series of steps to reach a rational and optimal solution. Most real-world problems, however, are characterized by uncertainty, the need to consider an enormous number of variables and possible courses of action at each stage in solving the problem, and the need to optimize the solution subject to multiple interacting constraints. There are reliable individual differences in people’s abilities to solve such realistic problems. It also seems likely that people’s ability to solve these difficult problems reflects, or depends on, their intelligence. We report on a study of N = 101 adults who completed a series of visual optimization problems (Traveling Salesperson, Minimum Spanning Tree, and Generalized Steiner Tree Problems), as well as a cognitive optimization problem (a version of the Secretary Problem). We also characterized these individuals along three relevant and important cognitive abilities dimensions—fluid ability, visuo-spatial ability, and cognitive processing speed. Modeling of covariance structures indicated that performance on both types of optimization problems relies on general intelligence and raises the possibility that they can be used to assess intelligence. Individual Differences in Problem Solving and Intelligence This paper describes a study on individual differences in two classes of decision-making problems: (a) difficult optimization problems that are presented visually and can be thought of as perceptual problems, and (b) a difficult sequential decision-making task that involves uncertainty and places demands on working memory and can be thought of as a cognitive problem. Recent research has explored whether performance on perceptual optimization problems, particularly the Traveling Salesperson Problem (TSP; Lawler, Lenstra, Rinooy Kan, & Schmoys, 1985), depends on psychometric intelligence (e.g., Vickers, Butavicius, Lee, & Medvedev, 2001; Vickers, Mayo, Heitmann, Lee, & Hughes, 2004; Vickers et al., *Department of Psychology, University of Adelaide, Australia Correspondence concerning this article should be addressed to: Nicholas Burns, School of Psychology, The Journal of Problem Solving • volume 1, no. 1 (Fall 2006) 5 University of Adelaide, South Australia, 5005, Email: [email protected] http://dx.doi.org/10.7771/1932-6246.1003 2004) reported that, in two separate studies, performance on TSP correlated with scores on Raven’s Advanced Progressive Matrices (Raven, Court, & Raven, 1988) to the extent of about 25% shared variance. Correlations were of similar magnitude for two other perceptual optimization problems known as the Minimum Spanning Tree Problem (MSTP: Ahuja, Magnanti, & Orlin, 1993) and Generalized Steiner Tree Problem (GSTP: Hwang, Richards, & Winter, 1992). There are no published reports of relationships between sequential decision-making tasks and psychometric intelligence, but clear and reliable individual differences in performance on one such task, the full-information version of the Secretary Problem, have been described (Lee, O’Connor, & Welsh, 2004). Meanwhile, theories on the structure of human intelligence have converged in a model that incorporates at least two strata but arguably three. The first stratum comprises over 60 abilities that are rather narrow and correspond conceptually to Thurstone’s Primary Mental Abilities (Thurstone, 1938, 1947). The pattern of intercorrelations among these first-stratum abilities defines about ten broad abilities at the second stratum. These second-stratum abilities include fluid and crystallized intelligence, as first described by Cattell (1943, 1963), along with others more recently described, primarily by Horn and co-workers (see Horn & Noll, 1997). The interpretation of the pattern of intercorrelations among these broad second-order abilities remains controversial. Many researchers and theorists argue for the existence and primacy of a third-stratum general factor (g; see Carroll, 1993; Jensen, 1998), whereas others dismiss the importance of g (e.g., Stankov, 2002). Deary and Caryl (1997) make the point that whether the broad second-order abilities or the putative third-order general factor is considered most important depends on the particular research question at hand. The point of all this, however, is that it is no longer sufficient to attempt to understand human intelligence, its determinants, or consequences, in terms of scores on a single psychometric instrument such as Raven’s Matrices. Here, we examine the relationship of individual differences on difficult perceptual and cognitive problems with psychometric tests chosen to define the three most relevant broad cognitive abilities identified by modern theories of human intelligence: fluid ability (Gf), visuo-spatial ability (Gv), and cognitive processing speed (Gs). Perceptual Optimization Problems As described in more detail elsewhere (Vickers et al., 2004), much research into the relationship between problem solving processes and other cognitive abilities has concentrated either on knowledge-lean problems suitable for experimental study or on complex but domain-specific real-world problems. Vickers et al. argued that difficult combinatorial optimization problems have the advantage that, although there is often no algorithm that can produce a definitive solution in a reasonable time, they can be simply stated and readily understood. Moreover, they can be representative of 6 Nicholas R. Burns, Michael D. Lee, and Douglas Vickers