# Fishing policy exploration

## Parameters

**Discount rate**: What is it worth for you today to get a million Euro next year, compared to getting it today? Economists discount the present value of future income by using a discount rate. The optimization routine uses a default a discount rate of 4%, which means that the current value of getting a Euro in one year is €0.96 (= (1+Discount rate)^{-1}). (*Use default if you don’t have a prescribed discount rate to use*)

**Number of runs:** If you set the **Initialize using** option to “Random F”, the optimization routine will use a random starting point. As the routine may get stuck on local minima, it makes sense to try several times. (*perhaps 10*). In nonlinear optimization practice, this is called “multiple shooting”.

**Initialize using: **There are three options,

- Ecopath base F: Starts with the Ecopath base fishing effort, (which typically will be 1)
- Current F: when used with a base year that’s different from year 1, selecting this option will make the policy search start with the effort of the base year
- Random F: selects random effort for each fleet. This option is important to evaluate if there are local minima. The policy search can get stuck on local minima, and the best way to evaluate the risk of that is to run a number of trials, starting each with random effort.

Note that if the**Number of runs**is set to more than 1, the**Initialize using**will change to using Random F.

**Max. no of evals:** The optimization routine does a large number of Ecosim runs during an optimization, often several hundred. The parameter sets a limit for how many. (*Use default setting unless your model won’t converge with this*).

**Base year:** By default this is year *1*, and if so, your economic parameters should be for the Ecopath base year (= year 1). Assuming your model is fitted to time series data, e.g., for years *1* to *n*, it may make sense to do the optimization looking forward to the post-fitting period (year *n+1 on*). In that case, add, e.g., 20-30 year to the run time *(Ecosim > Input > Ecosim parameters > Duration of simulation (years)),* and change the Base year accordingly. If you increase the base year, the interface will block out (in black) the years prior to the base year, i.e. Ecosim will run with stored effort for those years, not try to estimate any.

To minimize the risk that the optimization will result in overexploitation towards the end of the simulation, the simulation routine will run for an additional 20 years beyond the last year, and the results for that last block of years will be included in the output.

**Max effort change: **Provides a limit for how much effort is allowed to change from one year to the next. The parameter should be entered as a factor 𝛼 ≥ 1. With a value of, e.g., 𝛼 = 1.1, the routine will at most accept a change in effort for the following year in the range [0.909, 1.1]. With the default value of 0, there is no limit for how much effort can change.

The changes are only for between-blocks years, for instance where there are several blocks for a given fleet, perhaps to have some additional years for rebuilding a stock followed by a different management patterns for later years. In that case, the max. effort change will be evaluated only when changing from one block of years to the next.

**Search using: **Decides which search algorithm to use for the minimization, either DFPmin or Fletch,

*DFPmin*: The Davidson-Fletcher-Powell^{[1]}optimization procedure is a nonlinear optimization procedure to iteratively improve an objective function by changing relative fishing rates, where each colour-coded “year/fleet block” defines one parameter to be varied by the procedure, (e.g., setting four colour code blocks means a 4-parameter nonlinear search). DFP runs the Ecosim model repeatedly while varying these parameters; in the search output display, each simulation trial is labelled an “eval” or function evaluation. So if you are running a large model for many years, where each simulation takes several seconds to do, the search may take quite a long time to do enough function evaluations to find a maximum for the objective function.

The parameter variation scheme used by DFP is known as a ‘conjugate-gradient’ method, which involves testing alternative parameter values so as to locally approximate the objective function as a quadratic function of the parameter values, and using this approximation to make parameter update steps. It is one of the more efficient algorithms for complex and highly nonlinear optimization problems like the one of finding a best fishing pattern over time for a nonlinear dynamic model.*Fletch*: An efficient non-linear search routine, older and less-well known than DFP, but faster and more efficient for many problems. Used by default.

**Use plug-in economic data: **When defining a fleet in the Ecopath base model, there are input values for costs as a fraction of income *(Ecopath > Input > Fishery > Fleets) *based on which the baseline costs are obtained (*default is that cost is 80% of revenue*). The revenue is obtained from the Ecopath baseline landings times off-vessel price. In Ecosim, revenue for each time step will be calculated the same way, while cost will change proportionally to effort.

