Concept Architecture
Concept
Theoretically, Genetic Algorithm is a population-based stochastic optimisation method inspired by the principles of natural selection and biological evolution. Candidate solutions evolve iteratively through selection, crossover and mutation, with fitter solutions having a greater probability of contributing to subsequent generations. In health economics, genetic algorithms are used to optimise complex decision problems where conventional optimisation methods are computationally difficult or where objective functions are highly nonlinear, discontinuous or multimodal.
Mathematically, a Genetic Algorithm searches the solution space by maintaining a population of candidate solutions represented as chromosomes. Each solution is evaluated using an objective (fitness) function, after which probabilistic selection, recombination and mutation operators generate new candidate solutions. The optimisation process continues until a stopping criterion is satisfied, such as convergence, a predefined number of generations or negligible improvement in fitness.
In practice, Genetic Algorithms are implemented to optimise resource allocation, intervention portfolios, screening strategies, parameter calibration and health service planning models. Algorithm parameters, including population size, crossover probability and mutation rate, are selected before optimisation begins. Although computationally intensive, genetic algorithms are particularly valuable when objective functions are non-convex or when traditional gradient-based optimisation methods cannot be applied.
Purpose
Used to identify near-optimal solutions to complex health economic optimisation problems involving nonlinear, constrained or high-dimensional decision spaces where exact optimisation methods are impractical.
Mathematical Formulae
Primary Formula
There is no universally recognised canonical mathematical formula.
Supporting Formulae
Fitness evaluation:
f(x)
where:
- x = candidate solution
- f(x) = objective (fitness) function to be maximised or minimised
Selection probability (fitness-proportionate selection):
P? = f? / ????? f?
where:
- P? = probability of selecting candidate i
- f? = fitness of candidate i
- N = population size
Related Mathematical Methods
- Evolutionary optimisation
- Stochastic optimisation
- Global optimisation
- Integer programming
- Simulated annealing
- Particle swarm optimisation
- Bayesian optimisation
Example
A health authority seeks the optimal allocation of a fixed vaccination budget across multiple age groups while maximising incremental net monetary benefit.
Each candidate allocation is represented as a chromosome. The fitness function calculates total net monetary benefit after simulating disease outcomes. Over successive generations, crossover combines successful allocation strategies and mutation introduces new alternatives. After 500 generations, the algorithm identifies an allocation producing the highest estimated population net benefit while satisfying the available budget constraint.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| RAND | =RAND() | Generate random values for mutation and selection. |
| RANK | =RANK(D2,$D$2:$D$101,0) | Rank candidate solutions according to fitness. |
| INDEX | =INDEX(Population,MATCH(MAX(Fitness),Fitness,0)) | Retrieve the highest-performing candidate solution. |
| MAX | =MAX(D2:D101) | Identify the best fitness value in the current generation. |
VBA (Optional)
Automate population generation, fitness evaluation, crossover, mutation and iterative optimisation across successive generations of candidate health economic solutions.
Sources
- Goldberg DE. Genetic Algorithms in Search, Optimization and Machine Learning.
- Holland JH. Adaptation in Natural and Artificial Systems.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed.
- ISPOR-SMDM Modeling Good Research Practices Task Force Reports.
Related Concepts (2)
Library
Publications
1
A Taxonomy of Model Structures for Economic Evaluation of Health Technologies — Brennan, Chick & Davies, Vol. 15, No. 12 ed., 2006 (Health Economics)
An influential paper classifying decision-analytic model structures along axes of expected value vs randomness, entity heterogeneity, and Markovian vs non-Markovian structure — providing a framework for choosing between decision trees, Markov cohort models, microsimulation, discrete event simulation and system dynamics.
Journal ArticleView source →
Frequently Asked Questions (6)
What is a genetic algorithm?
An optimisation technique inspired by evolution that iteratively selects and combines the best candidate solutions across generations to improve results.
Source: Holland 1975
What inspired the genetic algorithm?
The method borrows its logic from biological evolution. It keeps a population of candidate solutions and improves them over successive generations, favouring the better ones to reproduce, combining parts of two solutions to make new ones, and occasionally altering a solution at random. Over many generations this selection and recombination tends to produce steadily better answers. The analogy with natural selection is the source of both its name and its design. Goldberg (1989) set out the approach.
Source: Goldberg 1989
How does a genetic algorithm work?
A genetic algorithm works by maintaining a population of candidate solutions, each evaluated by a fitness measure of how well it solves the problem. Better solutions are more likely to be selected to produce the next generation, which is formed by combining pairs of solutions, through crossover, and randomly altering them, through mutation. Over many generations, this selection, recombination, and variation tend to improve the population's fitness, so the algorithm converges toward good solutions without needing to examine every possibility.
Source: Holland 1975
What are the key operations in a genetic algorithm?
The key operations are selection, crossover, and mutation. Selection chooses which solutions reproduce, favouring those with higher fitness. Crossover combines parts of two parent solutions to create offspring, mixing their features. Mutation randomly changes elements of a solution, introducing variation and helping avoid getting stuck. Together, over successive generations, these operations balance exploiting good solutions found so far with exploring new ones, driving the population toward better solutions to the optimisation problem.
Source: Holland 1975
When is a genetic algorithm useful?
A genetic algorithm is useful for optimisation problems where the search space is large, complex, or irregular, and where conventional methods struggle, for instance because the objective is not smooth, has many local optima, or cannot be differentiated. Because it searches by evolving a population rather than following gradients, it can explore difficult landscapes and find good solutions where exact methods are impractical. It suits problems where a good solution is sought and the structure does not permit more direct optimisation techniques.
Source: Holland 1975
What are the limitations of genetic algorithms?
Genetic algorithms do not guarantee finding the best solution, only good ones, and their performance depends on choices such as population size, and the rates of crossover and mutation, which may need tuning. They can be computationally expensive, since many candidate solutions must be evaluated over many generations, and they may converge prematurely to a suboptimal solution. Where a more direct optimisation method applies, it is usually preferred, so genetic algorithms are reserved for problems that resist such methods.
Source: Holland 1975
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 30 Sep 2025
Content version: 1.0.0
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- Persistent URI
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- Term code
- HE-EM-DM-038
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