# How Optimisation works

**On this page**

# What is Optimisation?

## Overview

**Mathematical optimisation** is the selection of the best outcome based on a particular criterion from a set of available alternatives. In simple cases, a specific optimisation problem involves minimizing or maximizing an 'objective function' systematically by choosing input values within an allotted set and finding the function’s value. Optimisation involves determining “best available” values of the particular **objective function** in a defined **domain**.

## Optimisation in Pathfinder

In Pathfinder, the 'objective function' is to **maximise net wealth** at the end of the projection period. The 'domain' is defined by a **set of constraints** which are applied based on the input values and goals you set for your client.

Any constraint is the quantity that has to be true irrespective of the solution. A simple example is the constraint that your client has a minimum cash reserve of $5,000 in a particular financial year. The solution to the optimisation problem will ensure that this constraint holds true.

An overview of the interaction between data input, setting goals, and maximising your clients' net wealth through our optimisation algorithm can be seen as follows:

# Why use Mathematical Optimisation

Optimisation is a mathematical approach that considers all the factors that influence decisions. Optimisation means careful modeling of the your clients' cases, a process which itself provides valuable information. In Pathfinder, the benefits of mathematical optimisations include understanding the effects of any variations made to input data and goals. This means, in Websolve, by creating various scenarios you can easily compare strategies based on the financial risk versus the best outcome.

Important factors when optimising include:

- Decisions - these are the things that can vary, the things you need to choose upon. For example, whether your client decides to retire earlier or later. You can set up scenarios to explore these decisions in Websolve.
- Constraints - this is the limitations of our decisions. For example, a client may want to investigate a decision to retire sooner or later, but is constrained by the age at which they can access their super funds.

# Making best use of our optimiser

See Recommended approach for modelling a case in Pathfinder and Minimum data required for Pathfinder.

# A simple optimisation example

To give you an idea of how a small optimisation problem might work, let's assume you've been asked to find material for your home renovations at the lowest cost. You decide on three possibilities described as follows:

- Option 1: Colours are red, purple, and orange and cost is $10/metre
- Option 2: Colours are red, blue, and yellow and cost is $12/metre
- Option 3: Colours are red, green, and yellow and cost is $14/metre.

With no constraints, the optimal solution to our problem is Option 1 costing $10/metre. However, your interior designer, who might be yourself, has specified that the material must have the colour yellow. With this additional constraint, your best option is now Option 2 at $12/metre.

We can see from this simple problem that there are other possibilities. For example, your interior designer may have said it must have the colour red as well, and, in this case, the optimal solution is also Option 2. This can happen, that is, an additional constraint has no effect on the outcome. However, had we said it must have the colour green as well, then Option 3 would be the best option.

For Pathfinder's complex optimisation problems, it is difficult to ascertain whether an additional constraint will have a negative effect on its objective to maximise net wealth, but, in general, we like to assume that it will, and so prefer to limit the number of constraints and allow Pathfinder to optimise as much as possible.

# Working with your set of constraints

## Types of constraints

Further to our discussion on constraints and how they affect the outcome is the idea that for Pathfinder's optimisation problems we can split our set of constraints into two groups, that is:

- constraints imposed by Government rules and regulations, such as, Family Tax Benefit eligibility and payments, income tax thresholds, etc, and
- constraints that are your choices for your client, such as, a goal to invest a specific amount each year, purchasing a family home in a particular year, etc.

## Your scenario has a cash shortfall

When you've decided on your strategies and setup your scenarios, you may see the solver message that you have a cash shortfall in particular year/s. **Don't panic! ** It just means that one, or more, of your constraints has violated the rule that 'any constraint is the quantity that has to be true irrespective of the solution'. That is the solution has a quantity which is not true for one, or more, constraints.

This type of error can be readily solved by investigating which of your constraints has caused the shortfall and adjusting it, or allowing its optimisation. For example, you have a strategy to purchase a family home in a particular year, however, there's a cash shortfall in that year. We can then assume that there isn't enough funds and borrowing capacity to purchase the property. In your goals for the scenario, you can either purchase the property in a later year, or not specify a year so that Pathfinder makes the choice for you of when to buy. There are more tips on our help page How to investigate and fix cash shortfalls.

Let Pathfinder find the best path to maximising your client's net wealth by allowing it to make the choices for you.

## Constraint violations

Sometimes, when you solve, in the 'Solve events' you will get a constraint violation message like 'Violation in (constraint name) equal to $19,061 in 2029. Reported in (report name)':

Constraint violations occur because the case has constraint/s that Pathfinder cannot obey, and so Pathfinder has ignored the instruction. Usually, Pathfinder has a constraint violation because:

- If it followed the constraint, it would not keep within the legislation. For example, if you have set an exact concessional contribution which is more than the legislated concessional caps, Pathfinder will keep to the cap.
- It is clashing with another constraint entered in the case. For example, if you have set on-going exact deposits to a managed fund, a maximum balance and a minimum investment period that is the length of the analysis, then, once the maximum balance is reached it clashes with your instruction to continue to make deposits, and the minimum investment period prevents Pathfinder from making withdrawals to stay under the maximum. So Pathfinder will have to ignore one of the constraints.

When there are constraint violations, it is strongly recommended that you review the violation message and adjust your inputs, and re-solve the scenario so that the violation no longer occurs. If your case has constraint violation/s, Pathfinder may have taken unusual actions to minimise how many constraints it violates or to avoid violating other constraints, so it is best to correct them. The message should tell you which constraint was violated, by how much and in what year(s). Once again, the best way to avoid constraint violations, or work out a feasible value that does will not cause a constraint violation, is to use the Robot button on the item that has the constraint violation. If you are not sure of the cause of the violation, you can Contact Optimo Financial.

# Related pages

- Tips for creating scenarios (Cashflows & Goals step)
- How to investigate and fix cash shortfalls
- Recommended approach for modelling a case in Pathfinder
- Minimum data required for Pathfinder