The checkbox will be enabled if a value chain has been defined for the model, and the “*Run with searches”* option has been checked (at Ecopath* > Output > Tools > Value chain > Parameters). *If the **Use plug-in economic data **is checked, the fishing policy search routine will run the value chain for each run and obtain revenue and costs by fleet and time from there.

**Limit cost > earnings: **When maximizing for jobs (landed value) the search routine can create rather extreme policies, often driving the system towards mono-culture system configuration or fishing at a loss (implied subsidy to increase jobs). For Anchovy Bay, as an example, this may result in higher landed value, comprised almost exclusively of shrimp and anchovies. This corresponds to a “sole owner” or societal approach (see textbox in Fishing policy exploration chapter), and it is implemented if you do not check the **Limit cost > earnings** option (*default option*).

Checking the **Limit cost > earnings** option, leads to an optimization where the policy search will seek to make each fleet profitable, corresponding to a “multiple fishing rights” approach, (see textbox in Fishing policy exploration chapter).

The **Limit cost > earnings** will only have impact if the **Net economic value** is included in the objective function.

**Maximize portfolio utility: **As described in the Fishing policy exploration chapter, there are two alternative objective functions in the policy search. Checking the **Maximize portfolio utility** option invokes the alternative objective function that invokes risk-averse utility measures that favour a balanced ‘investment portfolio’ of fishing activities. See the Risk-averse portfolio utility chapter for details.

## Blocks

This section of the interface is designed to set up how many fishing effort fleet-time blocks that the fishing policy search should try to optimize. A block is represented by a colour, and by default the routine searches for one fishing effort per fleet (one time block). The base year (by default year 1) and any preceding year are by default coloured black, that means that the routine will not search for those years but instead retain whatever the fishing effort variable has in memory.

If you as an example colour the whole spreadsheet with one colour, the policy search will find the one (relative) fishing effort across all fleets that optimizes the objective function

**A colour in the block spreadsheet means: “find me a fishing effort for this fleet(s)/year(s) combination”**

**No of blocks: **Use this to get more colours = blocks

**Selected: **With many colours (blocks) it can be difficult to see which one is selected. It can be easier to change the number of **Selected** to selectively set blocks. The horizontal slider under the colours indicate which one is selected.

If the optimizations starts at a point where the system is degraded/overfished, it can make sense to have an initial rebuilding period followed by sustainable use. This can be set with by setting two colours blocks per fleet, one for the rebuilding period and one for the sustainable use period.

## Set block year and sequence

This, somewhat complex part of the interface, can be used to set blocks of years. The default is that there is one block per fleet spanning from year 2 to the end, the optimization thus starting in Year 2 and ending in the last year of simulation.

**Year**: Gives number of years per block. The default is number of years in simulation. Changing this, for instance to 10 years, will signal that there should be one block for each 10 years simulated for each fleet

**Set**: Clicking will set the number of blocks by fleet based on the **Year** setting.

**Start**: Increasing the start year will result in the years prior be blackened out and not included in simulations

**End**: Decreasing the end year will cause the following years to be blackened out and not included in simulations.

## Objectives, iteration results and plot results

The lower panel has three tabs, each explained next.

### Objectives

This tab will be displayed while setting up the policy scenario. The objectives are described above, this section deals with how they are implemented.

**Search objective and relative weight: **List the five objectives (or three if the **Maximize ****portfolio utility** option has been checked) with relative weights. Be aware that putting the same weight on two or more objectives does not translate into these objectives actually being balanced. This is because changing for instance how much *ecosystem structure* may change will be much harder than changing *net economic value*. To get an overview of the range for each objective it may be advisable to conduct a series of optimizations placing weight on one objective at the time.

If the **Maximize ****portfolio utility** option is checked, there will be three objectives listed: *Net economic value*, *Prediction variance* and *Existence value*. The details of these are explained in the Risk-averse portfolio utility chapter.

**Jobs/catch value**: d

**Mandated relative biomass**:

**Structure relative weight**:

**Maximum fishing mortality**:

**Acknowledgement**

- Fletcher, R. 1987. Practical methods of optimization. Wiley-Interscience, New York. 436 p. ↵