For a constrained-portfolio desk, just 143 of the 1,890 papers in this sample concern the problem at hand. Path planning, energy pricing, tunnelling and supply-chain research fill out the wider sample. The study's headline growth rates belong to that broader literature.

What did Saxena and colleagues count?

Saxena, Jain, Mehta, Anandani, Khemka and Parchani offer a bibliometric study: they count publications and map their connections, without claiming anything about returns. Their Scopus search on 16 September 2026 covered titles, abstracts and keywords. The query, "risk AND optimisation AND heuristic", returned 3,409 records. Filters then restricted the years to 2014 to 2027, with 2027 containing only articles in press, and narrowed the document types, languages and source types. That left 1,901 journal articles and reviews across 792 sources. Biblioshiny, the interface to the bibliometrix R package, supplied counts by year, journal and country, along with clusters of keywords that appear together.

Growth dominates the results. Annual output climbed from 49 papers in 2014 to 362 in 2026, a rate the authors put at 18.13% a year. An exponential trendline accounts for 98.09% of the variance in annual counts; the linear fit accounts for 85.09%. China records 1,532 author-country appearances, followed by the USA with 542. With 55 documents, IEEE Access leads the journals.

The thematic map arranges keyword clusters by centrality, their connections to the wider field, and density, their internal development. Its largest motor-theme cluster, high on both measures, contains 'optimization', 'heuristic algorithms' and 'heuristic methods'. The cluster frequency is 7,055. Generic noise forms the other cluster in that quadrant: 'algorithm', 'article', 'human'.

The counts are accompanied by a narrative review of about a dozen studies, most published in 2026. Carvalho, Peixoto and de Freitas provide the study most relevant to a desk. Their method uses simulated annealing to set portfolio weights and tabu search to select assets. They minimise downside risk subject to a cardinality constraint, testing on S&P 500 data from 2020 to 2024.

A broad search, a small portfolio subset

Portfolios never appear in the search string. Among the 1,890 records with complete keywords, filtering for "portfolio" produces 143 documents, or 7.6%. Even that group includes project portfolios and other non-financial applications, as the authors acknowledge. Their most-cited portfolio table includes Hall et al. (2015) on project portfolio selection. Across the full sample, Wei et al. (2015), a smart-grid retail-pricing paper, ranks among the most cited with 371 citations. The keyword counts give "path planning" and "portfolio optimization" 43 occurrences apiece.

The abstract acknowledges the narrow portfolio share explicitly, reporting both 143 and 7.6%. The limitations section also recognises that omitting "portfolio" from the query produces a dataset about heuristic optimization under risk more generally. The authors respond by examining the portfolio subset separately. Yet the title promises "a Focus on Portfolio Optimization", making the mismatch harder to overlook. They recommend portfolio-specific search terms for future reviews as well.

Their defence rests on "portfolio optimization" and "investments" appearing in the largest co-occurrence cluster alongside risk management and the named metaheuristics. It offers less support than they suggest. Community-detection modularity for the thematic map is 0.197, which the authors interpret as substantial overlap between themes. They see that overlap as evidence of a multidisciplinary field. It cannot also establish portfolio research as central. The clusters use the same keyword data; membership in a shared cluster says little about a topic when the clusters barely separate.

Portfolio papers grow 8.52% a year, the full sample 18.13%

Portfolio output rose from 6 documents in 2014 to 16 in 2026, after reaching a peak of 20 in 2025. Its 8.52% annual growth rate is less than half the full sample's 18.13%. Both rates follow exactly from compounding the first and last year's counts. Each therefore depends on two data points. For the portfolio subset, whose annual counts range from 6 to 20, that dependence matters particularly.

The final year is unfinished. Collection stopped on 16 September 2026, and the authors describe the resulting 18.13% as conservative. The subset deserves the same qualification. About 13 annual observations underlie the exponential fit. We did not find a normalisation for growth in Scopus indexing overall, leaving open the possibility that an expanding index explains some of the curve.

Geography changes with the sample and counting method. Among portfolio papers, counting documents with at least one author from a country puts Iran first with 26 documents and China next with 25. Author-country appearances across the full sample give China 1,532 and Iran 303. Expert Systems with Applications (7) and the European Journal of Operational Research (6) lead the portfolio venues. IEEE Access, first in the full sample, falls outside the portfolio subset's leading sources.

The ten most-cited papers make a reading list

The most-cited portfolio table is the useful product here. Reviews occupy its top three places: Mansini, Ogryczak and Speranza (2014) on linear-programming models, with 177 citations; Kalayci, Ertenlice and Akbay (2019) on mean-variance models, with 162; and Ertenlice and Kalayci (2018) on swarm intelligence, with 152. Another survey follows, alongside a project-portfolio paper and several heuristic or learning methods. Soler-Dominguez et al. (2017) supply the survey, covering financial applications of metaheuristics. Hall et al. supply the project-portfolio paper.

The methods include Khan et al.'s quantum beetle antennae search (95) and Vercher and Bermúdez's credibility mean-absolute semi-deviation model. Also present are Zhao et al.'s multi-population PSO for cardinality-constrained portfolios, Cui et al.'s deep reinforcement learning hyper-heuristic (70) and Filippi et al.'s index-tracking heuristic.

Citations measure attention.

These counts have no age adjustment, and the full sample's average document age is 3.6 years. We did not find a Sharpe ratio, turnover figure or net-of-cost return reported in the review for any of these studies.

The authors' own list of research gaps asks for precisely that evidence. They want new heuristics benchmarked against one another using common datasets, realistic constraints and out-of-sample tests. Their summary says heuristics help "because they provide practical ways of working with that complexity". No study receives a quoted net-of-cost return in the review. Blomvall et al. incorporate proportional costs into their model and report outperforming benchmark heuristics. The review supplies no figure for that result.

Before commissioning a backtest

Choosing a method from this table begins a fresh empirical project. The Carvalho study settles some choices already: downside risk, a cardinality cap, and comparisons against differential evolution, PSO, genetic algorithms and exact mixed-integer benchmarks. The desk still has to set the target return and asset count. Trading costs, the rebalance schedule and the benchmark also remain to be chosen. Each choice is a research decision.

We ran no backtest. The review defines no strategy of its own. The nearest experiment requires historical S&P 500 membership, which our data lacks. Using our yearly capitalization-ranked universe would produce a broad US-equity test of a method covered by the review. Such a result would neither replicate that study nor test this paper itself.

Read the 143-document subset and its ten most-cited entries. The 18.13% growth rate describes 1,890 papers, of which 143 concern portfolios.