Application Analysis on PSO Algorithm in the Discrete Optimization Problems

Particle Swarm Optimization (PSO) is kind of algorithm that can be used to solve optimization problems. In practice, many optimization problems are discrete but PSO algorithm was initially designed to meet the requirements of continuous problems. A lot of researches had made efforts to handle this case and varieties of discrete PSO algorithms were proposed. However, these algorithms just focus on the specific problem, and the performance of it significantly degrades when extending the algorithm to other problems. For now, there is no reasonable unified principle or method for analyzing the application of PSO algorithm in discrete optimization problem, which limits the development of discrete PSO algorithm. To address the challenge, we first give an investigation of PSO algorithm from the perspective of spatial search, then, try to give a novel analysis of the key feature changes when PSO algorithm is applied to discrete optimization, and propose a classification method to summary existing discrete PSO algorithms.

Dirac Spatial Search with Electric Fields

Electric Dirac quantum walks, which are a discretisation of the Dirac equation for a spinor coupled to an electric field, are revisited in order to perform spatial searches. The Coulomb electric field of a point charge is used as a non local oracle to perform a spatial search on a 2D grid of N points. As other quantum walks proposed for spatial search, these walks localise partially on the charge after a finite period of time. However, contrary to other walks, this localisation time scales as N for small values of N and tends asymptotically to a constant for larger Ns, thus offering a speed-up over conventional methods.

Welfare Implications of Congestion Pricing: Evidence from SFpark

Problem definition: Congestion pricing offers an appealing solution to urban parking problems—charging varying rates across time and space as a function of congestion may shift demand and improve allocation of limited resources. It aims to increase the accessibility of highly desired public goods and to reduce traffic caused by drivers who search for available parking spaces. At the same time, complex policies make it harder for consumers to make search-based decisions. We investigate the effect of congestion pricing on consumer and social welfare. Academic/practical relevance: This paper contributes to the theory and practice of the management of scarce resources in the public sector, where welfare is of particular interest. Methodologically, we contribute to the literature on structural estimation of dynamic spatial search models. Methodology: Using data from the City of San Francisco, both before and after the implementation of a congestion-pricing parking program, SFpark, we estimate the welfare implications of the policy. We use a dynamic spatial search model to structurally estimate consumers’ search costs, distance disutilities, price sensitivities, and trip valuations. Results: We find that congestion pricing increases consumer and social welfare by more than 4% and reduces search traffic by more than 10% in congested regions compared with fixed pricing. However, congestion pricing may hurt welfare in uncongested regions, in which the focus should be on increasing utilization. Moreover, an unnecessarily complex congestion-pricing scheme makes it difficult for consumers to make search-based decisions. We find that a simpler pricing policy may yield higher welfare than a complex one. Lastly, compared with a policy that imposes limits on parking durations, congestion pricing increases social welfare by allocating the scarce resource to consumers who value it most. Managerial implications: The insights from SFpark offer important implications for local governments that consider alternatives for managing parking and congestion and for public-sector managers who evaluate the tradeoffs between approaches to manage public resources.

Priming exploration across domains: does search in a spatial environment influence search in a cognitive environment?

Is there a general tendency to explore that connects search behaviour across different domains? Although the experimental evidence collected so far suggests an affirmative answer, this fundamental question about human behaviour remains open. A feasible way to test the domain-generality hypothesis is that of testing the so-called priming hypothesis: priming explorative behaviour in one domain should subsequently influence explorative behaviour in another domain. However, only a limited number of studies have experimentally tested this priming hypothesis, and the evidence is mixed. We tested the priming hypothesis in a registered report. We manipulated explorative behaviour in a spatial search task by randomly allocating people to search environments with resources that were either clustered together or dispersedly distributed. We hypothesized that, in a subsequent anagram task, participants who searched in clustered spatial environments would search for words in a more clustered way than participants who searched in the dispersed spatial environments. The pre-registered hypothesis was not supported. An equivalence test showed that the difference between conditions was smaller than the smallest effect size of interest ( d = 0.36). Out of several exploratory analyses, we found only one inferential result in favour of priming. We discuss implications of these findings for the theory and propose future tests of the hypothesis.