Diet planning is an optimization problem only after its decision variables, nutritional requirements and measures of acceptability have been specified. A low-cost combination of foods can satisfy nutrient targets while remaining difficult to prepare, culturally unsuitable or unacceptable to the intended person. Diet-modeling reviews therefore treat nutrient, cost, environmental and acceptability constraints as distinct modeling requirements [1], [2]. This review examines the role of metaheuristics in nutritional optimization and personalized menu planning through that formulation-first perspective.

Linear programming provides an established starting point when food quantities, nutrient totals and cost are linear. Discrete food inclusion, portion alternatives, meal timing, repetition restrictions and nonlinear preference models can require integer or nonlinear formulations. Metaheuristics supply search procedures for such formulations, but their usefulness must be assessed against the strongest applicable exact or specialized methods rather than inferred from biological inspiration [3].

The No Free Lunch results concern averages over specified collections of objective functions [4]. They do not require continual invention of new metaphor-based algorithms and do not preclude useful performance differences on structured diet problems. For menu planning, the relevant questions are whether the representation preserves meal structure, whether feasibility is maintained, and whether search improves a decision-relevant objective within a defined budget.

The central comparison in this review is between the mathematical structure of a dietary decision and the mechanisms offered by an optimizer. Genetic algorithms can manipulate food and meal assignments; particle swarm optimization and differential evolution operate naturally on real-valued quantities or parameters [5], [6]. A multi-objective approach can retain trade-offs among cost, dietary change and other objectives, provided that hard nutritional requirements remain explicit.

The contribution is a critical organization of formulation choices, search mechanisms and validation requirements for diet planning. Sections 2 and 3 establish the modeling context and the narrative review boundary. Section 4 discusses search architectures, Section 5 connects them to meal and menu decisions, and Sections 6 and 7 examine evaluation and future research. The conclusions concern methodological choices rather than field-wide algorithm frequencies or pooled clinical effects.

Personalization requires more than replacing a demographic average with an individual record. The model must identify which requirements are established nutritional constraints, which preferences are elicited, and which response estimates come from predictive models. The optimization layer cannot confer clinical validity on an unvalidated response model. Recommendations intended for a medical condition require independently justified, condition-specific constraints and appropriate professional assessment.

The modeling background connects dietary quantities and schedules to feasibility, objectives and the distinction between a computational optimum and a usable menu.

This article is a narrative methodological review of nutritional optimization and personalized menu planning. The literature is used to connect established dietary formulations to search and validation choices. No reproducible search log, deduplicated inclusion list or study-level extraction database is available for the numerical search compilation in Table 1. Its reported counts are therefore not used to define a systematic-review population or to estimate algorithm prevalence.

The analytic synthesis is based on identifiable source connections rather than the counts in Table 1. In particular, van Dooren examines nutritional, economic, environmental and acceptability constraints [1], Donkor and colleagues review linear-programming formulations [2], and Koroušić Seljak [9] describes multi-level evolutionary menu planning. Their differing questions and evaluation settings preclude a pooled comparison of optimizer performance.

The following algorithm families are considered through their representations and constraint mechanisms. No claim is made that their relative popularity or performance has been measured across a complete diet-

The underlying predictions, outcomes and bin counts are unspecified, so the plot supplies no evidence of calibration quality for a dietary prediction or recommendation system (Fig. 2).

Dietary applications differ in the decision they optimize: food quantities, multi-day menus, individual preference adaptation or the balance of nutritional and environmental objectives. This distinction determines what a useful search procedure must preserve.

The principal limitations concern the formulation, the evidence for numerical comparisons and the relationship between a feasible menu and a useful dietary intervention. The unverified tables and quantitative graphics cannot establish algorithm superiority, publication trends or clinical effectiveness.

A useful research agenda begins with diet-specific benchmarks and transparent formulations. The main questions are feasibility, acceptability, uncertainty in food data and the practical value of additional optimization complexity.

Surrogate models can approximate expensive preference or response calculations, but optimizer evaluations should be periodically checked against the underlying model or observations. When machine learning predicts an individual response, predictive performance must be evaluated on information unavailable during model selection. Optimizing that prediction is a subsequent decision step and does not repair a biased predictor. Multi-objective search should present feasible alternatives whose cost, nutritional adequacy, environmental footprint and departure from current habits can be interpreted by the intended decision-maker. Changes in these objectives or in elicited preferences should be examined for their effect on the chosen menu. A stable numerical ranking alone does not demonstrate that users accept the resulting choices.

Future comparative studies should release food-data versions, constraint definitions, menu instances, algorithm configurations, independent seeds and the scripts used to calculate results. Reporting should distinguish simulated user profiles from observed participants and distinguish computational feasibility from adoption and health outcomes. Prospective deployment requires appropriate nutritional expertise and study design.

This review has a bounded narrative evidence base. It does not provide an exhaustive systematic search, a reproducible bibliometric survey or a new benchmark experiment. The numerical search counts, ordinal ratings and quantitative figures remain outside the validated conclusions until their source records and generating procedures are established.

Metaheuristics can contribute to nutritional optimization when the dietary decision contains discrete, nonlinear or expensive components that justify the search architecture. The strongest methodological principle is to formulate and validate the decision before selecting an optimizer. Linear and mixed-integer programming remain essential baselines, while evolutionary menu planning illustrates how constraints at meal, daily and weekly levels can be coordinated.

The available source connections support careful treatment of nutritional feasibility, acceptability and trade-offs rather than a universal algorithm ranking. Computational comparisons should account for tuning and evaluation budgets, maintain matched instances and verify every final menu against its constraints. Clinical effectiveness and sustained adoption require evidence beyond optimization scores.

Progress depends on transparent dietary models and validation that follows the path from data to menu, from menu to use, and from use to outcomes. A reproducible, domain-specific comparison has greater scientific value than an unsupported claim of optimizer superiority.

This research received no external funding.

Sufficient data is available upon request.

No potential conflict of interest was reported by the authors.

All authors have provided their consent for the publication of this manuscript.

This article does not involve studies with human participants or animals conducted by any authors.